1 | !> @file wall_fluxes.f90 |
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2 | !------------------------------------------------------------------------------! |
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3 | ! This file is part of PALM. |
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4 | ! |
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5 | ! PALM is free software: you can redistribute it and/or modify it under the |
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6 | ! terms of the GNU General Public License as published by the Free Software |
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7 | ! Foundation, either version 3 of the License, or (at your option) any later |
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8 | ! version. |
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9 | ! |
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10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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13 | ! |
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14 | ! You should have received a copy of the GNU General Public License along with |
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15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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16 | ! |
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17 | ! Copyright 1997-2017 Leibniz Universitaet Hannover |
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18 | !------------------------------------------------------------------------------! |
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19 | ! |
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20 | ! Current revisions: |
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21 | ! ----------------- |
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22 | ! OpenACC versions of subroutines removed |
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23 | ! |
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24 | ! Former revisions: |
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25 | ! ----------------- |
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26 | ! $Id: wall_fluxes.f90 2118 2017-01-17 16:38:49Z raasch $ |
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27 | ! |
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28 | ! 2000 2016-08-20 18:09:15Z knoop |
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29 | ! Forced header and separation lines into 80 columns |
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30 | ! |
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31 | ! 1873 2016-04-18 14:50:06Z maronga |
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32 | ! Module renamed (removed _mod) |
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33 | ! |
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34 | ! |
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35 | ! 1850 2016-04-08 13:29:27Z maronga |
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36 | ! Module renamed |
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37 | ! |
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38 | ! |
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39 | ! 1691 2015-10-26 16:17:44Z maronga |
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40 | ! Renamed rif_min and rif_max with zeta_min and zeta_max, respectively. |
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41 | ! |
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42 | ! 1682 2015-10-07 23:56:08Z knoop |
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43 | ! Code annotations made doxygen readable |
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44 | ! |
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45 | ! 1374 2014-04-25 12:55:07Z raasch |
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46 | ! pt removed from acc-present-list |
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47 | ! |
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48 | ! 1353 2014-04-08 15:21:23Z heinze |
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49 | ! REAL constants provided with KIND-attribute |
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50 | ! |
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51 | ! 1320 2014-03-20 08:40:49Z raasch |
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52 | ! ONLY-attribute added to USE-statements, |
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53 | ! kind-parameters added to all INTEGER and REAL declaration statements, |
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54 | ! kinds are defined in new module kinds, |
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55 | ! old module precision_kind is removed, |
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56 | ! revision history before 2012 removed, |
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57 | ! comment fields (!:) to be used for variable explanations added to |
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58 | ! all variable declaration statements |
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59 | ! |
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60 | ! 1257 2013-11-08 15:18:40Z raasch |
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61 | ! openacc loop and loop vector clauses removed |
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62 | ! |
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63 | ! 1153 2013-05-10 14:33:08Z raasch |
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64 | ! code adjustments of accelerator version required by PGI 12.3 / CUDA 5.0 |
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65 | ! |
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66 | ! 1128 2013-04-12 06:19:32Z raasch |
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67 | ! loop index bounds in accelerator version replaced by i_left, i_right, j_south, |
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68 | ! j_north |
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69 | ! |
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70 | ! 1036 2012-10-22 13:43:42Z raasch |
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71 | ! code put under GPL (PALM 3.9) |
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72 | ! |
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73 | ! 1015 2012-09-27 09:23:24Z raasch |
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74 | ! accelerator version (*_acc) added |
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75 | ! |
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76 | ! Initial version (2007/03/07) |
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77 | ! |
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78 | ! Description: |
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79 | ! ------------ |
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80 | !> Calculates momentum fluxes at vertical walls assuming Monin-Obukhov |
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81 | !> similarity. |
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82 | !> Indices: usvs a=1, vsus b=1, wsvs c1=1, wsus c2=1 (other=0). |
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83 | !> The all-gridpoint version of wall_fluxes_e is not used so far, because |
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84 | !> it gives slightly different results from the ij-version for some unknown |
