C $Header: /u/gcmpack/MITgcm/pkg/obcs/orlanski_north.F,v 1.9 2012/09/18 20:09:17 jmc Exp $
C $Name: $
#include "OBCS_OPTIONS.h"
SUBROUTINE ORLANSKI_NORTH( bi, bj, futureTime,
I uVel, vVel, wVel, theta, salt,
I myThid )
C /==========================================================\
C | SUBROUTINE OBCS_RADIATE |
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 == 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_NORTH
C == Local variables ==
INTEGER I, K, J_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 Northern OB (Orlanski Radiation Condition)
DO K=1,Nr
DO I=1-OLx,sNx+OLx
J_obc=OB_Jn(I,bi,bj)
IF ( J_obc.NE.OB_indexNone ) THEN
C uVel
IF ((UN_STORE_2(I,K,bi,bj).eq.0.).and.
& (UN_STORE_3(I,K,bi,bj).eq.0.)) THEN
CL=0.
ELSE
CL=-(uVel(I,J_obc-1,K,bi,bj)-UN_STORE_1(I,K,bi,bj))/
& (ab1*UN_STORE_2(I,K,bi,bj) + ab2*UN_STORE_3(I,K,bi,bj))
ENDIF
IF (CL.lt.0.) THEN
CL=0.
ELSEIF (CL.gt.CMAX) THEN
CL=CMAX
ENDIF
CVEL_UN(I,K,bi,bj) = f1*(CL*dyU(I,J_obc-1,bi,bj)/deltaT)+
& f2*CVEL_UN(I,K,bi,bj)
C update OBC to next timestep
OBNu(I,K,bi,bj)=uVel(I,J_obc,K,bi,bj)-
& CVEL_UN(I,K,bi,bj)*deltaT*recip_dyU(I,J_obc,bi,bj)*
& (ab1*(uVel(I,J_obc,K,bi,bj)-uVel(I,J_obc-1,K,bi,bj)) +
& ab2*(UN_STORE_4(I,K,bi,bj)-UN_STORE_1(I,K,bi,bj)))
C vVel
IF ((VN_STORE_2(I,K,bi,bj).eq.0.).and.
& (VN_STORE_3(I,K,bi,bj).eq.0.)) THEN
CL=0.
ELSE
CL=-(vVel(I,J_obc-1,K,bi,bj)-VN_STORE_1(I,K,bi,bj))/
& (ab1*VN_STORE_2(I,K,bi,bj) + ab2*VN_STORE_3(I,K,bi,bj))
ENDIF
IF (CL.lt.0.) THEN
CL=0.
ELSEIF (CL.gt.CMAX) THEN
CL=CMAX
ENDIF
CVEL_VN(I,K,bi,bj) = f1*(CL*dyF(I,J_obc-2,bi,bj)/deltaT)+
& f2*CVEL_VN(I,K,bi,bj)
C update OBC to next timestep
OBNv(I,K,bi,bj)=vVel(I,J_obc,K,bi,bj)-
& CVEL_VN(I,K,bi,bj)*deltaT*recip_dyF(I,J_obc-1,bi,bj)*
& (ab1*(vVel(I,J_obc,K,bi,bj)-vVel(I,J_obc-1,K,bi,bj)) +
& ab2*(VN_STORE_4(I,K,bi,bj)-VN_STORE_1(I,K,bi,bj)))
C Temperature
IF ((TN_STORE_2(I,K,bi,bj).eq.0.).and.
& (TN_STORE_3(I,K,bi,bj).eq.0.)) THEN
CL=0.
ELSE
CL=-(theta(I,J_obc-1,K,bi,bj)-TN_STORE_1(I,K,bi,bj))/
& (ab1*TN_STORE_2(I,K,bi,bj) + ab2*TN_STORE_3(I,K,bi,bj))
ENDIF
IF (CL.lt.0.) THEN
CL=0.
ELSEIF (CL.gt.CMAX) THEN
CL=CMAX
ENDIF
CVEL_TN(I,K,bi,bj) = f1*(CL*dyC(I,J_obc-1,bi,bj)/deltaT)+
& f2*CVEL_TN(I,K,bi,bj)
C update OBC to next timestep
OBNt(I,K,bi,bj)=theta(I,J_obc,K,bi,bj)-
& CVEL_TN(I,K,bi,bj)*deltaT*recip_dyC(I,J_obc,bi,bj)*
& (ab1*(theta(I,J_obc,K,bi,bj)-theta(I,J_obc-1,K,bi,bj))+
& ab2*(TN_STORE_4(I,K,bi,bj)-TN_STORE_1(I,K,bi,bj)))
C Salinity
IF ((SN_STORE_2(I,K,bi,bj).eq.0.).and.
& (SN_STORE_3(I,K,bi,bj).eq.0.)) THEN
CL=0.
ELSE
CL=-(salt(I,J_obc-1,K,bi,bj)-SN_STORE_1(I,K,bi,bj))/
& (ab1*SN_STORE_2(I,K,bi,bj) + ab2*SN_STORE_3(I,K,bi,bj))
ENDIF
IF (CL.lt.0.) THEN
CL=0.
