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wall_fluxes.f90 @ 757

Last change on this file since 757 was 667, checked in by suehring, 14 years ago

summary:

Gryschka:

Coupling with different resolution and different numbers of PEs in ocean and atmosphere is available
Exchange of u and v from ocean surface to atmosphere surface
Mirror boundary condition for u and v at the bottom are replaced by dirichlet boundary conditions
Inflow turbulence is now defined by flucuations around spanwise mean
Bugfixes for cyclic_fill and constant_volume_flow

Suehring:

New advection added ( Wicker and Skamarock 5th order ), therefore:
- New module advec_ws.f90
- Modified exchange of ghost boundaries.
- Modified evaluation of turbulent fluxes
- New index bounds nxlg, nxrg, nysg, nyng

advec_ws.f90

Advection scheme for scalars and momentum using the flux formulation of
Wicker and Skamarock 5th order.
Additionally the module contains of a routine using for initialisation and
steering of the statical evaluation. The computation of turbulent fluxes takes
place inside the advection routines.
In case of vector architectures Dirichlet and Radiation boundary conditions are
outstanding and not available. Furthermore simulations within topography are
not possible so far. A further routine local_diss_ij is available and is used
if a control of dissipative fluxes is desired.

check_parameters.f90

Exchange of parameters between ocean and atmosphere via PE0
Check for illegal combination of ws-scheme and timestep scheme.
Check for topography and ws-scheme.
Check for not cyclic boundary conditions in combination with ws-scheme and
loop_optimization = 'vector'.
Check for call_psolver_at_all_substeps and ws-scheme for momentum_advec.

Different processor/grid topology in atmosphere and ocean is now allowed!
Bugfixes in checking for conserve_volume_flow_mode.

exchange_horiz.f90

Dynamic exchange of ghost points with nbgp_local to ensure that no useless
ghost points exchanged in case of multigrid. type_yz(0) and type_xz(0) used for
normal grid, the remaining types used for the several grid levels.
Exchange is done via MPI-Vectors with a dynamic value of ghost points which
depend on the advection scheme. Exchange of left and right PEs is 10% faster
with MPI-Vectors than without.

flow_statistics.f90

When advection is computed with ws-scheme, turbulent fluxes are already
computed in the respective advection routines and buffered in arrays
sums_xxxx_ws_l(). This is due to a consistent treatment of statistics
with the numerics and to avoid unphysical kinks near the surface. So some if-
requests has to be done to dicern between fluxes from ws-scheme other advection
schemes. Furthermore the computation of z_i is only done if the heat flux
exceeds a minimum value. This affects only simulations of a neutral boundary
layer and is due to reasons of computations in the advection scheme.

inflow_turbulence.f90

Using nbgp recycling planes for a better resolution of the turbulent flow near
the inflow.

init_grid.f90

Definition of new array bounds nxlg, nxrg, nysg, nyng on each PE.
Furthermore the allocation of arrays and steering of loops is done with these
parameters. Call of exchange_horiz are modified.
In case of dirichlet bounday condition at the bottom zu(0)=0.0
dzu_mg has to be set explicitly for a equally spaced grid near bottom.
ddzu_pres added to use a equally spaced grid near bottom.

init_pegrid.f90

Moved determination of target_id's from init_coupling
Determination of parameters needed for coupling (coupling_topology, ngp_a, ngp_o)
with different grid/processor-topology in ocean and atmosphere

Adaption of ngp_xy, ngp_y to a dynamic number of ghost points.
The maximum_grid_level changed from 1 to 0. 0 is the normal grid, 1 to
maximum_grid_level the grids for multigrid, in which 0 and 1 are normal grids.
This distinction is due to reasons of data exchange and performance for the
normal grid and grids in poismg.
The definition of MPI-Vectors adapted to a dynamic numer of ghost points.
New MPI-Vectors for data exchange between left and right boundaries added.
This is due to reasons of performance (10% faster).