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85 | !> reason. |
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86 | !> |
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87 | !> @todo Rename rif to zeta throughout the routine |
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88 | !------------------------------------------------------------------------------! |
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89 | MODULE wall_fluxes_mod |
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90 | |
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91 | PRIVATE |
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92 | PUBLIC wall_fluxes, wall_fluxes_e |
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93 | |
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94 | INTERFACE wall_fluxes |
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95 | MODULE PROCEDURE wall_fluxes |
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96 | MODULE PROCEDURE wall_fluxes_ij |
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97 | END INTERFACE wall_fluxes |
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98 | |
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99 | INTERFACE wall_fluxes_e |
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100 | MODULE PROCEDURE wall_fluxes_e |
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101 | MODULE PROCEDURE wall_fluxes_e_ij |
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102 | END INTERFACE wall_fluxes_e |
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103 | |
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104 | CONTAINS |
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105 | |
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106 | !------------------------------------------------------------------------------! |
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107 | ! Description: |
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108 | ! ------------ |
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109 | !> Call for all grid points |
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110 | !------------------------------------------------------------------------------! |
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111 | SUBROUTINE wall_fluxes( wall_flux, a, b, c1, c2, nzb_uvw_inner, & |
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112 | nzb_uvw_outer, wall ) |
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113 | |
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114 | USE arrays_3d, & |
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115 | ONLY: rif_wall, u, v, w, z0, pt |
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116 | |
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117 | USE control_parameters, & |
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118 | ONLY: g, kappa, zeta_max, zeta_min |
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119 | |
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120 | USE grid_variables, & |
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121 | ONLY: dx, dy |
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122 | |
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123 | USE indices, & |
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124 | ONLY: nxl, nxlg, nxr, nxrg, nyn, nyng, nys, nysg, nzb, nzt |
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125 | |
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126 | USE kinds |
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127 | |
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128 | USE statistics, & |
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129 | ONLY: hom |
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130 | |
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131 | IMPLICIT NONE |
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132 | |
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133 | INTEGER(iwp) :: i !< |
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134 | INTEGER(iwp) :: j !< |
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135 | INTEGER(iwp) :: k !< |
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136 | INTEGER(iwp) :: wall_index !< |
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137 | |
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138 | INTEGER(iwp), & |
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139 | DIMENSION(nysg:nyng,nxlg:nxrg) :: & |
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140 | nzb_uvw_inner !< |
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141 | INTEGER(iwp), & |
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142 | DIMENSION(nysg:nyng,nxlg:nxrg) :: & |
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143 | nzb_uvw_outer !< |
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144 | |
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145 | REAL(wp) :: a !< |
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146 | REAL(wp) :: b !< |
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147 | REAL(wp) :: c1 !< |
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148 | REAL(wp) :: c2 !< |
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149 | REAL(wp) :: h1 !< |
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150 | REAL(wp) :: h2 !< |
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151 | REAL(wp) :: zp !< |
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152 | REAL(wp) :: pts !< |
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153 | REAL(wp) :: pt_i !< |
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154 | REAL(wp) :: rifs !< |
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155 | REAL(wp) :: u_i !< |
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156 | REAL(wp) :: v_i !< |
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157 | REAL(wp) :: us_wall !< |
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158 | REAL(wp) :: vel_total !< |
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159 | REAL(wp) :: ws !< |
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160 | REAL(wp) :: wspts !< |
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161 | |
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162 | REAL(wp), & |
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163 | DIMENSION(nysg:nyng,nxlg:nxrg) :: & |
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164 | wall !< |
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165 | |
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166 | REAL(wp), & |
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167 | DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: & |
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168 | wall_flux !< |
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169 | |
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170 | |
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171 | zp = 0.5_wp * ( (a+c1) * dy + (b+c2) * dx ) |
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172 | wall_flux = 0.0_wp |
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173 | wall_index = NINT( a+ 2*b + 3*c1 + 4*c2 ) |
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174 | |
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175 | DO i = nxl, nxr |
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176 | DO j = nys, nyn |
