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mixing_isopycnal.f90
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mixing_isopycnal.f90
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subroutine mixing_isopycnal(var,vardif,rv_kr)
! ---------------------------------------------
! diffusion along isopycnals.
! 06 Feb 2013. JBG.
!
USE header
!
IMPLICIT NONE
INTEGER :: i,j,k
INTEGER :: ip1,im1
REAL :: rv_kr
REAL(kind=rc_kind), dimension( 0:NI+1,0:NJ+1, 0:NK+1) :: var
REAL(kind=rc_kind) :: vardif(NI,NJ,NK)
REAL(kind=rc_kind) :: sxfx(0:NI), sxfy(0:NJ),sxfz(0:NK)
REAL(kind=rc_kind) :: syfx(0:NI), syfy(0:NJ),syfz(0:NK)
REAL(kind=rc_kind) :: drdxfx(0:NI), drdxfy(0:NJ),drdxfz(0:NK)
REAL(kind=rc_kind) :: drdyfx(0:NI), drdyfy(0:NJ),drdyfz(0:NK)
REAL(kind=rc_kind) :: drdzfx(0:NI), drdzfy(0:NJ),drdzfz(0:NK)
REAL(kind=rc_kind) :: dvdxfx(0:NI), dvdxfy(0:NJ),dvdxfz(0:NK)
REAL(kind=rc_kind) :: dvdyfx(0:NI), dvdyfy(0:NJ),dvdyfz(0:NK)
REAL(kind=rc_kind) :: dvdzfx(0:NI), dvdzfy(0:NJ),dvdzfz(0:NK)
REAL(kind=rc_kind) :: flfx(0:NI), flfy(0:NJ),flfz(0:NK)
REAL(kind=rc_kind), dimension(0:NI+1,0:NJ+1, 0:NK+1) :: kredi
REAL(kind=rc_kind) :: fac
LOGICAL :: lv_smsl=.FALSE.
kredi(:,:,:)=rv_kr
fac= 1.0/(UL*LEN)
!*********************
! FLUX IN X-DIRECTION
!---------------------
DO k=1,NK
DO j=1,NJ
DO i=1,NI ! For all faces_x (face 0 will be equal to face NI),
IF(i==NI) then ! For the case of face_x(NI), the neighbour on the right is the cell 1.
ip1=1
ELSE
ip1=i+1
ENDIF
!----------------
! VARIATIONS IN X
! delta_var / delta_x
drdxfx(i)=( rho(ip1,j,k)-rho(i,j,k) ) * ( 0.5d0*(ux(i,j)+ux(ip1,j)) )
dvdxfx(i)=( var(ip1,j,k)-var(i,j,k) ) * ( 0.5d0*(ux(i,j)+ux(ip1,j)) )
!----------------
! VARIATIONS IN Y
if(j==1) then
! [ rho_face_x(i,j+1,k) - rho_face_x(i,j,k) ] / [ vy estimated between faces_x (i,j) and (i,j+1) ]
drdyfx(i)=( 0.5*(rho(i,j+1,k)+rho(ip1,j+1,k)) - 0.5*(rho(i,1,k)+rho(ip1,1,k) ) ) &
& * ( ( 0.25d0* (vy(i,j)+vy(ip1,j)+vy(i,j+1)+vy(ip1,j+1)) ))
dvdyfx(i)=( 0.5*(var(i,j+1,k)+var(ip1,j+1,k)) - 0.5*(var(i,1,k)+var(ip1,1,k) ) ) &
