| 1 | MODULE diffusion_v_mod |
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| 2 | |
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| 3 | !------------------------------------------------------------------------------! |
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| 4 | ! Current revisions: |
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| 5 | ! ----------------- |
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| 6 | ! |
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| 7 | ! |
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| 8 | ! Former revisions: |
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| 9 | ! ----------------- |
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| 10 | ! $Id: diffusion_v.f90 1002 2012-09-13 15:12:24Z raasch $ |
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| 11 | ! |
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| 12 | ! 1001 2012-09-13 14:08:46Z raasch |
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| 13 | ! arrays comunicated by module instead of parameter list |
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| 14 | ! |
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| 15 | ! 978 2012-08-09 08:28:32Z fricke |
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| 16 | ! outflow damping layer removed |
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| 17 | ! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp |
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| 18 | ! |
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| 19 | ! 667 2010-12-23 12:06:00Z suehring/gryschka |
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| 20 | ! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng |
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| 21 | ! |
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| 22 | ! 366 2009-08-25 08:06:27Z raasch |
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| 23 | ! bc_lr replaced by bc_lr_cyc |
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| 24 | ! |
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| 25 | ! 106 2007-08-16 14:30:26Z raasch |
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| 26 | ! Momentumflux at top (vswst) included as boundary condition, |
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| 27 | ! j loop is starting from nysv (needed for non-cyclic boundary conditions) |
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| 28 | ! |
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| 29 | ! 75 2007-03-22 09:54:05Z raasch |
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| 30 | ! Wall functions now include diabatic conditions, call of routine wall_fluxes, |
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| 31 | ! z0 removed from argument list, vynp eliminated |
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| 32 | ! |
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| 33 | ! 20 2007-02-26 00:12:32Z raasch |
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| 34 | ! Bugfix: ddzw dimensioned 1:nzt"+1" |
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| 35 | ! |
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| 36 | ! RCS Log replace by Id keyword, revision history cleaned up |
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| 37 | ! |
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| 38 | ! Revision 1.15 2006/02/23 10:36:00 raasch |
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| 39 | ! nzb_2d replaced by nzb_v_outer in horizontal diffusion and by nzb_v_inner |
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| 40 | ! or nzb_diff_v, respectively, in vertical diffusion, |
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| 41 | ! wall functions added for north and south walls, +z0 in argument list, |
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| 42 | ! terms containing w(k-1,..) are removed from the Prandtl-layer equation |
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| 43 | ! because they cause errors at the edges of topography |
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| 44 | ! WARNING: loops containing the MAX function are still not properly vectorized! |
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| 45 | ! |
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| 46 | ! Revision 1.1 1997/09/12 06:24:01 raasch |
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| 47 | ! Initial revision |
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| 48 | ! |
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| 49 | ! |
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| 50 | ! Description: |
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| 51 | ! ------------ |
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| 52 | ! Diffusion term of the v-component |
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| 53 | !------------------------------------------------------------------------------! |
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| 54 | |
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| 55 | USE wall_fluxes_mod |
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| 56 | |
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| 57 | PRIVATE |
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| 58 | PUBLIC diffusion_v |
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| 59 | |
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| 60 | INTERFACE diffusion_v |
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| 61 | MODULE PROCEDURE diffusion_v |
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| 62 | MODULE PROCEDURE diffusion_v_ij |
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| 63 | END INTERFACE diffusion_v |
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| 64 | |
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| 65 | CONTAINS |
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| 66 | |
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| 67 | |
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| 68 | !------------------------------------------------------------------------------! |
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| 69 | ! Call for all grid points |
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| 70 | !------------------------------------------------------------------------------! |
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| 71 | SUBROUTINE diffusion_v |
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| 72 | |
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| 73 | USE arrays_3d |
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| 74 | USE control_parameters |
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| 75 | USE grid_variables |
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| 76 | USE indices |
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| 77 | |
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| 78 | IMPLICIT NONE |
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| 79 | |
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| 80 | INTEGER :: i, j, k |
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| 81 | REAL :: kmxm, kmxp, kmzm, kmzp |
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| 82 | |
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| 83 | REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus |
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| 84 | |
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| 85 | ! |
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| 86 | !-- First calculate horizontal momentum flux v'u' at vertical walls, |
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| 87 | !-- if neccessary |
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| 88 | IF ( topography /= 'flat' ) THEN |
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| 89 | CALL wall_fluxes( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, & |
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| 90 | nzb_v_outer, wall_v ) |
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| 91 | ENDIF |
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| 92 | |
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| 93 | DO i = nxl, nxr |
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| 94 | DO j = nysv, nyn |
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| 95 | ! |
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| 96 | !-- Compute horizontal diffusion |
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| 97 | DO k = nzb_v_outer(j,i)+1, nzt |
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| 98 | ! |
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| 99 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 100 | kmxp = 0.25 * & |
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| 101 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 102 | kmxm = 0.25 * & |
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| 103 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 104 | |
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| 105 | tend(k,j,i) = tend(k,j,i) & |
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| 106 | & + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 107 | & + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 108 | & - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 109 | & - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 110 | & ) * ddx & |