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177 | |
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178 | IF ( wall(j,i) /= 0.0_wp ) THEN |
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179 | ! |
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180 | !-- All subsequent variables are computed for the respective |
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181 | !-- location where the respective flux is defined. |
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182 | DO k = nzb_uvw_inner(j,i)+1, nzb_uvw_outer(j,i) |
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183 | |
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184 | ! |
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185 | !-- (1) Compute rifs, u_i, v_i, ws, pt' and w'pt' |
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186 | rifs = rif_wall(k,j,i,wall_index) |
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187 | |
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188 | u_i = a * u(k,j,i) + c1 * 0.25_wp * & |
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189 | ( u(k+1,j,i+1) + u(k+1,j,i) + u(k,j,i+1) + u(k,j,i) ) |
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190 | |
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191 | v_i = b * v(k,j,i) + c2 * 0.25_wp * & |
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192 | ( v(k+1,j+1,i) + v(k+1,j,i) + v(k,j+1,i) + v(k,j,i) ) |
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193 | |
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194 | ws = ( c1 + c2 ) * w(k,j,i) + 0.25_wp * ( & |
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195 | a * ( w(k-1,j,i-1) + w(k-1,j,i) + w(k,j,i-1) + w(k,j,i) ) & |
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196 | + b * ( w(k-1,j-1,i) + w(k-1,j,i) + w(k,j-1,i) + w(k,j,i) ) & |
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197 | ) |
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198 | pt_i = 0.5_wp * ( pt(k,j,i) + a * pt(k,j,i-1) + & |
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199 | b * pt(k,j-1,i) + ( c1 + c2 ) * pt(k+1,j,i) ) |
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200 | |
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201 | pts = pt_i - hom(k,1,4,0) |
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202 | wspts = ws * pts |
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203 | |
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204 | ! |
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205 | !-- (2) Compute wall-parallel absolute velocity vel_total |
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206 | vel_total = SQRT( ws**2 + (a+c1) * u_i**2 + (b+c2) * v_i**2 ) |
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207 | |
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208 | ! |
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209 | !-- (3) Compute wall friction velocity us_wall |
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210 | IF ( rifs >= 0.0_wp ) THEN |
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211 | |
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212 | ! |
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213 | !-- Stable stratification (and neutral) |
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214 | us_wall = kappa * vel_total / ( LOG( zp / z0(j,i) ) + & |
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215 | 5.0_wp * rifs * ( zp - z0(j,i) ) / zp & |
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216 | ) |
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217 | ELSE |
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218 | |
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219 | ! |
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220 | !-- Unstable stratification |
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221 | h1 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs ) ) |
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222 | h2 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs * z0(j,i) / zp ) ) |
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223 | |
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224 | us_wall = kappa * vel_total / ( & |
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225 | LOG( zp / z0(j,i) ) - & |
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226 | LOG( ( 1.0_wp + h1 )**2 * ( 1.0_wp + h1**2 ) / ( & |
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227 | ( 1.0_wp + h2 )**2 * ( 1.0_wp + h2**2 ) ) ) +& |
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228 | 2.0_wp * ( ATAN( h1 ) - ATAN( h2 ) ) & |
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229 | ) |
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230 | ENDIF |
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231 | |
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232 | ! |
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233 | !-- (4) Compute zp/L (corresponds to neutral Richardson flux |
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234 | !-- number rifs) |
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235 | rifs = -1.0_wp * zp * kappa * g * wspts / & |
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236 | ( pt_i * ( us_wall**3 + 1E-30 ) ) |
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237 | |
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238 | ! |
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239 | !-- Limit the value range of the Richardson numbers. |
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240 | !-- This is necessary for very small velocities (u,w --> 0), |
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241 | !-- because the absolute value of rif can then become very |
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242 | !-- large, which in consequence would result in very large |
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243 | !-- shear stresses and very small momentum fluxes (both are |
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244 | !-- generally unrealistic). |
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245 | IF ( rifs < zeta_min ) rifs = zeta_min |
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246 | IF ( rifs > zeta_max ) rifs = zeta_max |
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247 | |
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248 | ! |
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249 | !-- (5) Compute wall_flux (u'v', v'u', w'v', or w'u') |
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250 | IF ( rifs >= 0.0_wp ) THEN |
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251 | |
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252 | ! |
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253 | !-- Stable stratification (and neutral) |
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254 | wall_flux(k,j,i) = kappa * & |
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255 | ( a*u(k,j,i) + b*v(k,j,i) + (c1+c2)*w(k,j,i) ) / & |
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256 | ( LOG( zp / z0(j,i) ) + & |
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257 | 5.0_wp * rifs * ( zp - z0(j,i) ) / zp & |
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258 | ) |
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259 | ELSE |
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260 | |
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261 | ! |