& * ( ( 0.25d0* (vy(i,j)+vy(ip1,j)+vy(i,j+1)+vy(ip1,j+1)) ))
elseif(j==NJ) then
! [ rho_face_x(i,j,k) - rho_face_x(i,j-1,k) ] / [ vy estimated between faces_x (i,j) and (i,j-1) ]
drdyfx(i)=( 0.5*(rho(i,NJ,k)+rho(ip1,NJ,k)) - 0.5*(rho(i,j-1,k)+rho(ip1,j-1,k) ) ) &
& * ( ( 0.25d0* (vy(i,NJ)+vy(ip1,NJ)+vy(i,j-1)+vy(ip1,j-1))) )
dvdyfx(i)=( 0.5*(var(i,NJ,k)+var(ip1,NJ,k)) - 0.5*(var(i,j-1,k)+var(ip1,j-1,k) ) ) &
& * ( ( 0.25d0* (vy(i,NJ)+vy(ip1,NJ)+vy(i,j-1)+vy(ip1,j-1))) )
else
! [ rho_face_x(i,j+1,k) - rho_face_x(i,j-1,k) ] &
! & / [ vy estimated between faces_x (i,j) and (i,j+1) + vy estimated between faces_x (i,j) and (i,j-1) ]
drdyfx(i)=( 0.5*(rho(i,j+1,k)+rho(ip1,j+1,k)) - 0.5*(rho(i,j-1,k)+rho(ip1,j-1,k) ) ) &
& * 0.25d0 * ( ( 0.25d0* (vy(i,j)+vy(ip1,j)+vy(i,j+1)+vy(ip1,j+1)) &
& + 0.25d0*(vy(i,j)+vy(ip1,j)+vy(i,j-1)+vy(ip1,j-1)) ) )
dvdyfx(i)=( 0.5*(var(i,j+1,k)+var(ip1,j+1,k)) - 0.5*(var(i,j-1,k)+var(ip1,j-1,k) ) ) &
& * 0.25d0 * ( ( 0.25d0* (vy(i,j)+vy(ip1,j)+vy(i,j+1)+vy(ip1,j+1)) + 0.25d0*(vy(i,j)+vy(ip1,j)+vy(i,j-1)+vy(ip1,j-1)) ) )
endif
!----------------
! VARIATIONS IN Z
if(k==1) then
! [ rho_face_x(i,j,k+1) - rho_face_x(i,j,k) ] &
!& / [ wz estimated between faces_x (i,j,k) and (i,j,k+1) ]
drdzfx(i)=( 0.5*(rho(i,j,k+1)+rho(ip1,j,k+1)) - 0.5*(rho(i,j,k)+rho(ip1,j,k) ) ) &
& * ( ( 0.25d0* (wz(i,j,k)+wz(ip1,j,k)+wz(i,j,k+1)+wz(ip1,j,k+1)) ) )
dvdzfx(i)=( 0.5*(var(i,j,k+1)+var(ip1,j,k+1)) - 0.5*(var(i,j,k)+var(ip1,j,k) ) ) &
& * ( ( 0.25d0* (wz(i,j,k)+wz(ip1,j,k)+wz(i,j,k+1)+wz(ip1,j,k+1)) ) )
elseif(k==NK) then
! [ rho_face_x(i,j,k) - rho_face_x(i,j,k-1) ] &
!& / [ wz estimated between faces_x (i,j,k) and (i,j,k-1) ]
drdzfx(i)=( 0.5*(rho(i,j,NK)+rho(ip1,j,NK)) - 0.5*(rho(i,j,k-1)+rho(ip1,j,k-1) ) ) &
& * ( ( 0.25d0*(wz(i,j,NK)+wz(ip1,j,NK)+wz(i,j,k-1)+wz(ip1,j,k-1)) ) )
dvdzfx(i)=( 0.5*(var(i,j,NK)+var(ip1,j,NK)) - 0.5*(var(i,j,k-1)+var(ip1,j,k-1) ) ) &
& * ( ( 0.25d0*(wz(i,j,NK)+wz(ip1,j,NK)+wz(i,j,k-1)+wz(ip1,j,k-1)) ) )
else
! [ rho_face_x(i,j,k+1) - rho_face_x(i,j,k-1) ] &
!& / [ wz estimated between faces_x (i,j,k) and (i,j,k+1) + wz estimated between faces_x (i,j,k) and (i,j,k-1) ]