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| 111 | & + 2.0 * ( & |
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| 112 | & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 113 | & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 114 | & ) * ddy2 |
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| 115 | ENDDO |
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| 116 | |
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| 117 | ! |
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| 118 | !-- Wall functions at the left and right walls, respectively |
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| 119 | IF ( wall_v(j,i) /= 0.0 ) THEN |
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| 120 | |
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| 121 | DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) |
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| 122 | kmxp = 0.25 * & |
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| 123 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 124 | kmxm = 0.25 * & |
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| 125 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 126 | |
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| 127 | tend(k,j,i) = tend(k,j,i) & |
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| 128 | + 2.0 * ( & |
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| 129 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 130 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 131 | ) * ddy2 & |
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| 132 | + ( fxp(j,i) * ( & |
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| 133 | kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 134 | + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 135 | ) & |
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| 136 | - fxm(j,i) * ( & |
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| 137 | kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 138 | + kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 139 | ) & |
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| 140 | + wall_v(j,i) * vsus(k,j,i) & |
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| 141 | ) * ddx |
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| 142 | ENDDO |
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| 143 | ENDIF |
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| 144 | |
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| 145 | ! |
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| 146 | !-- Compute vertical diffusion. In case of simulating a Prandtl |
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| 147 | !-- layer, index k starts at nzb_v_inner+2. |
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| 148 | DO k = nzb_diff_v(j,i), nzt_diff |
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| 149 | ! |
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| 150 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 151 | kmzp = 0.25 * & |
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| 152 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 153 | kmzm = 0.25 * & |
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| 154 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 155 | |
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| 156 | tend(k,j,i) = tend(k,j,i) & |
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| 157 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 158 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 159 | & ) & |
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| 160 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 161 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 162 | & ) & |
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| 163 | & ) * ddzw(k) |
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| 164 | ENDDO |
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| 165 | |
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| 166 | ! |
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| 167 | !-- Vertical diffusion at the first grid point above the surface, |
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| 168 | !-- if the momentum flux at the bottom is given by the Prandtl law |
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| 169 | !-- or if it is prescribed by the user. |
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| 170 | !-- Difference quotient of the momentum flux is not formed over |
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| 171 | !-- half of the grid spacing (2.0*ddzw(k)) any more, since the |
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| 172 | !-- comparison with other (LES) modell showed that the values of |
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| 173 | !-- the momentum flux becomes too large in this case. |
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| 174 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 175 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 176 | IF ( use_surface_fluxes ) THEN |
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| 177 | k = nzb_v_inner(j,i)+1 |
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| 178 | ! |
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| 179 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 180 | kmzp = 0.25 * & |
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| 181 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 182 | kmzm = 0.25 * & |
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| 183 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 184 | |
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| 185 | tend(k,j,i) = tend(k,j,i) & |
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| 186 | & + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 187 | & ) * ddzw(k) & |
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| 188 | & + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 189 | & + vsws(j,i) & |
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| 190 | & ) * ddzw(k) |
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| 191 | ENDIF |
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| 192 | |
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| 193 | ! |
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| 194 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
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| 195 | !-- if the momentum flux at the top is prescribed by the user |
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| 196 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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| 197 | k = nzt |
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| 198 | ! |
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| 199 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 200 | kmzp = 0.25 * & |
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| 201 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 202 | kmzm = 0.25 * & |
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| 203 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 204 | |
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| 205 | tend(k,j,i) = tend(k,j,i) & |
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| 206 | & - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 207 | & ) * ddzw(k) & |
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| 208 | & + ( -vswst(j,i) & |
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| 209 | & - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 210 | & ) * ddzw(k) |
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| 211 | ENDIF |
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| 212 | |
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| 213 | ENDDO |
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| 214 | ENDDO |
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| 215 | |
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| 216 | END SUBROUTINE diffusion_v |
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| 217 | |
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| 218 | |
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| 219 | !------------------------------------------------------------------------------! |
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| 220 | ! Call for grid point i,j |
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| 221 | !------------------------------------------------------------------------------! |
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| 222 | SUBROUTINE diffusion_v_ij( i, j ) |
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| 223 | |
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| 224 | USE arrays_3d |
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| 225 | USE control_parameters |
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| 226 | USE grid_variables |
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| 227 | USE indices |
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| 228 | |
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| 229 | IMPLICIT NONE |
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| 230 | |
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| 231 | INTEGER :: i, j, k |
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| 232 | REAL :: kmxm, kmxp, kmzm, kmzp |