ATTENTION: nnz_x undefined problem still has to be solved!!!!!!!!
TEST OUTPUT (TO BE REMOVED) logging mpi2 ierr values

parin.f90

Steering parameter dissipation_control added in inipar.

Makefile

Module advec_ws added.

Modules

Removed u_nzb_p1_for_vfc and v_nzb_p1_for_vfc

For coupling with different resolution in ocean and atmophere:
+nx_a, +nx_o, ny_a, +ny_o, ngp_a, ngp_o, +total_2d_o, +total_2d_a,
+coupling_topology

Buffer arrays for the left sided advective fluxes added in arrays_3d.
+flux_s_u, +flux_s_v, +flux_s_w, +diss_s_u, +diss_s_v, +diss_s_w,
+flux_s_pt, +diss_s_pt, +flux_s_e, +diss_s_e, +flux_s_q, +diss_s_q,
+flux_s_sa, +diss_s_sa
3d arrays for dissipation control added. (only necessary for vector arch.)
+var_x, +var_y, +var_z, +gamma_x, +gamma_y, +gamma_z
Default of momentum_advec and scalar_advec changed to 'ws-scheme' .
+exchange_mg added in control_parameters to steer the data exchange.
Parameters +nbgp, +nxlg, +nxrg, +nysg, +nyng added in indices.
flag array +boundary_flags added in indices to steer the degradation of order
of the advective fluxes when non-cyclic boundaries are used.
MPI-datatypes +type_y, +type_y_int and +type_yz for data_exchange added in
pegrid.
+sums_wsus_ws_l, +sums_wsvs_ws_l, +sums_us2_ws_l, +sums_vs2_ws_l,
+sums_ws2_ws_l, +sums_wspts_ws_l, +sums_wssas_ws_l, +sums_wsqs_ws_l
and +weight_substep added in statistics to steer the statistical evaluation
of turbulent fluxes in the advection routines.
LOGICALS +ws_scheme_sca and +ws_scheme_mom added to get a better performance
in prognostic_equations.
LOGICAL +dissipation_control control added to steer numerical dissipation
in ws-scheme.

Changed length of string run_description_header

pres.f90

New allocation of tend when ws-scheme and multigrid is used. This is due to
reasons of perforance of the data_exchange. The same is done with p after
poismg is called.
nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng when no
multigrid is used. Calls of exchange_horiz are modified.

bugfix: After pressure correction no volume flow correction in case of
non-cyclic boundary conditions
(has to be done only before pressure correction)

Call of SOR routine is referenced with ddzu_pres.

prognostic_equations.f90

Calls of the advection routines with WS5 added.
Calls of ws_statistics added to set the statistical arrays to zero after each
time step.

advec_particles.f90

Declaration of de_dx, de_dy, de_dz adapted to additional ghost points.
Furthermore the calls of exchange_horiz were modified.

asselin_filter.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

average_3d_data.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

boundary_conds.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng
Removed mirror boundary conditions for u and v at the bottom in case of
ibc_uv_b == 0. Instead, dirichelt boundary conditions (u=v=0) are set
in init_3d_model

calc_liquid_water_content.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

calc_spectra.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng for
allocation of tend.

check_open.f90

Output of total array size was adapted to nbgp.

data_output_2d.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng in loops and
allocation of arrays local_2d and total_2d.
Calls of exchange_horiz are modified.

data_output_2d.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng in loops and
allocation of arrays. Calls of exchange_horiz are modified.
Skip-value skip_do_avs changed to a dynamic adaption of ghost points.

data_output_mask.f90

Calls of exchange_horiz are modified.

diffusion_e.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusion_s.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusion_u.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusion_v.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusion_w.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusivities.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusivities.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.
Calls of exchange_horiz are modified.

exchange_horiz_2d.f90

Dynamic exchange of ghost points with nbgp, which depends on the advection
scheme. Exchange between left and right PEs is now done with MPI-vectors.

global_min_max.f90

Adapting of the index arrays, because MINLOC assumes lowerbound
at 1 and not at nbgp.

