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Add an optional side drag at walls #169

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46 changes: 42 additions & 4 deletions src/parameterizations/lateral/MOM_hor_visc.F90
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Original file line number Diff line number Diff line change
Expand Up @@ -127,6 +127,8 @@ module MOM_hor_visc
logical :: bound_Coriolis ! If true & SMAGORINSKY_AH is used, the biharmonic
! viscosity is modified to include a term that
! scales quadratically with the velocity shears.
logical :: side_drag ! Use side drag (Deremble et al., 2011)
real :: Cd ! Drag coefficient for side drag, nondimensional.

real ALLOCABLE_, dimension(NIMEM_,NJMEM_) :: &
Kh_bg_xx, &! The background Laplacian viscosity at h points, in units
Expand Down Expand Up @@ -244,7 +246,8 @@ subroutine horizontal_viscosity(u, v, h, diffu, diffv, MEKE, VarMix, G, CS, OBC)

real, dimension(SZIB_(G),SZJB_(G)) :: &
sh_xy, & ! horizontal shearing strain (du/dy + dv/dx) (1/sec) including metric terms
str_xy, & ! str_xy is the cross term in the stress tensor (H m2 s-2)
str_xy, & ! str_xy and str_yx are cross terms in the stress tensor (H m2 s-2)
str_yx, &
FrictWorkIntz ! depth integrated energy dissipated by lateral friction (W/m2)

real, dimension(SZIB_(G),SZJB_(G),SZK_(G)) :: &
Expand Down Expand Up @@ -277,6 +280,9 @@ subroutine horizontal_viscosity(u, v, h, diffu, diffv, MEKE, VarMix, G, CS, OBC)
logical :: rescale_Kh
logical :: find_FrictWork
logical :: apply_OBC = .false.
real :: vel_gam ! drag scaling factor in H m s-1.
real :: u_loc, v_loc, uvmag ! velocity at boundary and magnitude in m s-1.
real :: drag_stress_u, drag_stress_v ! side drag stresses in H m2 s-2.
logical :: use_MEKE_Ku
integer :: is, ie, js, je, Isq, Ieq, Jsq, Jeq, nz
integer :: i, j, k
Expand Down Expand Up @@ -525,7 +531,30 @@ subroutine horizontal_viscosity(u, v, h, diffu, diffv, MEKE, VarMix, G, CS, OBC)
endif ! biharmonic

str_xy(I,J) = str_xy(I,J) * (hq * G%mask2dBu(I,J) * CS%reduction_xy(I,J))
enddo ; enddo

! stress tensor is symmetric except when side drag is applied
str_yx(i,j) = str_xy(i,j)

if (CS%side_drag) then
! since drag is applied on mask2dBu, at most one of the surrounding
! velocity components is non-zero
u_loc = u(i,j,k) + u(i,j+1,k)
v_loc = v(i,j,k) + v(i+1,j,k)
uvmag = sqrt(u_loc**2 + v_loc**2)
vel_gam = hq * CS%Cd * uvmag

! calculate the stress due to drag from the wall. we need to take into
! account the orientation of the wall relative to the current cell
! corner on which the stress is being calculated
drag_stress_u = vel_gam * u_loc * (2.0 * G%mask2dT(i,j) - 1.0)
drag_stress_v = vel_gam * v_loc * (2.0 * G%mask2dT(i,j) - 1.0)

! modify the str_xy and str_yx terms to include a drag
! when next to a wall
str_xy(i,j) = str_xy(i,j) + drag_stress_u*(1.0 - G%mask2dBu(i,j))
str_yx(i,j) = str_yx(i,j) + drag_stress_v*(1.0 - G%mask2dBu(i,j))
endif
enddo; enddo

do j=js,je ; do i=isq,ieq
! Evaluate 1/h x.Div(h Grad u) or the biharmonic equivalent.
Expand All @@ -543,8 +572,8 @@ subroutine horizontal_viscosity(u, v, h, diffu, diffv, MEKE, VarMix, G, CS, OBC)

! Evaluate 1/h y.Div(h Grad u) or the biharmonic equivalent.
do J=Jsq,Jeq ; do i=is,ie
diffv(i,J,k) = ((G%IdyCv(i,J)*(CS%DY2q(I-1,J)*str_xy(I-1,J) - &
CS%DY2q(I,J) *str_xy(I,J)) - &
diffv(i,J,k) = ((G%IdyCv(i,J)*(CS%DY2q(I-1,J)*str_yx(I-1,J) - &
CS%DY2q(I,J) *str_yx(I,J)) - &
G%IdxCv(i,J)*(CS%DX2h(i,j) *str_xx(i,j) - &
CS%DX2h(i,j+1)*str_xx(i,j+1))) * &
G%IareaCv(i,J)) / (0.5*(h(i,j+1,k) + h(i,j,k)) + h_neglect)
Expand Down Expand Up @@ -795,6 +824,15 @@ subroutine hor_visc_init(Time, G, param_file, diag, CS)
"is strongly encouraged, and no slip BCs are not used with \n"//&
"the biharmonic viscosity.", default=.false.)

call get_param(param_file, mod, "SIDE_DRAG", CS%side_drag, &
"If true, a drag is applied to horizontal boundaries \n"//&
"proportional to velocity through SIDE_DRAG_CD.", &
default=.false.)
if (CS%side_drag) &
call get_param(param_file, mod, "SIDE_DRAG_CD", CS%Cd, &
"Drag coefficient to use for SIDE_DRAG.", &
units="nondim", default=0.0)

if (CS%bound_Kh .or. CS%bound_Ah .or. CS%better_bound_Kh .or. CS%better_bound_Ah) &
call get_param(param_file, mod, "DT", dt, &
"The (baroclinic) dynamics time step.", units = "s", &
Expand Down
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