drdzfx(i)=( 0.5*(rho(i,j,k+1)+rho(ip1,j,k+1)) - 0.5*(rho(i,j,k-1)+rho(ip1,j,k-1) ) ) &
& * 0.25d0 * ( ( 0.25d0* (wz(i,j,k)+wz(ip1,j,k)+wz(i,j,k+1)+wz(ip1,j,k+1)) &
& + 0.25d0*(wz(i,j,k)+wz(ip1,j,k)+wz(i,j,k-1)+wz(ip1,j,k-1)) ) )
dvdzfx(i)=( 0.5*(var(i,j,k+1)+var(ip1,j,k+1)) - 0.5*(var(i,j,k-1)+var(ip1,j,k-1) ) ) &
& * 0.25d0 * ( ( 0.25d0* (wz(i,j,k)+wz(ip1,j,k)+wz(i,j,k+1)+wz(ip1,j,k+1)) &
& + 0.25d0*(wz(i,j,k)+wz(ip1,j,k)+wz(i,j,k-1)+wz(ip1,j,k-1)) ) )
endif
!------------------------
! COMPUTATION OF THE FLUX
if(lv_smsl) then
flfx(i)=kredi(i,j,k)/( drdzfx(i)**2) &
& * ( ( drdzfx(i)**2)*dvdxfx(i) - 0*dvdyfx(i) - drdxfx(i)*drdzfx(i)*dvdzfx(i) )
else
flfx(i)=kredi(i,j,k)/(drdxfx(i)**2+drdyfx(i)**2+drdzfx(i)**2) &
& * ( (drdyfx(i)**2+drdzfx(i)**2)*dvdxfx(i) - drdxfx(i)*drdyfx(i)*dvdyfx(i) - drdxfx(i)*drdzfx(i)*dvdzfx(i) )
endif
ENDDO !_ i
flfx(0)=flfx(NI)
!-------------------------------
! COMPUTATION OF THE SOURCE TERM
do i=1,NI
vardif(i,j,k)= 0 + fac*Jac(i,j,k)*ux(i,j)* ( flfx(i) - flfx(i-1) )
! IF(i==48 .AND. k==18 .AND. j==131) then
! PRINT*,vardif(i,j,k),flfx(i),flfx(i-1)
! ENDIF
enddo
ENDDO !_ j
ENDDO !_ k
!*********************
! FLUX IN Y-DIRECTION
!---------------------
DO i=1,NI
IF(i==1) then
im1=NI;ip1=i+1
elseif(i==NI) then
im1=i-1;ip1=1
else
im1=i-1;ip1=i+1
ENDIF
DO k=1,NK
DO j=1,NJ-1 ! For all faces_y
!----------------
! VARIATIONS IN X
! [ rho_face_y(i+1,j,k) - rho_face_y(i-1,j,k) ] &
!& / [ ux estimated between faces_y (i,j) and (i+1,j) + ux estimated between faces_y (i,j) and (i-1,j) ]
drdxfy(j)=( 0.5*(rho(ip1,j,k)+rho(ip1,j+1,k)) - 0.5*(rho(im1,j,k)+rho(im1,j+1,k) ) ) * 0.25d0 * &
& ( ( 0.25d0* (ux(i,j)+ux(i,j+1)+ux(ip1,j)+ux(ip1,j+1)) + 0.25d0*(ux(i,j)+ux(i,j+1)+ux(im1,j)+ux(im1,j+1)) ) )
dvdxfy(j)=( 0.5*(var(ip1,j,k)+var(ip1,j+1,k)) - 0.5*(var(im1,j,k)+var(im1,j+1,k) ) ) * 0.25d0 * &
& ( ( 0.25d0* (ux(i,j)+ux(i,j+1)+ux(ip1,j)+ux(ip1,j+1)) + 0.25d0*(ux(i,j)+ux(i,j+1)+ux(im1,j)+ux(im1,j+1)) ) )
!----------------
! VARIATIONS IN Y
! delta_var / delta_y