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262 | !-- Unstable stratification |
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263 | h1 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs ) ) |
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264 | h2 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs * z0(j,i) / zp ) ) |
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265 | |
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266 | wall_flux(k,j,i) = kappa * & |
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267 | ( a*u(k,j,i) + b*v(k,j,i) + (c1+c2)*w(k,j,i) ) / ( & |
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268 | LOG( zp / z0(j,i) ) - & |
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269 | LOG( ( 1.0_wp + h1 )**2 * ( 1.0_wp + h1**2 ) / ( & |
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270 | ( 1.0_wp + h2 )**2 * ( 1.0_wp + h2**2 ) ) ) +& |
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271 | 2.0_wp * ( ATAN( h1 ) - ATAN( h2 ) ) & |
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272 | ) |
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273 | ENDIF |
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274 | wall_flux(k,j,i) = -wall_flux(k,j,i) * us_wall |
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275 | |
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276 | ! |
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277 | !-- store rifs for next time step |
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278 | rif_wall(k,j,i,wall_index) = rifs |
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279 | |
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280 | ENDDO |
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281 | |
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282 | ENDIF |
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283 | |
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284 | ENDDO |
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285 | ENDDO |
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286 | |
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287 | END SUBROUTINE wall_fluxes |
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288 | |
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289 | |
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290 | !------------------------------------------------------------------------------! |
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291 | ! Description: |
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292 | ! ------------ |
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293 | !> Call for all grid point i,j |
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294 | !------------------------------------------------------------------------------! |
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295 | SUBROUTINE wall_fluxes_ij( i, j, nzb_w, nzt_w, wall_flux, a, b, c1, c2 ) |
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296 | |
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297 | USE arrays_3d, & |
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298 | ONLY: rif_wall, pt, u, v, w, z0 |
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299 | |
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300 | USE control_parameters, & |
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301 | ONLY: g, kappa, zeta_max, zeta_min |
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302 | |
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303 | USE grid_variables, & |
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304 | ONLY: dx, dy |
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305 | |
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306 | USE indices, & |
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307 | ONLY: nzb, nzt |
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308 | |
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309 | USE kinds |
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310 | |
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311 | USE statistics, & |
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312 | ONLY: hom |
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313 | |
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314 | IMPLICIT NONE |
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315 | |
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316 | INTEGER(iwp) :: i !< |
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317 | INTEGER(iwp) :: j !< |
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318 | INTEGER(iwp) :: k !< |
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319 | INTEGER(iwp) :: nzb_w !< |
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320 | INTEGER(iwp) :: nzt_w !< |
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321 | INTEGER(iwp) :: wall_index !< |
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322 | |
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323 | REAL(wp) :: a !< |
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324 | REAL(wp) :: b !< |
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325 | REAL(wp) :: c1 !< |
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326 | REAL(wp) :: c2 !< |
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327 | REAL(wp) :: h1 !< |
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328 | REAL(wp) :: h2 !< |
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329 | REAL(wp) :: zp !< |
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330 | REAL(wp) :: pts !< |
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331 | REAL(wp) :: pt_i !< |
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332 | REAL(wp) :: rifs !< |
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333 | REAL(wp) :: u_i !< |
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334 | REAL(wp) :: v_i !< |
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335 | REAL(wp) :: us_wall !< |
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336 | REAL(wp) :: vel_total !< |
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337 | REAL(wp) :: ws !< |
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338 | REAL(wp) :: wspts !< |
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339 | |
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340 | REAL(wp), DIMENSION(nzb:nzt+1) :: wall_flux !< |
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341 | |
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342 | |
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343 | zp = 0.5_wp * ( (a+c1) * dy + (b+c2) * dx ) |
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344 | wall_flux = 0.0_wp |
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345 | wall_index = NINT( a+ 2*b + 3*c1 + 4*c2 ) |
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346 | |
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347 | ! |
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348 | !-- All subsequent variables are computed for the respective location where |
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349 | !-- the respective flux is defined. |
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350 | DO k = nzb_w, nzt_w |
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351 | |
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352 | ! |
