C $Header: /u/gcmpack/MITgcm/pkg/obcs/orlanski_west.F,v 1.13 2012/09/18 20:09:17 jmc Exp $
C $Name: $
cc
#include "OBCS_OPTIONS.h"
SUBROUTINE ORLANSKI_WEST( bi, bj, futureTime,
I uVel, vVel, wVel, theta, salt,
I myThid )
C /==========================================================\
C | SUBROUTINE ORLANSKI_WEST |
C | o Calculate future boundary data at open boundaries |
C | at time = futureTime by applying Orlanski radiation |
C | conditions. |
C |==========================================================|
C | |
C \==========================================================/
IMPLICIT NONE
C === Global variables ===
#include "SIZE.h"
#include "EEPARAMS.h"
#include "PARAMS.h"
#include "GRID.h"
#include "OBCS_PARAMS.h"
#include "OBCS_GRID.h"
#include "OBCS_FIELDS.h"
#include "ORLANSKI.h"
C SPK 6/2/00: Added radiative OBCs for salinity.
C SPK 6/6/00: Changed calculation of OB*w. When K=1, the
C upstream value is used. For example on the eastern OB:
C IF (K.EQ.1) THEN
C OBEw(J,K,bi,bj)=wVel(I_obc-1,J,K,bi,bj)
C ENDIF
C
C SPK 7/7/00: 1) Removed OB*w fix (see above).
C 2) Added variable CMAX. Maximum diagnosed phase speed is now
C clamped to CMAX. For stability of AB-II scheme (CFL) the
C (non-dimensional) phase speed must be <0.5
C 3) (Sonya Legg) Changed application of uVel and vVel.
C uVel on the western OB is actually applied at I_obc+1
C while vVel on the southern OB is applied at J_obc+1.
C 4) (Sonya Legg) Added templates for forced OBs.
C
C SPK 7/17/00: Non-uniform resolution is now taken into account in diagnosing
C phase speeds and time-stepping OB values. CL is still the
C non-dimensional phase speed; CVEL is the dimensional phase
C speed: CVEL = CL*(dx or dy)/dt, where dx and dy is the
C appropriate grid spacings. Note that CMAX (with which CL
C is compared) remains non-dimensional.
C
C SPK 7/18/00: Added code to allow filtering of phase speed following
C Blumberg and Kantha. There is now a separate array
C CVEL_**, where **=Variable(U,V,T,S,W)Boundary(E,W,N,S) for
C the dimensional phase speed. These arrays are initialized to
C zero in ini_obcs.F. CVEL_** is filtered according to
C CVEL_** = fracCVEL*CVEL(new) + (1-fracCVEL)*CVEL_**(old).
C fracCVEL=1.0 turns off filtering.
C
C SPK 7/26/00: Changed code to average phase speed. A new variable
C 'cvelTimeScale' was created. This variable must now be
C specified. Then, fracCVEL=deltaT/cvelTimeScale.
C Since the goal is to smooth out the 'singularities' in the
C diagnosed phase speed, cvelTimeScale could be picked as the
C duration of the singular period in the unfiltered case. Thus,
C for a plane wave cvelTimeScale might be the time take for the
C wave to travel a distance DX, where DX is the width of the region
C near which d(phi)/dx is small.
C
C JBG 3/24/03: Fixed phase speed at western boundary (as suggested by
C Dale Durran in his MWR paper). Fixed value (in m/s) is
C passed in as variable CFIX in data.obcs.
