[52] | 1 | SUBROUTINE wall_fluxes( i, j, nzb_w, nzt_w, wall_flux, a, b, c1, c2 ) |
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| 2 | !------------------------------------------------------------------------------! |
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| 3 | ! Actual revisions: |
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| 4 | ! ----------------- |
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| 5 | ! |
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| 6 | ! |
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| 7 | ! Former revisions: |
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| 8 | ! ----------------- |
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| 9 | ! $Id$ |
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| 10 | ! Initial version (2007/03/07) |
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| 11 | ! |
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| 12 | ! Description: |
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| 13 | ! ------------ |
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| 14 | ! Calculates momentum fluxes at vertical walls assuming Monin-Obukhov |
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| 15 | ! similarity. |
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| 16 | ! Indices: usvs a=1, vsus b=1, wsvs c1=1, wsus c2=1 (other=0). |
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| 17 | !------------------------------------------------------------------------------! |
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| 18 | |
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| 19 | USE arrays_3d |
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| 20 | USE control_parameters |
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| 21 | USE grid_variables |
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| 22 | USE indices |
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| 23 | USE statistics |
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| 24 | USE user |
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| 25 | |
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| 26 | IMPLICIT NONE |
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| 27 | |
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| 28 | INTEGER :: i, j, k, nzb_w, nzt_w |
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| 29 | REAL :: a, b, c1, c2, h1, h2, delta_p |
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| 30 | |
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| 31 | REAL :: pts, pt_i, rifs, u_i, v_i, us_wall, vel_total, ws, wspts |
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| 32 | |
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| 33 | REAL, DIMENSION(nzb:nzt+1) :: wall_flux |
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| 34 | |
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| 35 | |
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| 36 | delta_p = 0.5 * ( (a+c1) * dy + (b+c2) * dx ) |
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| 37 | wall_flux = 0.0 |
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| 38 | |
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| 39 | ! |
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| 40 | !-- All subsequent variables are computed for the respective location where |
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| 41 | !-- the relevant variable is defined |
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| 42 | DO k = nzb_w, nzt_w |
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| 43 | ! |
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| 44 | !-- (1) Compute rifs, u_i, v_i, ws, pt' and w'pt' |
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| 45 | rifs = rif_wall(k,j,i,NINT(a+2*b+3*c1+4*c2)) |
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| 46 | u_i = a * u(k,j,i) + & |
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| 47 | c1 * 0.25 * ( u(k+1,j,i+1) + u(k+1,j,i) + u(k,j,i+1) + u(k,j,i) ) |
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| 48 | v_i = b * v(k,j,i) + & |
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| 49 | c2 * 0.25 * ( v(k+1,j+1,i) + v(k+1,j,i) + v(k,j+1,i) + v(k,j,i) ) |
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| 50 | ws = ( c1 + c2 ) * w(k,j,i) + & |
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| 51 | a * 0.25 * ( w(k-1,j,i-1) + w(k-1,j,i) + w(k,j,i-1) + w(k,j,i) ) + & |
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| 52 | b * 0.25 * ( w(k-1,j-1,i) + w(k-1,j,i) + w(k,j-1,i) + w(k,j,i) ) |
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| 53 | pt_i = 0.5 * ( pt(k,j,i) + & |
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| 54 | a * pt(k,j,i-1) + b * pt(k,j-1,i) + ( c1 + c2 ) * pt(k+1,j,i) ) |
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| 55 | pts = pt_i - hom(k,1,4,0) |
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| 56 | wspts = ws * pts |
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| 57 | ! |
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| 58 | !-- (2) Compute wall-parallel absolute velocity vel_total |
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| 59 | vel_total = SQRT( ws**2 + ( a+c1 ) * u_i**2 + ( b+c2 ) * v_i**2 ) |
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| 60 | ! |
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| 61 | !-- (3) Compute wall friction velocity us_wall |
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| 62 | IF ( rifs >= 0.0 ) THEN |
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| 63 | ! |
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| 64 | !-- Stable stratification (and neutral) |
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| 65 | us_wall = kappa * vel_total / ( & |
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| 66 | LOG( delta_p / z0(j,i) ) + & |
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| 67 | 5.0 * rifs * ( delta_p - z0(j,i) ) / delta_p & |
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| 68 | ) |
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| 69 | ELSE |
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| 70 | ! |
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| 71 | !-- Unstable stratification |
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| 72 | h1 = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rifs ) ) |
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| 73 | h2 = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rifs / delta_p * z0(j,i) ) ) |
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| 74 | ! |