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353 | !-- (1) Compute rifs, u_i, v_i, ws, pt' and w'pt' |
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354 | rifs = rif_wall(k,j,i,wall_index) |
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355 | |
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356 | u_i = a * u(k,j,i) + c1 * 0.25_wp * & |
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357 | ( u(k+1,j,i+1) + u(k+1,j,i) + u(k,j,i+1) + u(k,j,i) ) |
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358 | |
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359 | v_i = b * v(k,j,i) + c2 * 0.25_wp * & |
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360 | ( v(k+1,j+1,i) + v(k+1,j,i) + v(k,j+1,i) + v(k,j,i) ) |
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361 | |
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362 | ws = ( c1 + c2 ) * w(k,j,i) + 0.25_wp * ( & |
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363 | a * ( w(k-1,j,i-1) + w(k-1,j,i) + w(k,j,i-1) + w(k,j,i) ) & |
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364 | + b * ( w(k-1,j-1,i) + w(k-1,j,i) + w(k,j-1,i) + w(k,j,i) ) & |
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365 | ) |
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366 | pt_i = 0.5_wp * ( pt(k,j,i) + a * pt(k,j,i-1) + b * pt(k,j-1,i) & |
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367 | + ( c1 + c2 ) * pt(k+1,j,i) ) |
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368 | |
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369 | pts = pt_i - hom(k,1,4,0) |
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370 | wspts = ws * pts |
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371 | |
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372 | ! |
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373 | !-- (2) Compute wall-parallel absolute velocity vel_total |
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374 | vel_total = SQRT( ws**2 + ( a+c1 ) * u_i**2 + ( b+c2 ) * v_i**2 ) |
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375 | |
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376 | ! |
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377 | !-- (3) Compute wall friction velocity us_wall |
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378 | IF ( rifs >= 0.0_wp ) THEN |
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379 | |
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380 | ! |
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381 | !-- Stable stratification (and neutral) |
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382 | us_wall = kappa * vel_total / ( LOG( zp / z0(j,i) ) + & |
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383 | 5.0_wp * rifs * ( zp - z0(j,i) ) / zp & |
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384 | ) |
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385 | ELSE |
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386 | |
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387 | ! |
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388 | !-- Unstable stratification |
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389 | h1 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs ) ) |
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390 | h2 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs * z0(j,i) / zp ) ) |
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391 | |
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392 | us_wall = kappa * vel_total / ( & |
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393 | LOG( zp / z0(j,i) ) - & |
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394 | LOG( ( 1.0_wp + h1 )**2 * ( 1.0_wp + h1**2 ) / ( & |
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395 | ( 1.0_wp + h2 )**2 * ( 1.0_wp + h2**2 ) ) ) + & |
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396 | 2.0_wp * ( ATAN( h1 ) - ATAN( h2 ) ) & |
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397 | ) |
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398 | ENDIF |
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399 | |
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400 | ! |
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401 | !-- (4) Compute zp/L (corresponds to neutral Richardson flux number |
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402 | !-- rifs) |
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403 | rifs = -1.0_wp * zp * kappa * g * wspts / & |
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404 | ( pt_i * (us_wall**3 + 1E-30) ) |
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405 | |
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406 | ! |
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407 | !-- Limit the value range of the Richardson numbers. |
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408 | !-- This is necessary for very small velocities (u,w --> 0), because |
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409 | !-- the absolute value of rif can then become very large, which in |
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410 | !-- consequence would result in very large shear stresses and very |
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411 | !-- small momentum fluxes (both are generally unrealistic). |
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412 | IF ( rifs < zeta_min ) rifs = zeta_min |
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413 | IF ( rifs > zeta_max ) rifs = zeta_max |
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414 | |
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415 | ! |
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416 | !-- (5) Compute wall_flux (u'v', v'u', w'v', or w'u') |
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417 | IF ( rifs >= 0.0_wp ) THEN |
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418 | |
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419 | ! |
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420 | !-- Stable stratification (and neutral) |
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421 | wall_flux(k) = kappa * & |
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422 | ( a*u(k,j,i) + b*v(k,j,i) + (c1+c2)*w(k,j,i) ) / & |
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423 | ( LOG( zp / z0(j,i) ) + & |
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424 | 5.0_wp * rifs * ( zp - z0(j,i) ) / zp & |
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425 | ) |
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426 | ELSE |
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427 | |
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428 | ! |
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429 | !-- Unstable stratification |
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430 | h1 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs ) ) |
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431 | h2 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs * z0(j,i) / zp ) ) |
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432 | |
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433 | wall_flux(k) = kappa * & |
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434 | ( a*u(k,j,i) + b*v(k,j,i) + (c1+c2)*w(k,j,i) ) / ( & |
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435 | LOG( zp / z0(j,i) ) - & |
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436 | LOG( ( 1.0_wp + h1 )**2 * ( 1.0_wp + h1**2 ) / ( & |