C
C JBG 4/10/03: allow choice of Orlanski or fixed wavespeed (by means of new
C booleans useFixedCEast and useFixedCWest) without
C having to recompile each time
c SAL 1/7/03: Fixed bug: implementation for salinity was incomplete
C
C == Routine arguments ==
INTEGER bi, bj
_RL futureTime
_RL uVel (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
_RL vVel (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
_RL wVel (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
_RL theta(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
_RL salt (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
INTEGER myThid
#ifdef ALLOW_ORLANSKI
#ifdef ALLOW_OBCS_WEST
C == Local variables ==
INTEGER J, K, I_obc
_RL CL, ab1, ab2, fracCVEL, f1, f2
ab1 = 1.5 _d 0 + abEps /* Adams-Bashforth coefficients */
ab2 = -0.5 _d 0 - abEps
/* CMAX is maximum allowable phase speed-CFL for AB-II */
/* cvelTimeScale is averaging period for phase speed in sec. */
fracCVEL = deltaT/cvelTimeScale /* fraction of new phase speed used*/
f1 = fracCVEL /* dont change this. Set cvelTimeScale */
f2 = 1.0-fracCVEL /* dont change this. set cvelTimeScale */
C Western OB (Orlanski Radiation Condition)
DO K=1,Nr
DO J=1-OLy,sNy+OLy
I_obc=OB_Iw(J,bi,bj)
IF ( I_obc.NE.OB_indexNone ) THEN
C uVel (to be applied at I_obc+1)
IF ((UW_STORE_2(J,K,bi,bj).eq.0.).and.
& (UW_STORE_3(J,K,bi,bj).eq.0.)) THEN
CL=0.
ELSE
CL=(uVel(I_obc+2,J,K,bi,bj)-UW_STORE_1(J,K,bi,bj))/
& (ab1*UW_STORE_2(J,K,bi,bj) + ab2*UW_STORE_3(J,K,bi,bj))
ENDIF
IF (CL.lt.0.) THEN
CL=0.
ELSEIF (CL.gt.CMAX) THEN
CL=CMAX
ENDIF
IF (useFixedCWest) THEN
C Fixed phase speed (ignoring all of that painstakingly
C saved data...)
CVEL_UW(J,K,bi,bj) = CFIX
ELSE
CVEL_UW(J,K,bi,bj) = f1*(CL*dxF(I_obc+2,J,bi,bj)/deltaT
& )+f2*CVEL_UW(J,K,bi,bj)
ENDIF
C update OBC to next timestep
OBWu(J,K,bi,bj)=uVel(I_obc+1,J,K,bi,bj)+
& CVEL_UW(J,K,bi,bj)*(deltaT*recip_dxF(I_obc+1,J,bi,bj))*
& (ab1*(uVel(I_obc+2,J,K,bi,bj)-uVel(I_obc+1,J,K,bi,bj))+
& ab2*(UW_STORE_1(J,K,bi,bj)-UW_STORE_4(J,K,bi,bj)))
C vVel
IF ((VW_STORE_2(J,K,bi,bj).eq.0.).and.
& (VW_STORE_3(J,K,bi,bj).eq.0.)) THEN
CL=0.
ELSE
CL=(vVel(I_obc+1,J,K,bi,bj)-VW_STORE_1(J,K,bi,bj))/
& (ab1*VW_STORE_2(J,K,bi,bj) + ab2*VW_STORE_3(J,K,bi,bj))
ENDIF
IF (CL.lt.0.) THEN
CL=0.
ELSEIF (CL.gt.CMAX) THEN
CL=CMAX
ENDIF
IF (useFixedCWest) THEN
C Fixed phase speed (ignoring all of that painstakingly
C saved data...)
CVEL_VW(J,K,bi,bj) = CFIX
ELSE
CVEL_VW(J,K,bi,bj) = f1*(CL*dxV(I_obc+2,J,bi,bj)/deltaT
& )+f2*CVEL_VW(J,K,bi,bj)
ENDIF
C update OBC to next timestep
OBWv(J,K,bi,bj)=vVel(I_obc,J,K,bi,bj)+
& CVEL_VW(J,K,bi,bj)*(deltaT*recip_dxV(I_obc+1,J,bi,bj))*
& (ab1*(vVel(I_obc+1,J,K,bi,bj)-vVel(I_obc,J,K,bi,bj))+
& ab2*(VW_STORE_1(J,K,bi,bj)-VW_STORE_4(J,K,bi,bj)))
C Temperature
IF ((TW_STORE_2(J,K,bi,bj).eq.0.).and.