init_3d_model.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng in loops and
allocation of arrays. Calls of exchange_horiz are modified.
Call ws_init to initialize arrays needed for statistical evaluation and
optimization when ws-scheme is used.
Initial volume flow is now calculated by using the variable hom_sum.
Therefore the correction of initial volume flow for non-flat topography
removed (removed u_nzb_p1_for_vfc and v_nzb_p1_for_vfc)
Changed surface boundary conditions for u and v in case of ibc_uv_b == 0 from
mirror bc to dirichlet boundary conditions (u=v=0), so that k=nzb is
representative for the height z0

Bugfix: type conversion of '1' to 64bit for the MAX function (ngp_3d_inner)

init_coupling.f90

determination of target_id's moved to init_pegrid

init_pt_anomaly.f90

Call of exchange_horiz are modified.

init_rankine.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.
Calls of exchange_horiz are modified.

init_slope.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

header.f90

Output of advection scheme.

poismg.f90

Calls of exchange_horiz are modified.

prandtl_fluxes.f90

Changed surface boundary conditions for u and v from mirror bc to dirichelt bc,
therefore u(uzb,:,:) and v(nzb,:,:) is now representative for the height z0
nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

production_e.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

read_3d_binary.f90

+/- 1 replaced with +/- nbgp when swapping and allocating variables.

sor.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.
Call of exchange_horiz are modified.
bug removed in declaration of ddzw(), nz replaced by nzt+1

subsidence.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

sum_up_3d_data.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

surface_coupler.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng in
MPI_SEND() and MPI_RECV.
additional case for nonequivalent processor and grid topopolgy in ocean and
atmosphere added (coupling_topology = 1)

Added exchange of u and v from Ocean to Atmosphere

time_integration.f90

Calls of exchange_horiz are modified.
Adaption to slooping surface.

timestep.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

user_3d_data_averaging.f90, user_data_output_2d.f90, user_data_output_3d.f90,
user_actions.f90, user_init.f90, user_init_plant_canopy.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

user_read_restart_data.f90

Allocation with nbgp.

wall_fluxes.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

write_compressed.f90

Array bounds and nx, ny adapted with nbgp.