drdyfy(j)=( rho(i,j+1,k)-rho(i,j,k) ) * ( 0.5d0*(vy(i,j)+vy(i,j+1)) )
dvdyfy(j)=( var(i,j+1,k)-var(i,j,k) ) * ( 0.5d0*(vy(i,j)+vy(i,j+1)) )
!----------------
! VARIATIONS IN Z
IF(k==1) then
! [ rho_face_y(i,j,k+1) - rho_face_y(i,j,k-1) ] &
!& / [ wz estimated between faces_x (i,j,k) and (i,j,k+1) + vy estimated between faces_x (i,j,k) and (i,j,k-1) ]
drdzfy(j)=( 0.5*(rho(i,j,k+1)+rho(i,j+1,k+1)) - 0.5*(rho(i,j,k)+rho(i,j+1,k) ) ) &
& * ( ( 0.25d0* (wz(i,j,k)+wz(i,j+1,k)+wz(i,j,k+1)+wz(i,j+1,k+1)) ))
dvdzfy(j)=( 0.5*(var(i,j,k+1)+var(i,j+1,k+1)) - 0.5*(var(i,j,k)+var(i,j+1,k) ) ) &
& * ( ( 0.25d0* (wz(i,j,k)+wz(i,j+1,k)+wz(i,j,k+1)+wz(i,j+1,k+1)) ))
elseif(k==NK) then
! [ rho_face_y(i,j,k+1) - rho_face_y(i,j,k-1) ] &
!& / [ wz estimated between faces_x (i,j,k) and (i,j,k+1) + vy estimated between faces_x (i,j,k) and (i,j,k-1) ]
drdzfy(j)=( 0.5*(rho(i,j,k)+rho(i,j+1,k)) - 0.5*(rho(i,j,k-1)+rho(i,j+1,k-1) ) ) &
& * ( ( 0.25d0* (wz(i,j,k)+wz(i,j+1,k)+wz(i,j,k-1)+wz(i,j+1,k-1)) ) )
dvdzfy(j)=( 0.5*(var(i,j,k)+var(i,j+1,k)) - 0.5*(var(i,j,k-1)+var(i,j+1,k-1) ) ) &
& * ( ( 0.25d0* (wz(i,j,k)+wz(i,j+1,k)+wz(i,j,k-1)+wz(i,j+1,k-1)) ) )
else
! [ rho_face_y(i,j,k+1) - rho_face_y(i,j,k-1) ] &
!& / [ wz estimated between faces_x (i,j,k) and (i,j,k+1) + vy estimated between faces_x (i,j,k) and (i,j,k-1) ]
drdzfy(j)=( 0.5*(rho(i,j,k+1)+rho(i,j+1,k+1)) - 0.5*(rho(i,j,k-1)+rho(i,j+1,k-1) ) ) &
& * 0.25d0 * ( ( 0.25d0* (wz(i,j,k)+wz(i,j+1,k)+wz(i,j,k+1)+wz(i,j+1,k+1)) &
& + 0.25d0*(wz(i,j,k)+wz(i,j+1,k)+wz(i,j,k-1)+wz(i,j+1,k-1)) ) )
dvdzfy(j)=( 0.5*(var(i,j,k+1)+var(i,j+1,k+1)) - 0.5*(var(i,j,k-1)+var(i,j+1,k-1) ) ) &
& * 0.25d0 * ( ( 0.25d0* (wz(i,j,k)+wz(i,j+1,k)+wz(i,j,k+1)+wz(i,j+1,k+1)) &
& + 0.25d0*(wz(i,j,k)+wz(i,j+1,k)+wz(i,j,k-1)+wz(i,j+1,k-1)) ) )
ENDIF
!------------------------
! COMPUTATION OF THE FLUX
if(lv_smsl) then
flfy(j)=kredi(i,j,k)/( drdzfy(j)**2) &
& * ( - 0*dvdxfy(j) + ( drdzfy(j)**2)*dvdyfy(j) - drdyfy(j)*drdzfy(j)*dvdzfy(j) )
else
flfy(j)=kredi(i,j,k)/(drdxfy(j)**2+drdyfy(j)**2+drdzfy(j)**2) &