ELSEIF (CL.gt.CMAX) THEN
CL=CMAX
ENDIF
CVEL_SN(I,K,bi,bj) = f1*(CL*dyC(I,J_obc-1,bi,bj)/deltaT)+
& f2*CVEL_SN(I,K,bi,bj)
C update OBC to next timestep
OBNs(I,K,bi,bj)=salt(I,J_obc,K,bi,bj)-
& CVEL_SN(I,K,bi,bj)*deltaT*recip_dyC(I,J_obc,bi,bj)*
& (ab1*(salt(I,J_obc,K,bi,bj)-salt(I,J_obc-1,K,bi,bj)) +
& ab2*(SN_STORE_4(I,K,bi,bj)-SN_STORE_1(I,K,bi,bj)))
#ifdef ALLOW_NONHYDROSTATIC
IF ( nonHydrostatic ) THEN
C wVel
IF ((WN_STORE_2(I,K,bi,bj).eq.0.).and.
& (WN_STORE_3(I,K,bi,bj).eq.0.)) THEN
CL=0.
ELSE
CL=-(wVel(I,J_obc-1,K,bi,bj)-WN_STORE_1(I,K,bi,bj))/
& (ab1*WN_STORE_2(I,K,bi,bj)+ab2*WN_STORE_3(I,K,bi,bj))
ENDIF
IF (CL.lt.0.) THEN
CL=0.
ELSEIF (CL.gt.CMAX) THEN
CL=CMAX
ENDIF
CVEL_WN(I,K,bi,bj)=f1*(CL*dyC(I,J_obc-1,bi,bj)/deltaT)
& + f2*CVEL_WN(I,K,bi,bj)
C update OBC to next timestep
OBNw(I,K,bi,bj)=wVel(I,J_obc,K,bi,bj)-
& CVEL_WN(I,K,bi,bj)*deltaT*recip_dyC(I,J_obc,bi,bj)*
& (ab1*(wVel(I,J_obc,K,bi,bj)-wVel(I,J_obc-1,K,bi,bj))+
& ab2*(WN_STORE_4(I,K,bi,bj)-WN_STORE_1(I,K,bi,bj)))
ENDIF
#endif /* ALLOW_NONHYDROSTATIC */
C update/save storage arrays
C uVel
C copy t-1 to t-2 array
UN_STORE_3(I,K,bi,bj)=UN_STORE_2(I,K,bi,bj)
C copy (current time) t to t-1 arrays
UN_STORE_2(I,K,bi,bj)=uVel(I,J_obc-1,K,bi,bj) -
& uVel(I,J_obc-2,K,bi,bj)
UN_STORE_1(I,K,bi,bj)=uVel(I,J_obc-1,K,bi,bj)
UN_STORE_4(I,K,bi,bj)=uVel(I,J_obc,K,bi,bj)
C vVel
C copy t-1 to t-2 array
VN_STORE_3(I,K,bi,bj)=VN_STORE_2(I,K,bi,bj)
C copy (current time) t to t-1 arrays
VN_STORE_2(I,K,bi,bj)=vVel(I,J_obc-1,K,bi,bj) -
& vVel(I,J_obc-2,K,bi,bj)
VN_STORE_1(I,K,bi,bj)=vVel(I,J_obc-1,K,bi,bj)
VN_STORE_4(I,K,bi,bj)=vVel(I,J_obc,K,bi,bj)
C Temperature
C copy t-1 to t-2 array
TN_STORE_3(I,K,bi,bj)=TN_STORE_2(I,K,bi,bj)
C copy (current time) t to t-1 arrays
TN_STORE_2(I,K,bi,bj)=theta(I,J_obc-1,K,bi,bj) -
& theta(I,J_obc-2,K,bi,bj)
TN_STORE_1(I,K,bi,bj)=theta(I,J_obc-1,K,bi,bj)
TN_STORE_4(I,K,bi,bj)=theta(I,J_obc,K,bi,bj)
C Salinity
C copy t-1 to t-2 array
SN_STORE_3(I,K,bi,bj)=SN_STORE_2(I,K,bi,bj)
C copy (current time) t to t-1 arrays
SN_STORE_2(I,K,bi,bj)=salt(I,J_obc-1,K,bi,bj) -
& salt(I,J_obc-2,K,bi,bj)
SN_STORE_1(I,K,bi,bj)=salt(I,J_obc-1,K,bi,bj)
SN_STORE_4(I,K,bi,bj)=salt(I,J_obc,K,bi,bj)
#ifdef ALLOW_NONHYDROSTATIC
IF ( nonHydrostatic ) THEN
C wVel
C copy t-1 to t-2 array
WN_STORE_3(I,K,bi,bj)=WN_STORE_2(I,K,bi,bj)
C copy (current time) t to t-1 arrays
WN_STORE_2(I,K,bi,bj)=wVel(I,J_obc-1,K,bi,bj) -
& wVel(I,J_obc-2,K,bi,bj)
WN_STORE_1(I,K,bi,bj)=wVel(I,J_obc-1,K,bi,bj)
WN_STORE_4(I,K,bi,bj)=wVel(I,J_obc,K,bi,bj)
ENDIF
#endif /* ALLOW_NONHYDROSTATIC */
ENDIF
ENDDO
ENDDO
#endif /* ALLOW_OBCS_NORTH */
#endif /* ALLOW_ORLANSKI */
RETURN
END