sor.f90

bug removed in declaration of ddzw(), nz replaced by nzt+1

Property svn:keywords set to Id

File size: 20.8 KB

Line
1	MODULE wall_fluxes_mod
2	!------------------------------------------------------------------------------!
3	! Current revisions:
4	! -----------------
5	!
6	!
7	! Former revisions:
8	! -----------------
9	! $Id: wall_fluxes.f90 667 2010-12-23 12:06:00Z helmke $
10	!
11	! 187 2008-08-06 16:25:09Z letzel
12	! Bugfix: Modification of the evaluation of the vertical turbulent momentum
13	! fluxes u'w' and v'w (see prandtl_fluxes), this requires the calculation of
14	! us_wall (and vel_total, u_i, v_i, ws) also in wall_fluxes_e.
15	! Bugfix: change definition of us_wall from 1D to 2D
16	! Bugfix: storage of rifs to rifs_wall in wall_fluxes_e removed
17	! Change: add 'minus' sign to fluxes produced by subroutine wall_fluxes_e for
18	! consistency with subroutine wall_fluxes
19	! Change: Modification of the integrated version of the profile function for
20	! momentum for unstable stratification
21	!
22	! Initial version (2007/03/07)
23	!
24	! Description:
25	! ------------
26	! Calculates momentum fluxes at vertical walls assuming Monin-Obukhov
27	! similarity.
28	! Indices: usvs a=1, vsus b=1, wsvs c1=1, wsus c2=1 (other=0).
29	! The all-gridpoint version of wall_fluxes_e is not used so far, because
30	! it gives slightly different results from the ij-version for some unknown
31	! reason.
32	!------------------------------------------------------------------------------!
33	PRIVATE
34	PUBLIC wall_fluxes, wall_fluxes_e
35
36	INTERFACE wall_fluxes
37	MODULE PROCEDURE wall_fluxes
38	MODULE PROCEDURE wall_fluxes_ij
39	END INTERFACE wall_fluxes
40
41	INTERFACE wall_fluxes_e
42	MODULE PROCEDURE wall_fluxes_e
43	MODULE PROCEDURE wall_fluxes_e_ij
44	END INTERFACE wall_fluxes_e
45
46	CONTAINS
47
48	!------------------------------------------------------------------------------!
49	! Call for all grid points
50	!------------------------------------------------------------------------------!
51	SUBROUTINE wall_fluxes( wall_flux, a, b, c1, c2, nzb_uvw_inner, &
52	nzb_uvw_outer, wall )
53
54	USE arrays_3d
55	USE control_parameters
56	USE grid_variables
57	USE indices
58	USE statistics
59
60	IMPLICIT NONE
61
62	INTEGER :: i, j, k, wall_index
63
64	INTEGER, DIMENSION(nysg:nyng,nxlg:nxrg) :: nzb_uvw_inner, &
65	nzb_uvw_outer
66	REAL :: a, b, c1, c2, h1, h2, zp
67	REAL :: pts, pt_i, rifs, u_i, v_i, us_wall, vel_total, ws, wspts
68
69	REAL, DIMENSION(nysg:nyng,nxlg:nxrg) :: wall
70	REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: wall_flux
71
72
73	zp = 0.5 * ( (a+c1) * dy + (b+c2) * dx )
74	wall_flux = 0.0
75	wall_index = NINT( a+ 2b + 3c1 + 4*c2 )
76
77	DO i = nxl, nxr
78	DO j = nys, nyn
79
80	IF ( wall(j,i) /= 0.0 ) THEN
81	!
82	!-- All subsequent variables are computed for the respective
83	!-- location where the respective flux is defined.
84	DO k = nzb_uvw_inner(j,i)+1, nzb_uvw_outer(j,i)
85
86	!
87	!-- (1) Compute rifs, u_i, v_i, ws, pt' and w'pt'
88	rifs = rif_wall(k,j,i,wall_index)
89
90	u_i = a * u(k,j,i) + c1 * 0.25 * &
91	( u(k+1,j,i+1) + u(k+1,j,i) + u(k,j,i+1) + u(k,j,i) )
92
93	v_i = b * v(k,j,i) + c2 * 0.25 * &
94	( v(k+1,j+1,i) + v(k+1,j,i) + v(k,j+1,i) + v(k,j,i) )
95
96	ws = ( c1 + c2 ) * w(k,j,i) + 0.25 * ( &
97	a * ( w(k-1,j,i-1) + w(k-1,j,i) + w(k,j,i-1) + w(k,j,i) ) &
98	+ b * ( w(k-1,j-1,i) + w(k-1,j,i) + w(k,j-1,i) + w(k,j,i) ) &