& (TW_STORE_3(J,K,bi,bj).eq.0.)) THEN
CL=0.
ELSE
CL=(theta(I_obc+1,J,K,bi,bj)-TW_STORE_1(J,K,bi,bj))/
& (ab1*TW_STORE_2(J,K,bi,bj) + ab2*TW_STORE_3(J,K,bi,bj))
ENDIF
IF (CL.lt.0.) THEN
CL=0.
ELSEIF (CL.gt.CMAX) THEN
CL=CMAX
ENDIF
IF (useFixedCWest) THEN
C Fixed phase speed (ignoring all of that painstakingly
C saved data...)
CVEL_TW(J,K,bi,bj) = CFIX
ELSE
CVEL_TW(J,K,bi,bj) = f1*(CL*dxC(I_obc+2,J,bi,bj)/deltaT
& )+f2*CVEL_TW(J,K,bi,bj)
ENDIF
C update OBC to next timestep
OBWt(J,K,bi,bj)=theta(I_obc,J,K,bi,bj)+
& CVEL_TW(J,K,bi,bj)*(deltaT*recip_dxC(I_obc+1,J,bi,bj))*
& (ab1*(theta(I_obc+1,J,K,bi,bj)-theta(I_obc,J,K,bi,bj))+
& ab2*(TW_STORE_1(J,K,bi,bj)-TW_STORE_4(J,K,bi,bj)))
C Salinity
IF ((SW_STORE_2(J,K,bi,bj).eq.0.).and.
& (SW_STORE_3(J,K,bi,bj).eq.0.)) THEN
CL=0.
ELSE
CL=(salt(I_obc+1,J,K,bi,bj)-SW_STORE_1(J,K,bi,bj))/
& (ab1*SW_STORE_2(J,K,bi,bj) + ab2*SW_STORE_3(J,K,bi,bj))
ENDIF
IF (CL.lt.0.) THEN
CL=0.
ELSEIF (CL.gt.CMAX) THEN
CL=CMAX
ENDIF
IF (useFixedCWest) THEN
C Fixed phase speed (ignoring all of that painstakingly
C saved data...)
CVEL_SW(J,K,bi,bj) = CFIX
ELSE
CVEL_SW(J,K,bi,bj) = f1*(CL*dxC(I_obc+2,J,bi,bj)/deltaT
& )+f2*CVEL_SW(J,K,bi,bj)
ENDIF
C update OBC to next timestep
OBWs(J,K,bi,bj)=salt(I_obc,J,K,bi,bj)+
& CVEL_SW(J,K,bi,bj)*(deltaT*recip_dxC(I_obc+1,J,bi,bj))*
& (ab1*(salt(I_obc+1,J,K,bi,bj)-salt(I_obc,J,K,bi,bj))+
& ab2*(SW_STORE_1(J,K,bi,bj)-SW_STORE_4(J,K,bi,bj)))
#ifdef ALLOW_NONHYDROSTATIC
IF ( nonHydrostatic ) THEN
C wVel
IF ((WW_STORE_2(J,K,bi,bj).eq.0.).and.
& (WW_STORE_3(J,K,bi,bj).eq.0.)) THEN
CL=0.
ELSE
CL=(wVel(I_obc+1,J,K,bi,bj)-WW_STORE_1(J,K,bi,bj))/
& (ab1*WW_STORE_2(J,K,bi,bj)+ab2*WW_STORE_3(J,K,bi,bj))
ENDIF
IF (CL.lt.0.) THEN
CL=0.
ELSEIF (CL.gt.CMAX) THEN
CL=CMAX
ENDIF
IF (useFixedCWest) THEN
C Fixed phase speed (ignoring all of that painstakingly
C saved data...)