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437 | ( 1.0_wp + h2 )**2 * ( 1.0_wp + h2**2 ) ) ) + & |
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438 | 2.0_wp * ( ATAN( h1 ) - ATAN( h2 ) ) & |
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439 | ) |
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440 | ENDIF |
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441 | wall_flux(k) = -wall_flux(k) * us_wall |
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442 | |
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443 | ! |
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444 | !-- store rifs for next time step |
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445 | rif_wall(k,j,i,wall_index) = rifs |
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446 | |
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447 | ENDDO |
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448 | |
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449 | END SUBROUTINE wall_fluxes_ij |
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450 | |
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451 | |
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452 | |
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453 | !------------------------------------------------------------------------------! |
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454 | ! Description: |
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455 | ! ------------ |
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456 | !> Call for all grid points |
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457 | !> Calculates momentum fluxes at vertical walls for routine production_e |
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458 | !> assuming Monin-Obukhov similarity. |
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459 | !> Indices: usvs a=1, vsus b=1, wsvs c1=1, wsus c2=1 (other=0). |
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460 | !------------------------------------------------------------------------------! |
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461 | |
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462 | SUBROUTINE wall_fluxes_e( wall_flux, a, b, c1, c2, wall ) |
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463 | |
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464 | |
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465 | USE arrays_3d, & |
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466 | ONLY: rif_wall, u, v, w, z0 |
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467 | |
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468 | USE control_parameters, & |
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469 | ONLY: kappa |
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470 | |
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471 | USE grid_variables, & |
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472 | ONLY: dx, dy |
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473 | |
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474 | USE indices, & |
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475 | ONLY: nxl, nxlg, nxr, nxrg, nyn, nyng, nys, nysg, nzb, & |
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476 | nzb_diff_s_inner, nzb_diff_s_outer, nzt |
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477 | |
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478 | USE kinds |
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479 | |
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480 | IMPLICIT NONE |
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481 | |
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482 | INTEGER(iwp) :: i !< |
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483 | INTEGER(iwp) :: j !< |
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484 | INTEGER(iwp) :: k !< |
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485 | INTEGER(iwp) :: kk !< |
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486 | INTEGER(iwp) :: wall_index !< |
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487 | |
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488 | REAL(wp) :: a !< |
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489 | REAL(wp) :: b !< |
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490 | REAL(wp) :: c1 !< |
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491 | REAL(wp) :: c2 !< |
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492 | REAL(wp) :: h1 !< |
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493 | REAL(wp) :: h2 !< |
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494 | REAL(wp) :: u_i !< |
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495 | REAL(wp) :: v_i !< |
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496 | REAL(wp) :: us_wall !< |
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497 | REAL(wp) :: vel_total !< |
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498 | REAL(wp) :: vel_zp !< |
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499 | REAL(wp) :: ws !< |
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500 | REAL(wp) :: zp !< |
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501 | REAL(wp) :: rifs !< |
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502 | |
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503 | REAL(wp), & |
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504 | DIMENSION(nysg:nyng,nxlg:nxrg) :: & |
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505 | wall !< |
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506 | |
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507 | REAL(wp), & |
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508 | DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: & |
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509 | wall_flux !< |
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510 | |
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511 | |
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512 | zp = 0.5_wp * ( (a+c1) * dy + (b+c2) * dx ) |
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513 | wall_flux = 0.0_wp |
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514 | wall_index = NINT( a+ 2*b + 3*c1 + 4*c2 ) |
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515 | |
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516 | DO i = nxl, nxr |
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517 | DO j = nys, nyn |
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518 | |
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519 | IF ( wall(j,i) /= 0.0_wp ) THEN |
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520 | ! |
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521 | !-- All subsequent variables are computed for scalar locations. |
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522 | DO k = nzb_diff_s_inner(j,i)-1, nzb_diff_s_outer(j,i)-2 |
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523 | ! |
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524 | !-- (1) Compute rifs, u_i, v_i, and ws |
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525 | IF ( k == nzb_diff_s_inner(j,i)-1 ) THEN |
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526 | kk = nzb_diff_s_inner(j,i)-1 |
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527 | ELSE |