99	)
100	pt_i = 0.5 * ( pt(k,j,i) + a * pt(k,j,i-1) + &
101	b * pt(k,j-1,i) + ( c1 + c2 ) * pt(k+1,j,i) )
102
103	pts = pt_i - hom(k,1,4,0)
104	wspts = ws * pts
105
106	!
107	!-- (2) Compute wall-parallel absolute velocity vel_total
108	vel_total = SQRT( ws*2 + (a+c1) u_i*2 + (b+c2) v_i**2 )
109
110	!
111	!-- (3) Compute wall friction velocity us_wall
112	IF ( rifs >= 0.0 ) THEN
113
114	!
115	!-- Stable stratification (and neutral)
116	us_wall = kappa * vel_total / ( LOG( zp / z0(j,i) ) + &
117	5.0 * rifs * ( zp - z0(j,i) ) / zp &
118	)
119	ELSE
120
121	!
122	!-- Unstable stratification
123	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
124	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
125
126	us_wall = kappa * vel_total / ( &
127	LOG( zp / z0(j,i) ) - &
128	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
129	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
130	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
131	)
132	ENDIF
133
134	!
135	!-- (4) Compute zp/L (corresponds to neutral Richardson flux
136	!-- number rifs)
137	rifs = -1.0 * zp * kappa * g * wspts / ( pt_i * &
138	( us_wall**3 + 1E-30 ) )
139
140	!
141	!-- Limit the value range of the Richardson numbers.
142	!-- This is necessary for very small velocities (u,w --> 0),
143	!-- because the absolute value of rif can then become very
144	!-- large, which in consequence would result in very large
145	!-- shear stresses and very small momentum fluxes (both are
146	!-- generally unrealistic).
147	IF ( rifs < rif_min ) rifs = rif_min
148	IF ( rifs > rif_max ) rifs = rif_max
149
150	!
151	!-- (5) Compute wall_flux (u'v', v'u', w'v', or w'u')
152	IF ( rifs >= 0.0 ) THEN
153
154	!
155	!-- Stable stratification (and neutral)
156	wall_flux(k,j,i) = kappa * &
157	( au(k,j,i) + bv(k,j,i) + (c1+c2)*w(k,j,i) ) / &
158	( LOG( zp / z0(j,i) ) + &
159	5.0 * rifs * ( zp - z0(j,i) ) / zp &
160	)
161	ELSE
162
163	!
164	!-- Unstable stratification
165	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
166	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
167
168	wall_flux(k,j,i) = kappa * &
169	( au(k,j,i) + bv(k,j,i) + (c1+c2)*w(k,j,i) ) / ( &
170	LOG( zp / z0(j,i) ) - &
171	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
172	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
173	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
174	)
175	ENDIF
176	wall_flux(k,j,i) = -wall_flux(k,j,i) * us_wall
177
178	!
179	!-- store rifs for next time step
180	rif_wall(k,j,i,wall_index) = rifs
181
182	ENDDO
183
184	ENDIF
185
186	ENDDO
187	ENDDO
188
189	END SUBROUTINE wall_fluxes
190
191
192
193	!------------------------------------------------------------------------------!
194	! Call for all grid point i,j
195	!------------------------------------------------------------------------------!
196	SUBROUTINE wall_fluxes_ij( i, j, nzb_w, nzt_w, wall_flux, a, b, c1, c2 )
197
198	USE arrays_3d
199	USE control_parameters
200	USE grid_variables
201	USE indices
202	USE statistics
203
204	IMPLICIT NONE
205
206	INTEGER :: i, j, k, nzb_w, nzt_w, wall_index
207	REAL :: a, b, c1, c2, h1, h2, zp
208
209	REAL :: pts, pt_i, rifs, u_i, v_i, us_wall, vel_total, ws, wspts
210
211	REAL, DIMENSION(nzb:nzt+1) :: wall_flux
212
213
214	zp = 0.5 * ( (a+c1) * dy + (b+c2) * dx )
215	wall_flux = 0.0
216	wall_index = NINT( a+ 2b + 3c1 + 4*c2 )
217
218	!
219	!-- All subsequent variables are computed for the respective location where
