C $Header: /u/gcmpack/MITgcm/pkg/obcs/orlanski_east.F,v 1.13 2012/09/18 20:09:17 jmc Exp $
C $Name: $
cc
#include "OBCS_OPTIONS.h"
SUBROUTINE ORLANSKI_EAST( bi, bj, futureTime,
I uVel, vVel, wVel, theta, salt,
I myThid )
C /==========================================================\
C | SUBROUTINE ORLANSKI_EAST |
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 4/10/03: 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 also now allow choice of Orlanski or fixed wavespeed
C (by means of new booleans useFixedCEast and
C useFixedCWest) without having to recompile each time
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_EAST
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 Eastern OB (Orlanski Radiation Condition)
DO K=1,Nr
DO J=1-OLy,sNy+OLy
I_obc=OB_Ie(J,bi,bj)
IF ( I_obc.NE.OB_indexNone ) THEN
C uVel
IF ((UE_STORE_2(J,K,bi,bj).eq.0.).and.
& (UE_STORE_3(J,K,bi,bj).eq.0.)) THEN
CL=0.
ELSE
CL=-(uVel(I_obc-1,J,K,bi,bj)-UE_STORE_1(J,K,bi,bj))/
& (ab1*UE_STORE_2(J,K,bi,bj) + ab2*UE_STORE_3(J,K,bi,bj))
ENDIF
IF (CL.lt.0.) THEN
CL=0.
ELSEIF (CL.gt.CMAX) THEN
CL=CMAX
ENDIF
IF (useFixedCEast) THEN
C Fixed phase speed (ignoring all of that painstakingly
C saved data...)
CVEL_UE(J,K,bi,bj) = CFIX
ELSE
CVEL_UE(J,K,bi,bj) = f1*(CL*dxF(I_obc-2,J,bi,bj)/deltaT
& )+f2*CVEL_UE(J,K,bi,bj)
ENDIF
C update OBC to next timestep
OBEu(J,K,bi,bj)=uVel(I_obc,J,K,bi,bj)-
& CVEL_UE(J,K,bi,bj)*(deltaT*recip_dxF(I_obc-1,J,bi,bj))*
& (ab1*(uVel(I_obc,J,K,bi,bj)-uVel(I_obc-1,J,K,bi,bj)) +
& ab2*(UE_STORE_4(J,K,bi,bj)-UE_STORE_1(J,K,bi,bj)))
C vVel
IF ((VE_STORE_2(J,K,bi,bj).eq.0.).and.
& (VE_STORE_3(J,K,bi,bj).eq.0.)) THEN
CL=0.
ELSE
CL=-(vVel(I_obc-1,J,K,bi,bj)-VE_STORE_1(J,K,bi,bj))/
& (ab1*VE_STORE_2(J,K,bi,bj) + ab2*VE_STORE_3(J,K,bi,bj))
ENDIF
IF (CL.lt.0.) THEN
CL=0.
ELSEIF (CL.gt.CMAX) THEN
CL=CMAX
ENDIF
IF (useFixedCEast) THEN
C Fixed phase speed (ignoring all of that painstakingly
C saved data...)
CVEL_VE(J,K,bi,bj) = CFIX
ELSE
CVEL_VE(J,K,bi,bj) = f1*(CL*dxV(I_obc-1,J,bi,bj)
$ /deltaT)+f2*CVEL_VE(J,K,bi,bj)
ENDIF
C update OBC to next timestep
OBEv(J,K,bi,bj)=vVel(I_obc,J,K,bi,bj)-
& CVEL_VE(J,K,bi,bj)*(deltaT*recip_dxV(I_obc,J,bi,bj))*
& (ab1*(vVel(I_obc,J,K,bi,bj)-vVel(I_obc-1,J,K,bi,bj)) +
& ab2*(VE_STORE_4(J,K,bi,bj)-VE_STORE_1(J,K,bi,bj)))
C Temperature
IF ((TE_STORE_2(J,K,bi,bj).eq.0.).and.
& (TE_STORE_3(J,K,bi,bj).eq.0.)) THEN
CL=0.
ELSE
CL=-(theta(I_obc-1,J,K,bi,bj)-TE_STORE_1(J,K,bi,bj))/
& (ab1*TE_STORE_2(J,K,bi,bj) + ab2*TE_STORE_3(J,K,bi,bj))
ENDIF
IF (CL.lt.0.) THEN
CL=0.
ELSEIF (CL.gt.CMAX) THEN
CL=CMAX
ENDIF
IF (useFixedCEast) THEN
C Fixed phase speed (ignoring all of that painstakingly
C saved data...)
CVEL_TE(J,K,bi,bj) = CFIX
ELSE
CVEL_TE(J,K,bi,bj) = f1*(CL*dxC(I_obc-1,J,bi,bj)
$ /deltaT)+f2*CVEL_TE(J,K,bi,bj)
ENDIF
C update OBC to next timestep
OBEt(J,K,bi,bj)=theta(I_obc,J,K,bi,bj)-
& CVEL_TE(J,K,bi,bj)*(deltaT*recip_dxC(I_obc,J,bi,bj))*
& (ab1*(theta(I_obc,J,K,bi,bj)-theta(I_obc-1,J,K,bi,bj))+
& ab2*(TE_STORE_4(J,K,bi,bj)-TE_STORE_1(J,K,bi,bj)))
C Salinity
IF ((SE_STORE_2(J,K,bi,bj).eq.0.).and.
& (SE_STORE_3(J,K,bi,bj).eq.0.)) THEN
CL=0.