CVEL_WW(J,K,bi,bj) = CFIX
ELSE
CVEL_WW(J,K,bi,bj)=f1*(CL*dxC(I_obc+2,J,bi,bj)/deltaT)
& + f2*CVEL_WW(J,K,bi,bj)
ENDIF
C update OBC to next timestep
OBWw(J,K,bi,bj)=wVel(I_obc,J,K,bi,bj)+
& CVEL_WW(J,K,bi,bj)*(deltaT*recip_dxC(I_obc+1,J,bi,bj))*
& (ab1*(wVel(I_obc+1,J,K,bi,bj)-wVel(I_obc,J,K,bi,bj))+
& ab2*(WW_STORE_1(J,K,bi,bj)-WW_STORE_4(J,K,bi,bj)))
ENDIF
#endif /* ALLOW_NONHYDROSTATIC */
C update/save storage arrays
C uVel
C copy t-1 to t-2 array
UW_STORE_3(J,K,bi,bj)=UW_STORE_2(J,K,bi,bj)
C copy (current time) t to t-1 arrays
UW_STORE_2(J,K,bi,bj)=uVel(I_obc+3,J,K,bi,bj) -
& uVel(I_obc+2,J,K,bi,bj)
UW_STORE_1(J,K,bi,bj)=uVel(I_obc+2,J,K,bi,bj)
UW_STORE_4(J,K,bi,bj)=uVel(I_obc+1,J,K,bi,bj)
C vVel
C copy t-1 to t-2 array
VW_STORE_3(J,K,bi,bj)=VW_STORE_2(J,K,bi,bj)
C copy (current time) t to t-1 arrays
VW_STORE_2(J,K,bi,bj)=vVel(I_obc+2,J,K,bi,bj) -
& vVel(I_obc+1,J,K,bi,bj)
VW_STORE_1(J,K,bi,bj)=vVel(I_obc+1,J,K,bi,bj)
VW_STORE_4(J,K,bi,bj)=vVel(I_obc,J,K,bi,bj)
C Temperature
C copy t-1 to t-2 array
TW_STORE_3(J,K,bi,bj)=TW_STORE_2(J,K,bi,bj)
C copy (current time) t to t-1 arrays
TW_STORE_2(J,K,bi,bj)=theta(I_obc+2,J,K,bi,bj) -
& theta(I_obc+1,J,K,bi,bj)
TW_STORE_1(J,K,bi,bj)=theta(I_obc+1,J,K,bi,bj)
TW_STORE_4(J,K,bi,bj)=theta(I_obc,J,K,bi,bj)
c Salinity
C copy t-1 to t-2 array
SW_STORE_3(J,K,bi,bj)=SW_STORE_2(J,K,bi,bj)
C copy (current time) t to t-1 arrays
SW_STORE_2(J,K,bi,bj)=salt(I_obc+2,J,K,bi,bj) -
& salt(I_obc+1,J,K,bi,bj)
SW_STORE_1(J,K,bi,bj)=salt(I_obc+1,J,K,bi,bj)
SW_STORE_4(J,K,bi,bj)=salt(I_obc,J,K,bi,bj)
#ifdef ALLOW_NONHYDROSTATIC
IF ( nonHydrostatic ) THEN
C wVel
C copy t-1 to t-2 array
WW_STORE_3(J,K,bi,bj)=WW_STORE_2(J,K,bi,bj)
C copy (current time) t to t-1 arrays
WW_STORE_2(J,K,bi,bj)=wVel(I_obc+2,J,K,bi,bj) -
& wVel(I_obc+1,J,K,bi,bj)
WW_STORE_1(J,K,bi,bj)=wVel(I_obc+1,J,K,bi,bj)
WW_STORE_4(J,K,bi,bj)=wVel(I_obc,J,K,bi,bj)
ENDIF
#endif /* ALLOW_NONHYDROSTATIC */
ENDIF
ENDDO
ENDDO
#endif
#endif /* ALLOW_ORLANSKI */
RETURN
END