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528 | kk = k-1 |
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529 | ENDIF |
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530 | rifs = 0.5_wp * ( rif_wall(k,j,i,wall_index) + & |
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531 | a * rif_wall(k,j,i+1,1) + & |
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532 | b * rif_wall(k,j+1,i,2) + & |
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533 | c1 * rif_wall(kk,j,i,3) + & |
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534 | c2 * rif_wall(kk,j,i,4) & |
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535 | ) |
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536 | |
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537 | u_i = 0.5_wp * ( u(k,j,i) + u(k,j,i+1) ) |
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538 | v_i = 0.5_wp * ( v(k,j,i) + v(k,j+1,i) ) |
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539 | ws = 0.5_wp * ( w(k,j,i) + w(k-1,j,i) ) |
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540 | ! |
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541 | !-- (2) Compute wall-parallel absolute velocity vel_total and |
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542 | !-- interpolate appropriate velocity component vel_zp. |
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543 | vel_total = SQRT( ws**2 + (a+c1) * u_i**2 + (b+c2) * v_i**2 ) |
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544 | vel_zp = 0.5_wp * ( a * u_i + b * v_i + (c1+c2) * ws ) |
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545 | ! |
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546 | !-- (3) Compute wall friction velocity us_wall |
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547 | IF ( rifs >= 0.0_wp ) THEN |
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548 | |
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549 | ! |
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550 | !-- Stable stratification (and neutral) |
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551 | us_wall = kappa * vel_total / ( LOG( zp / z0(j,i) ) + & |
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552 | 5.0_wp * rifs * ( zp - z0(j,i) ) / zp & |
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553 | ) |
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554 | ELSE |
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555 | |
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556 | ! |
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557 | !-- Unstable stratification |
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558 | h1 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs ) ) |
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559 | h2 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs * z0(j,i) / zp ) ) |
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560 | |
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561 | us_wall = kappa * vel_total / ( & |
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562 | LOG( zp / z0(j,i) ) - & |
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563 | LOG( ( 1.0_wp + h1 )**2 * ( 1.0_wp + h1**2 ) / ( & |
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564 | ( 1.0_wp + h2 )**2 * ( 1.0_wp + h2**2 ) ) ) +& |
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565 | 2.0_wp * ( ATAN( h1 ) - ATAN( h2 ) ) & |
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566 | ) |
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567 | ENDIF |
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568 | |
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569 | ! |
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570 | !-- Skip step (4) of wall_fluxes, because here rifs is already |
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571 | !-- available from (1) |
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572 | ! |
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573 | !-- (5) Compute wall_flux (u'v', v'u', w'v', or w'u') |
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574 | |
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575 | IF ( rifs >= 0.0_wp ) THEN |
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576 | |
---|
577 | ! |
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578 | !-- Stable stratification (and neutral) |
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579 | wall_flux(k,j,i) = kappa * vel_zp / ( LOG( zp/z0(j,i) ) +& |
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580 | 5.0_wp * rifs * ( zp-z0(j,i) ) / zp ) |
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581 | ELSE |
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582 | |
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583 | ! |
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584 | !-- Unstable stratification |
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585 | h1 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs ) ) |
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586 | h2 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs * z0(j,i) / zp ) ) |
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587 | |
---|
588 | wall_flux(k,j,i) = kappa * vel_zp / ( & |
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589 | LOG( zp / z0(j,i) ) - & |
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590 | LOG( ( 1.0_wp + h1 )**2 * ( 1.0_wp + h1**2 ) / ( & |
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591 | ( 1.0_wp + h2 )**2 * ( 1.0_wp + h2**2 ) ) ) +& |
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592 | 2.0_wp * ( ATAN( h1 ) - ATAN( h2 ) ) & |
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593 | ) |
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594 | ENDIF |
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595 | wall_flux(k,j,i) = - wall_flux(k,j,i) * us_wall |
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596 | |
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597 | ENDDO |
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598 | |
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599 | ENDIF |
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600 | |
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601 | ENDDO |
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602 | ENDDO |
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603 | |
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604 | END SUBROUTINE wall_fluxes_e |
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605 | |
---|
606 | |
---|
607 | !------------------------------------------------------------------------------! |
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608 | ! Description: |
---|
609 | ! ------------ |
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610 | !> Call for grid point i,j |
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611 | !------------------------------------------------------------------------------! |
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612 | SUBROUTINE wall_fluxes_e_ij( i, j, nzb_w, nzt_w, wall_flux, a, b, c1, c2 ) |
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613 | |
---|
614 | USE arrays_3d, & |
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615 | ONLY: rif_wall, u, v, w, z0 |
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616 | |
---|
617 | USE control_parameters, & |
---|
618 | ONLY: kappa |
---|
619 | |