220	!-- the respective flux is defined.
221	DO k = nzb_w, nzt_w
222
223	!
224	!-- (1) Compute rifs, u_i, v_i, ws, pt' and w'pt'
225	rifs = rif_wall(k,j,i,wall_index)
226
227	u_i = a * u(k,j,i) + c1 * 0.25 * &
228	( u(k+1,j,i+1) + u(k+1,j,i) + u(k,j,i+1) + u(k,j,i) )
229
230	v_i = b * v(k,j,i) + c2 * 0.25 * &
231	( v(k+1,j+1,i) + v(k+1,j,i) + v(k,j+1,i) + v(k,j,i) )
232
233	ws = ( c1 + c2 ) * w(k,j,i) + 0.25 * ( &
234	a * ( w(k-1,j,i-1) + w(k-1,j,i) + w(k,j,i-1) + w(k,j,i) ) &
235	+ b * ( w(k-1,j-1,i) + w(k-1,j,i) + w(k,j-1,i) + w(k,j,i) ) &
236	)
237	pt_i = 0.5 * ( pt(k,j,i) + a * pt(k,j,i-1) + b * pt(k,j-1,i) &
238	+ ( c1 + c2 ) * pt(k+1,j,i) )
239
240	pts = pt_i - hom(k,1,4,0)
241	wspts = ws * pts
242
243	!
244	!-- (2) Compute wall-parallel absolute velocity vel_total
245	vel_total = SQRT( ws*2 + ( a+c1 ) u_i*2 + ( b+c2 ) v_i**2 )
246
247	!
248	!-- (3) Compute wall friction velocity us_wall
249	IF ( rifs >= 0.0 ) THEN
250
251	!
252	!-- Stable stratification (and neutral)
253	us_wall = kappa * vel_total / ( LOG( zp / z0(j,i) ) + &
254	5.0 * rifs * ( zp - z0(j,i) ) / zp &
255	)
256	ELSE
257
258	!
259	!-- Unstable stratification
260	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
261	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
262
263	us_wall = kappa * vel_total / ( &
264	LOG( zp / z0(j,i) ) - &
265	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
266	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
267	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
268	)
269	ENDIF
270
271	!
272	!-- (4) Compute zp/L (corresponds to neutral Richardson flux number
273	!-- rifs)
274	rifs = -1.0 * zp * kappa * g * wspts / ( pt_i * (us_wall**3 + 1E-30) )
275
276	!
277	!-- Limit the value range of the Richardson numbers.
278	!-- This is necessary for very small velocities (u,w --> 0), because
279	!-- the absolute value of rif can then become very large, which in
280	!-- consequence would result in very large shear stresses and very
281	!-- small momentum fluxes (both are generally unrealistic).
282	IF ( rifs < rif_min ) rifs = rif_min
283	IF ( rifs > rif_max ) rifs = rif_max
284
285	!
286	!-- (5) Compute wall_flux (u'v', v'u', w'v', or w'u')
287	IF ( rifs >= 0.0 ) THEN
288
289	!
290	!-- Stable stratification (and neutral)
291	wall_flux(k) = kappa * &
292	( au(k,j,i) + bv(k,j,i) + (c1+c2)*w(k,j,i) ) / &
293	( LOG( zp / z0(j,i) ) + &
294	5.0 * rifs * ( zp - z0(j,i) ) / zp &
295	)
296	ELSE
297
298	!
299	!-- Unstable stratification
300	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
301	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
302
303	wall_flux(k) = kappa * &
304	( au(k,j,i) + bv(k,j,i) + (c1+c2)*w(k,j,i) ) / ( &
305	LOG( zp / z0(j,i) ) - &
306	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
307	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
308	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
309	)
310	ENDIF
311	wall_flux(k) = -wall_flux(k) * us_wall
312
313	!
314	!-- store rifs for next time step
315	rif_wall(k,j,i,wall_index) = rifs
316
317	ENDDO
318
319	END SUBROUTINE wall_fluxes_ij
320
321
322
323	!------------------------------------------------------------------------------!
324	! Call for all grid points
325	!------------------------------------------------------------------------------!
326	SUBROUTINE wall_fluxes_e( wall_flux, a, b, c1, c2, wall )
327
328	!------------------------------------------------------------------------------!