& * ( - drdxfy(j)*drdyfy(j)*dvdxfy(j) + (drdxfy(j)**2+drdzfy(j)**2)*dvdyfy(j) - drdyfy(j)*drdzfy(j)*dvdzfy(j) )
endif
ENDDO !_ j
flfy(0)=0.;
flfy(NJ)=0.;
!-------------------------------
! COMPUTATION OF THE SOURCE TERM
do j=1,NJ
vardif(i,j,k)= vardif(i,j,k) + fac*Jac(i,j,k)*vy(i,j)* ( flfy(j) - flfy(j-1) )
!IF(i==48 .AND. k==18 .AND. j==131) then
! PRINT*,vardif(i,j,k),flfy(j),flfy(j-1)
!ENDIF
enddo
ENDDO !_ k
ENDDO !_ i
!*********************
! FLUX IN Z-DIRECTION
!---------------------
DO i=1,NI
IF(i==1) then
im1=NI;ip1=i+1
elseif(i==NI) then
im1=i-1;ip1=1
else
im1=i-1;ip1=i+1
ENDIF
DO j=1,NJ
DO k=1,NK-1 ! For all faces_k
!----------------
! VARIATIONS IN X
! [ rho_face_z(i+1,j,k) - rho_face_z(i-1,j,k) ] &
! & / [ ux estimated between faces_z (i,j,k) and (i+1,j,k) + ux estimated between faces_z (i,j,k) and (i-1,j,k) ]
drdxfz(k)=( 0.5*(rho(ip1,j,k)+rho(ip1,j,k+1)) - 0.5*(rho(im1,j,k)+rho(im1,j,k+1) ) ) * 0.25d0 * &
& ( ( 0.25d0* (ux(i,j)+ux(i,j)+ux(ip1,j)+ux(ip1,j)) + 0.25d0*(ux(i,j)+ux(i,j)+ux(im1,j)+ux(im1,j)) ) )
dvdxfz(k)=( 0.5*(var(ip1,j,k)+var(ip1,j,k+1)) - 0.5*(var(im1,j,k)+var(im1,j,k+1) ) ) * 0.25d0 * &
& ( ( 0.25d0* (ux(i,j)+ux(i,j)+ux(ip1,j)+ux(ip1,j)) + 0.25d0*(ux(i,j)+ux(i,j)+ux(im1,j)+ux(im1,j)) ) )
!----------------
! VARIATIONS IN Y
IF(j==1) then
! [ rho_face_z(i,j+1,k) - rho_face_z(i,j-1,k) ] &
! & / [ vy estimated between faces_z (i,j,k) and (i,j+1,k) + vy estimated between faces_z (i,j,k) and (i,j-1,k) ]
drdyfz(k)=( 0.5*(rho(i,j+1,k)+rho(i,j+1,k+1)) - 0.5*(rho(i,j,k)+rho(i,j,k+1) ) ) &
& * ( ( 0.25d0* (vy(i,j)+vy(i,j)+vy(i,j+1)+vy(i,j+1)) ) )
dvdyfz(k)=( 0.5*(var(i,j+1,k)+var(i,j+1,k+1)) - 0.5*(var(i,j,k)+var(i,j,k+1) ) ) &
& * ( ( 0.25d0* (vy(i,j)+vy(i,j)+vy(i,j+1)+vy(i,j+1)) ) )
elseif(j==NJ) then
! [ rho_face_z(i,j+1,k) - rho_face_z(i,j-1,k) ] &
! & / [ vy estimated between faces_z (i,j,k) and (i,j+1,k) + vy estimated between faces_z (i,j,k) and (i,j-1,k) ]
drdyfz(k)=( 0.5*(rho(i,j,k)+rho(i,j,k+1)) - 0.5*(rho(i,j-1,k)+rho(i,j-1,k+1) ) ) &
& * ( ( 0.25d0*(vy(i,j)+vy(i,j)+vy(i,j-1)+vy(i,j-1)) ) )
dvdyfz(k)=( 0.5*(var(i,j,k)+var(i,j,k+1)) - 0.5*(var(i,j-1,k)+var(i,j-1,k+1) ) ) &