---|
620 | USE grid_variables, & |
---|
621 | ONLY: dx, dy |
---|
622 | |
---|
623 | USE indices, & |
---|
624 | ONLY: nzb, nzt |
---|
625 | |
---|
626 | USE kinds |
---|
627 | |
---|
628 | IMPLICIT NONE |
---|
629 | |
---|
630 | INTEGER(iwp) :: i !< |
---|
631 | INTEGER(iwp) :: j !< |
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632 | INTEGER(iwp) :: k !< |
---|
633 | INTEGER(iwp) :: kk !< |
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634 | INTEGER(iwp) :: nzb_w !< |
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635 | INTEGER(iwp) :: nzt_w !< |
---|
636 | INTEGER(iwp) :: wall_index !< |
---|
637 | |
---|
638 | REAL(wp) :: a !< |
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639 | REAL(wp) :: b !< |
---|
640 | REAL(wp) :: c1 !< |
---|
641 | REAL(wp) :: c2 !< |
---|
642 | REAL(wp) :: h1 !< |
---|
643 | REAL(wp) :: h2 !< |
---|
644 | REAL(wp) :: u_i !< |
---|
645 | REAL(wp) :: v_i !< |
---|
646 | REAL(wp) :: us_wall !< |
---|
647 | REAL(wp) :: vel_total !< |
---|
648 | REAL(wp) :: vel_zp !< |
---|
649 | REAL(wp) :: ws !< |
---|
650 | REAL(wp) :: zp !< |
---|
651 | REAL(wp) :: rifs !< |
---|
652 | |
---|
653 | REAL(wp), DIMENSION(nzb:nzt+1) :: wall_flux !< |
---|
654 | |
---|
655 | |
---|
656 | zp = 0.5_wp * ( (a+c1) * dy + (b+c2) * dx ) |
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657 | wall_flux = 0.0_wp |
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658 | wall_index = NINT( a+ 2*b + 3*c1 + 4*c2 ) |
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659 | |
---|
660 | ! |
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661 | !-- All subsequent variables are computed for scalar locations. |
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662 | DO k = nzb_w, nzt_w |
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663 | |
---|
664 | ! |
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665 | !-- (1) Compute rifs, u_i, v_i, and ws |
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666 | IF ( k == nzb_w ) THEN |
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667 | kk = nzb_w |
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668 | ELSE |
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669 | kk = k-1 |
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670 | ENDIF |
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671 | rifs = 0.5_wp * ( rif_wall(k,j,i,wall_index) + & |
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672 | a * rif_wall(k,j,i+1,1) + & |
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673 | b * rif_wall(k,j+1,i,2) + & |
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674 | c1 * rif_wall(kk,j,i,3) + & |
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675 | c2 * rif_wall(kk,j,i,4) & |
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676 | ) |
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677 | |
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678 | u_i = 0.5_wp * ( u(k,j,i) + u(k,j,i+1) ) |
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679 | v_i = 0.5_wp * ( v(k,j,i) + v(k,j+1,i) ) |
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680 | ws = 0.5_wp * ( w(k,j,i) + w(k-1,j,i) ) |
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681 | ! |
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682 | !-- (2) Compute wall-parallel absolute velocity vel_total and |
---|
683 | !-- interpolate appropriate velocity component vel_zp. |
---|
684 | vel_total = SQRT( ws**2 + (a+c1) * u_i**2 + (b+c2) * v_i**2 ) |
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685 | vel_zp = 0.5_wp * ( a * u_i + b * v_i + (c1+c2) * ws ) |
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686 | ! |
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687 | !-- (3) Compute wall friction velocity us_wall |
---|
688 | IF ( rifs >= 0.0_wp ) THEN |
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689 | |
---|
690 | ! |
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691 | !-- Stable stratification (and neutral) |
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692 | us_wall = kappa * vel_total / ( LOG( zp / z0(j,i) ) + & |
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693 | 5.0_wp * rifs * ( zp - z0(j,i) ) / zp & |
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694 | ) |
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695 | ELSE |
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696 | |
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697 | ! |
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698 | !-- Unstable stratification |
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699 | h1 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs ) ) |
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700 | h2 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs * z0(j,i) / zp ) ) |
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701 | |
---|
702 | us_wall = kappa * vel_total / ( & |
---|
703 | LOG( zp / z0(j,i) ) - & |
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704 | LOG( ( 1.0_wp + h1 )**2 * ( 1.0_wp + h1**2 ) / ( & |
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705 | ( 1.0_wp + h2 )**2 * ( 1.0_wp + h2**2 ) ) ) + & |
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706 | 2.0_wp * ( ATAN( h1 ) - ATAN( h2 ) ) & |
---|
707 | ) |
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708 | ENDIF |
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709 | |
---|
710 | ! |
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711 | !-- Skip step (4) of wall_fluxes, because here rifs is already |
---|
712 | !-- available from (1) |
---|
713 | ! |
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714 | !-- (5) Compute wall_flux (u'v', v'u', w'v', or w'u') |
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715 | !-- First interpolate the velocity (this is different from |
---|
716 | !-- subroutine wall_fluxes because fluxes in subroutine |
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717 | !-- wall_fluxes_e are defined at scalar locations). |
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718 | vel_zp = 0.5_wp * ( a * ( u(k,j,i) + u(k,j,i+1) ) + & |
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719 | b * ( v(k,j,i) + v(k,j+1,i) ) + & |
---|
720 | (c1+c2) * ( w(k,j,i) + w(k-1,j,i) ) & |
---|
721 | ) |
---|
722 | |
---|
723 | IF ( rifs >= 0.0_wp ) THEN |
---|
724 | |
---|
725 | ! |
---|
726 | !-- Stable stratification (and neutral) |
---|
727 | wall_flux(k) = kappa * vel_zp / & |
---|
728 | ( LOG( zp/z0(j,i) ) + 5.0_wp * rifs * ( zp-z0(j,i) ) / zp ) |
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729 | ELSE |
---|
730 | |
---|
731 | ! |
---|
732 | !-- Unstable stratification |
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733 | h1 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs ) ) |
---|
734 | h2 = SQRT( SQRT( 1.0_wp - 16.0_wp * rifs * z0(j,i) / zp ) ) |
---|
735 | |
---|
736 | wall_flux(k) = kappa * vel_zp / ( & |
---|
737 | LOG( zp / z0(j,i) ) - & |
---|
738 | LOG( ( 1.0_wp + h1 )**2 * ( 1.0_wp + h1**2 ) / ( & |
---|
739 | ( 1.0_wp + h2 )**2 * ( 1.0_wp + h2**2 ) ) ) + & |
---|
740 | 2.0_wp * ( ATAN( h1 ) - ATAN( h2 ) ) & |
---|
741 | ) |
---|
742 | ENDIF |
---|
743 | wall_flux(k) = - wall_flux(k) * us_wall |
---|
744 | |
---|
745 | ENDDO |
---|
746 | |
---|
747 | END SUBROUTINE wall_fluxes_e_ij |
---|
748 | |
---|
749 | END MODULE wall_fluxes_mod |
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