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| 233 | |
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| 234 | REAL, DIMENSION(nzb:nzt+1) :: vsus |
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| 235 | |
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| 236 | ! |
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| 237 | !-- Compute horizontal diffusion |
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| 238 | DO k = nzb_v_outer(j,i)+1, nzt |
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| 239 | ! |
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| 240 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 241 | kmxp = 0.25 * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 242 | kmxm = 0.25 * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 243 | |
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| 244 | tend(k,j,i) = tend(k,j,i) & |
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| 245 | & + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 246 | & + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 247 | & - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 248 | & - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 249 | & ) * ddx & |
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| 250 | & + 2.0 * ( & |
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| 251 | & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 252 | & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 253 | & ) * ddy2 |
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| 254 | ENDDO |
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| 255 | |
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| 256 | ! |
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| 257 | !-- Wall functions at the left and right walls, respectively |
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| 258 | IF ( wall_v(j,i) /= 0.0 ) THEN |
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| 259 | |
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| 260 | ! |
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| 261 | !-- Calculate the horizontal momentum flux v'u' |
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| 262 | CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), & |
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| 263 | vsus, 0.0, 1.0, 0.0, 0.0 ) |
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| 264 | |
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| 265 | DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) |
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| 266 | kmxp = 0.25 * & |
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| 267 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 268 | kmxm = 0.25 * & |
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| 269 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 270 | |
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| 271 | tend(k,j,i) = tend(k,j,i) & |
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| 272 | + 2.0 * ( & |
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| 273 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 274 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 275 | ) * ddy2 & |
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| 276 | + ( fxp(j,i) * ( & |
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| 277 | kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 278 | + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 279 | ) & |
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| 280 | - fxm(j,i) * ( & |
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| 281 | kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 282 | + kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 283 | ) & |
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| 284 | + wall_v(j,i) * vsus(k) & |
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| 285 | ) * ddx |
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| 286 | ENDDO |
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| 287 | ENDIF |
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| 288 | |
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| 289 | ! |
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| 290 | !-- Compute vertical diffusion. In case of simulating a Prandtl layer, |
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| 291 | !-- index k starts at nzb_v_inner+2. |
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| 292 | DO k = nzb_diff_v(j,i), nzt_diff |
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| 293 | ! |
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| 294 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 295 | kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 296 | kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 297 | |
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| 298 | tend(k,j,i) = tend(k,j,i) & |
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| 299 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 300 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 301 | & ) & |
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| 302 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 303 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 304 | & ) & |
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| 305 | & ) * ddzw(k) |
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| 306 | ENDDO |
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| 307 | |
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| 308 | ! |
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| 309 | !-- Vertical diffusion at the first grid point above the surface, if the |
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| 310 | !-- momentum flux at the bottom is given by the Prandtl law or if it is |
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| 311 | !-- prescribed by the user. |
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| 312 | !-- Difference quotient of the momentum flux is not formed over half of |
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| 313 | !-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with |
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| 314 | !-- other (LES) modell showed that the values of the momentum flux becomes |
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| 315 | !-- too large in this case. |
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| 316 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 317 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 318 | IF ( use_surface_fluxes ) THEN |
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| 319 | k = nzb_v_inner(j,i)+1 |
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| 320 | ! |
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| 321 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 322 | kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 323 | kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 324 | |
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| 325 | tend(k,j,i) = tend(k,j,i) & |
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| 326 | & + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 327 | & ) * ddzw(k) & |
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| 328 | & + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 329 | & + vsws(j,i) & |
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| 330 | & ) * ddzw(k) |
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| 331 | ENDIF |
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| 332 | |
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| 333 | ! |
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| 334 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
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| 335 | !-- if the momentum flux at the top is prescribed by the user |
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| 336 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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| 337 | k = nzt |
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| 338 | ! |
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| 339 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 340 | kmzp = 0.25 * & |
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| 341 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 342 | kmzm = 0.25 * & |
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| 343 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 344 | |
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| 345 | tend(k,j,i) = tend(k,j,i) & |
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| 346 | & - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 347 | & ) * ddzw(k) & |
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| 348 | & + ( -vswst(j,i) & |
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| 349 | & - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 350 | & ) * ddzw(k) |
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| 351 | ENDIF |
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| 352 | |
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| 353 | END SUBROUTINE diffusion_v_ij |
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| 354 | |
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| 355 | END MODULE diffusion_v_mod |
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