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| 75 | !-- If a borderline case occurs, the formula for stable stratification |
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| 76 | !-- must be used anyway, or else a zero division would occur in the |
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| 77 | !-- argument of the logarithm. |
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| 78 | IF ( h1 == 1.0 .OR. h2 == 1.0 ) THEN |
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| 79 | us_wall = kappa * vel_total / ( & |
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| 80 | LOG( delta_p / z0(j,i) ) + & |
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| 81 | 5.0 * rifs * ( delta_p - z0(j,i) ) / delta_p & |
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| 82 | ) |
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| 83 | ELSE |
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| 84 | us_wall = kappa * vel_total / ( & |
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| 85 | LOG( (1.0+h2) / (1.0-h2) * (1.0-h1) / (1.0+h1) ) + & |
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| 86 | 2.0 * ( ATAN( h2 ) - ATAN( h1 ) ) & |
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| 87 | ) |
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| 88 | ENDIF |
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| 89 | ENDIF |
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| 90 | ! |
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| 91 | !-- (4) Compute delta_p/L (corresponds to neutral Richardson flux number |
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| 92 | !-- rifs) |
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| 93 | rifs = -1.0 * delta_p * kappa * g * wspts / & |
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| 94 | ( pt_i * ( us_wall**3 + 1E-30 ) ) |
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| 95 | ! |
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| 96 | !-- Limit the value range of the Richardson numbers. |
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| 97 | !-- This is necessary for very small velocities (u,w --> 0), because |
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| 98 | !-- the absolute value of rif can then become very large, which in |
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| 99 | !-- consequence would result in very large shear stresses and very |
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| 100 | !-- small momentum fluxes (both are generally unrealistic). |
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| 101 | IF ( rifs < rif_min ) rifs = rif_min |
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| 102 | IF ( rifs > rif_max ) rifs = rif_max |
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| 103 | ! |
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| 104 | !-- (5) Compute wall_flux (u'v', v'u', w'v', or w'u') |
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| 105 | IF ( rifs >= 0.0 ) THEN |
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| 106 | ! |
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| 107 | !-- Stable stratification (and neutral) |
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| 108 | wall_flux(k) = kappa * & |
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| 109 | ( a * u(k,j,i) + b * v(k,j,i) + (c1 + c2 ) * w(k,j,i) ) / ( & |
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| 110 | LOG( delta_p / z0(j,i) ) + & |
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| 111 | 5.0 * rifs * ( delta_p - z0(j,i) ) / delta_p & |
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| 112 | ) |
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| 113 | ELSE |
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| 114 | ! |
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| 115 | !-- Unstable stratification |
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| 116 | h1 = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rifs ) ) |
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| 117 | h2 = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rifs / delta_p * z0(j,i) ) ) |
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| 118 | ! |
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| 119 | !-- If a borderline case occurs, the formula for stable stratification |
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| 120 | !-- must be used anyway, or else a zero division would occur in the |
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| 121 | !-- argument of the logarithm. |
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| 122 | IF ( h1 == 1.0 .OR. h2 == 1.0 ) THEN |
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| 123 | wall_flux(k) = kappa * & |
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| 124 | ( a * u(k,j,i) + b * v(k,j,i) + (c1 + c2 ) * w(k,j,i) ) / ( & |
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| 125 | LOG( delta_p / z0(j,i) ) + & |
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| 126 | 5.0 * rifs * ( delta_p - z0(j,i) ) / delta_p & |
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| 127 | ) |
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| 128 | ELSE |
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| 129 | wall_flux(k) = kappa * & |
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| 130 | ( a * u(k,j,i) + b * v(k,j,i) + (c1 + c2 ) * w(k,j,i) ) / ( & |
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| 131 | LOG( (1.0+h2) / (1.0-h2) * (1.0-h1) / (1.0+h1) ) + & |
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| 132 | 2.0 * ( ATAN( h2 ) - ATAN( h1 ) ) & |
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| 133 | ) |
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| 134 | ENDIF |
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| 135 | ENDIF |
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| 136 | wall_flux(k) = -wall_flux(k) * ABS( wall_flux(k) ) |
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| 137 | |
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| 138 | ! |
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| 139 | !-- store rifs for next time step |
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| 140 | rif_wall(k,j,i,NINT(a+2*b+3*c1+4*c2)) = rifs |
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| 141 | |
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| 142 | ENDDO |
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| 143 | END SUBROUTINE wall_fluxes |
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