& * ( ( 0.25d0*(vy(i,j)+vy(i,j)+vy(i,j-1)+vy(i,j-1)) ) )
else
! [ rho_face_z(i,j+1,k) - rho_face_z(i,j-1,k) ] &
! & / [ vy estimated between faces_z (i,j,k) and (i,j+1,k) + vy estimated between faces_z (i,j,k) and (i,j-1,k) ]
drdyfz(k)=( 0.5*(rho(i,j+1,k)+rho(i,j+1,k+1)) - 0.5*(rho(i,j-1,k)+rho(i,j-1,k+1) ) ) * 0.25d0 * &
& ( ( 0.25d0* (vy(i,j)+vy(i,j)+vy(i,j+1)+vy(i,j+1)) + 0.25d0*(vy(i,j)+vy(i,j)+vy(i,j-1)+vy(i,j-1)) ) )
dvdyfz(k)=( 0.5*(var(i,j+1,k)+var(i,j+1,k+1)) - 0.5*(var(i,j-1,k)+var(i,j-1,k+1) ) ) * 0.25d0 * &
& ( ( 0.25d0* (vy(i,j)+vy(i,j)+vy(i,j+1)+vy(i,j+1)) + 0.25d0*(vy(i,j)+vy(i,j)+vy(i,j-1)+vy(i,j-1)) ) )
ENDIF
!----------------
! VARIATIONS IN Z
! delta_var / delta_z
drdzfz(k)=( rho(i,j,k+1)-rho(i,j,k) ) * ( 0.5d0*(wz(i,j,k)+wz(i,j,k+1)) )
dvdzfz(k)=( var(i,j,k+1)-var(i,j,k) ) * ( 0.5d0*(wz(i,j,k)+wz(i,j,k+1)) )
!------------------------
! COMPUTATION OF THE FLUX
if(lv_smsl) then
flfz(k)=kredi(i,j,k)/( drdzfz(k)**2)* ( - drdxfz(k)*drdyfz(k)*dvdxfz(k) &
& - drdyfz(k)*drdzfz(k)*dvdyfz(k) + (drdxfz(k)**2+drdyfz(k)**2)*dvdzfz(k) )
else
flfz(k)=kredi(i,j,k)/(drdxfz(k)**2+drdyfz(k)**2+drdzfz(k)**2)* ( - drdxfz(k)*drdyfz(k)*dvdxfz(k) &
& - drdyfz(k)*drdzfz(k)*dvdyfz(k) + (drdxfz(k)**2+drdyfz(k)**2)*dvdzfz(k) )
endif
ENDDO !_ k
flfz(0)=0.;
flfz(NK)=0.;
!-------------------------------
! COMPUTATION OF THE SOURCE TERM
do k=1,NK
vardif(i,j,k)= vardif(i,j,k) + fac*Jac(i,j,k)*wz(i,j,k)* ( flfz(k) - flfz(k-1) )
! IF(i==48 .AND. k>16.5 .AND. k<18.5 .AND. j==131) then
! PRINT*,k,vardif(i,j,k),flfz(k),flfz(k-1)
! PRINT*,kredi(i,j,k)/(drdxfz(k)**2+drdyfz(k)**2+drdzfz(k)**2)* ( - drdxfz(k)*drdyfz(k)*dvdxfz(k) )
! PRINT*,kredi(i,j,k)/(drdxfz(k)**2+drdyfz(k)**2+drdzfz(k)**2)* ( - drdyfz(k)*drdzfz(k)*dvdyfz(k) )
! PRINT*,kredi(i,j,k)/(drdxfz(k)**2+drdyfz(k)**2+drdzfz(k)**2)* ( + (drdxfz(k)**2+drdyfz(k)**2)*dvdzfz(k) )
! PRINT*,(drdxfz(k)**2+drdyfz(k)**2)
! PRINT*,dvdzfz(k)
! PRINT*,var(i,j+1,k),var(i,j+1,k+1),var(i,j-1,k),var(i,j-1,k+1)
! PRINT*,k,"-------"
! ENDIF
enddo
ENDDO !_ j
ENDDO !_ i
RETURN
END subroutine