ELSE
CL=-(salt(I_obc-1,J,K,bi,bj)-SE_STORE_1(J,K,bi,bj))/
& (ab1*SE_STORE_2(J,K,bi,bj) + ab2*SE_STORE_3(J,K,bi,bj))
ENDIF
IF (CL.lt.0.) THEN
CL=0.
ELSEIF (CL.gt.CMAX) THEN
CL=CMAX
ENDIF
IF (useFixedCEast) THEN
C Fixed phase speed (ignoring all of that painstakingly
C saved data...)
CVEL_SE(J,K,bi,bj) = CFIX
ELSE
CVEL_SE(J,K,bi,bj) = f1*(CL*dxC(I_obc-1,J,bi,bj)
$ /deltaT)+f2*CVEL_SE(J,K,bi,bj)
ENDIF
C update OBC to next timestep
OBEs(J,K,bi,bj)=salt(I_obc,J,K,bi,bj)-
& CVEL_SE(J,K,bi,bj)*(deltaT*recip_dxC(I_obc,J,bi,bj))*
& (ab1*(salt(I_obc,J,K,bi,bj)-salt(I_obc-1,J,K,bi,bj))+
& ab2*(SE_STORE_4(J,K,bi,bj)-SE_STORE_1(J,K,bi,bj)))
#ifdef ALLOW_NONHYDROSTATIC
IF ( nonHydrostatic ) THEN
C wVel
IF ((WE_STORE_2(J,K,bi,bj).eq.0.).and.
& (WE_STORE_3(J,K,bi,bj).eq.0.)) THEN
CL=0.
ELSE
CL=-(wVel(I_obc-1,J,K,bi,bj)-WE_STORE_1(J,K,bi,bj))/
& (ab1*WE_STORE_2(J,K,bi,bj)+ab2*WE_STORE_3(J,K,bi,bj))
ENDIF
IF (CL.lt.0.) THEN
CL=0.
ELSEIF (CL.gt.CMAX) THEN
CL=CMAX
ENDIF
IF (useFixedCEast) THEN
C Fixed phase speed (ignoring all of that painstakingly
C saved data...)
CVEL_WE(J,K,bi,bj) = CFIX
ELSE
CVEL_WE(J,K,bi,bj)=f1*(CL*dxC(I_obc-1,J,bi,bj)/deltaT)
& + f2*CVEL_WE(J,K,bi,bj)
ENDIF
C update OBC to next timestep
OBEw(J,K,bi,bj)=wVel(I_obc,J,K,bi,bj)-
& CVEL_WE(J,K,bi,bj)*(deltaT*recip_dxC(I_obc,J,bi,bj))*
& (ab1*(wVel(I_obc,J,K,bi,bj)-wVel(I_obc-1,J,K,bi,bj))+
& ab2*(WE_STORE_4(J,K,bi,bj)-WE_STORE_1(J,K,bi,bj)))
ENDIF
#endif /* ALLOW_NONHYDROSTATIC */
C update/save storage arrays
C uVel
C copy t-1 to t-2 array
UE_STORE_3(J,K,bi,bj)=UE_STORE_2(J,K,bi,bj)
C copy (current time) t to t-1 arrays
UE_STORE_2(J,K,bi,bj)=uVel(I_obc-1,J,K,bi,bj) -
& uVel(I_obc-2,J,K,bi,bj)
UE_STORE_1(J,K,bi,bj)=uVel(I_obc-1,J,K,bi,bj)
UE_STORE_4(J,K,bi,bj)=uVel(I_obc,J,K,bi,bj)
C vVel
C copy t-1 to t-2 array
VE_STORE_3(J,K,bi,bj)=VE_STORE_2(J,K,bi,bj)
C copy (current time) t to t-1 arrays
VE_STORE_2(J,K,bi,bj)=vVel(I_obc-1,J,K,bi,bj) -
& vVel(I_obc-2,J,K,bi,bj)
VE_STORE_1(J,K,bi,bj)=vVel(I_obc-1,J,K,bi,bj)
VE_STORE_4(J,K,bi,bj)=vVel(I_obc,J,K,bi,bj)
C Temperature
C copy t-1 to t-2 array
TE_STORE_3(J,K,bi,bj)=TE_STORE_2(J,K,bi,bj)
C copy (current time) t to t-1 arrays
TE_STORE_2(J,K,bi,bj)=theta(I_obc-1,J,K,bi,bj) -
& theta(I_obc-2,J,K,bi,bj)
TE_STORE_1(J,K,bi,bj)=theta(I_obc-1,J,K,bi,bj)
TE_STORE_4(J,K,bi,bj)=theta(I_obc,J,K,bi,bj)
C Salinity
C copy t-1 to t-2 array
SE_STORE_3(J,K,bi,bj)=SE_STORE_2(J,K,bi,bj)
C copy (current time) t to t-1 arrays
SE_STORE_2(J,K,bi,bj)=salt(I_obc-1,J,K,bi,bj) -
& salt(I_obc-2,J,K,bi,bj)
SE_STORE_1(J,K,bi,bj)=salt(I_obc-1,J,K,bi,bj)
SE_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
WE_STORE_3(J,K,bi,bj)=WE_STORE_2(J,K,bi,bj)
C copy (current time) t to t-1 arrays
WE_STORE_2(J,K,bi,bj)=wVel(I_obc-1,J,K,bi,bj) -
& wVel(I_obc-2,J,K,bi,bj)
WE_STORE_1(J,K,bi,bj)=wVel(I_obc-1,J,K,bi,bj)
WE_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