329	! Description:
330	! ------------
331	! Calculates momentum fluxes at vertical walls for routine production_e
332	! assuming Monin-Obukhov similarity.
333	! Indices: usvs a=1, vsus b=1, wsvs c1=1, wsus c2=1 (other=0).
334	!------------------------------------------------------------------------------!
335
336	USE arrays_3d
337	USE control_parameters
338	USE grid_variables
339	USE indices
340	USE statistics
341
342	IMPLICIT NONE
343
344	INTEGER :: i, j, k, kk, wall_index
345	REAL :: a, b, c1, c2, h1, h2, u_i, v_i, us_wall, vel_total, vel_zp, &
346	ws, zp
347
348	REAL :: rifs
349
350	REAL, DIMENSION(nysg:nyng,nxlg:nxrg) :: wall
351	REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: wall_flux
352
353
354	zp = 0.5 * ( (a+c1) * dy + (b+c2) * dx )
355	wall_flux = 0.0
356	wall_index = NINT( a+ 2b + 3c1 + 4*c2 )
357
358	DO i = nxl, nxr
359	DO j = nys, nyn
360
361	IF ( wall(j,i) /= 0.0 ) THEN
362	!
363	!-- All subsequent variables are computed for scalar locations.
364	DO k = nzb_diff_s_inner(j,i)-1, nzb_diff_s_outer(j,i)-2
365	!
366	!-- (1) Compute rifs, u_i, v_i, and ws
367	IF ( k == nzb_diff_s_inner(j,i)-1 ) THEN
368	kk = nzb_diff_s_inner(j,i)-1
369	ELSE
370	kk = k-1
371	ENDIF
372	rifs = 0.5 * ( rif_wall(k,j,i,wall_index) + &
373	a * rif_wall(k,j,i+1,1) + b * rif_wall(k,j+1,i,2) + &
374	c1 * rif_wall(kk,j,i,3) + c2 * rif_wall(kk,j,i,4) &
375	)
376
377	u_i = 0.5 * ( u(k,j,i) + u(k,j,i+1) )
378	v_i = 0.5 * ( v(k,j,i) + v(k,j+1,i) )
379	ws = 0.5 * ( w(k,j,i) + w(k-1,j,i) )
380	!
381	!-- (2) Compute wall-parallel absolute velocity vel_total and
382	!-- interpolate appropriate velocity component vel_zp.
383	vel_total = SQRT( ws*2 + (a+c1) u_i*2 + (b+c2) v_i**2 )
384	vel_zp = 0.5 * ( a * u_i + b * v_i + (c1+c2) * ws )
385	!
386	!-- (3) Compute wall friction velocity us_wall
387	IF ( rifs >= 0.0 ) THEN
388
389	!
390	!-- Stable stratification (and neutral)
391	us_wall = kappa * vel_total / ( LOG( zp / z0(j,i) ) + &
392	5.0 * rifs * ( zp - z0(j,i) ) / zp &
393	)
394	ELSE
395
396	!
397	!-- Unstable stratification
398	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
399	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
400
401	us_wall = kappa * vel_total / ( &
402	LOG( zp / z0(j,i) ) - &
403	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
404	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
405	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
406	)
407	ENDIF
408
409	!
410	!-- Skip step (4) of wall_fluxes, because here rifs is already
411	!-- available from (1)
412	!
413	!-- (5) Compute wall_flux (u'v', v'u', w'v', or w'u')
414
415	IF ( rifs >= 0.0 ) THEN
416
417	!
418	!-- Stable stratification (and neutral)
419	wall_flux(k,j,i) = kappa * vel_zp / &
420	( LOG( zp/z0(j,i) ) + 5.0rifs ( zp-z0(j,i) ) / zp )
421	ELSE
422
423	!
424	!-- Unstable stratification
425	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
426	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
427
428	wall_flux(k,j,i) = kappa * vel_zp / ( &
429	LOG( zp / z0(j,i) ) - &
430	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
431	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
432	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
433	)
434	ENDIF
435	wall_flux(k,j,i) = - wall_flux(k,j,i) * us_wall
436
437	ENDDO
438
439	ENDIF
440
441	ENDDO
442	ENDDO
443
444	END SUBROUTINE wall_fluxes_e
445
446
447
448	!------------------------------------------------------------------------------!
449	! Call for grid point i,j
450	!------------------------------------------------------------------------------!
451	SUBROUTINE wall_fluxes_e_ij( i, j, nzb_w, nzt_w, wall_flux, a, b, c1, c2 )
452
453	USE arrays_3d
454	USE control_parameters
455	USE grid_variables
456	USE indices
457	USE statistics
458
459	IMPLICIT NONE
460
461	INTEGER :: i, j, k, kk, nzb_w, nzt_w, wall_index
462	REAL :: a, b, c1, c2, h1, h2, u_i, v_i, us_wall, vel_total, vel_zp, &
463	ws, zp
464
465	REAL :: rifs
466
467	REAL, DIMENSION(nzb:nzt+1) :: wall_flux
468
469
470	zp = 0.5 * ( (a+c1) * dy + (b+c2) * dx )
471	wall_flux = 0.0
472	wall_index = NINT( a+ 2b + 3c1 + 4*c2 )
473
474	!
475	!-- All subsequent variables are computed for scalar locations.
476	DO k = nzb_w, nzt_w
477
478	!
479	!-- (1) Compute rifs, u_i, v_i, and ws
480	IF ( k == nzb_w ) THEN
481	kk = nzb_w
482	ELSE
483	kk = k-1
484	ENDIF
485	rifs = 0.5 * ( rif_wall(k,j,i,wall_index) + &
486	a * rif_wall(k,j,i+1,1) + b * rif_wall(k,j+1,i,2) + &
487	c1 * rif_wall(kk,j,i,3) + c2 * rif_wall(kk,j,i,4) &
488	)
489
490	u_i = 0.5 * ( u(k,j,i) + u(k,j,i+1) )
491	v_i = 0.5 * ( v(k,j,i) + v(k,j+1,i) )
492	ws = 0.5 * ( w(k,j,i) + w(k-1,j,i) )
493	!
494	!-- (2) Compute wall-parallel absolute velocity vel_total and
495	!-- interpolate appropriate velocity component vel_zp.
496	vel_total = SQRT( ws*2 + (a+c1) u_i*2 + (b+c2) v_i**2 )
497	vel_zp = 0.5 * ( a * u_i + b * v_i + (c1+c2) * ws )
498	!
499	!-- (3) Compute wall friction velocity us_wall
500	IF ( rifs >= 0.0 ) THEN
501
502	!
503	!-- Stable stratification (and neutral)
504	us_wall = kappa * vel_total / ( LOG( zp / z0(j,i) ) + &
505	5.0 * rifs * ( zp - z0(j,i) ) / zp &
506	)
507	ELSE
508
509	!
510	!-- Unstable stratification
511	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
512	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
513
514	us_wall = kappa * vel_total / ( &
515	LOG( zp / z0(j,i) ) - &
516	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
517	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
518	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
519	)
520	ENDIF
521
522	!
523	!-- Skip step (4) of wall_fluxes, because here rifs is already
524	!-- available from (1)
525	!
526	!-- (5) Compute wall_flux (u'v', v'u', w'v', or w'u')
527	!-- First interpolate the velocity (this is different from
528	!-- subroutine wall_fluxes because fluxes in subroutine
529	!-- wall_fluxes_e are defined at scalar locations).
530	vel_zp = 0.5 * ( a * ( u(k,j,i) + u(k,j,i+1) ) + &
531	b * ( v(k,j,i) + v(k,j+1,i) ) + &
532	(c1+c2) * ( w(k,j,i) + w(k-1,j,i) ) &
533	)
534
535	IF ( rifs >= 0.0 ) THEN
536
537	!
538	!-- Stable stratification (and neutral)
539	wall_flux(k) = kappa * vel_zp / &
540	( LOG( zp/z0(j,i) ) + 5.0rifs ( zp-z0(j,i) ) / zp )
541	ELSE
542
543	!
544	!-- Unstable stratification
545	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
546	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
547
548	wall_flux(k) = kappa * vel_zp / ( &
549	LOG( zp / z0(j,i) ) - &
550	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
551	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
552	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
553	)
554	ENDIF
555	wall_flux(k) = - wall_flux(k) * us_wall
556
557	ENDDO
558
559	END SUBROUTINE wall_fluxes_e_ij
560
561	END MODULE wall_fluxes_mod

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