rdb_ocean_horizontal_viscosity Module

Harmonic viscosity averaged onto Bu corners (m²/s), shape (nx+1, ny+1, nz). CFL-clamped per corner.

Harmonic viscosity averaged onto T-cell centres (m²/s), shape (nx, ny, nz). CFL-clamped per cell.

Precomputed direction-tensor factor (n1²−n2²)/(n1²+n2²) (MOM6 n1n1_m_n2n2). Default (1,0) ⇒ 1.

Precomputed direction-tensor factor 2·n1·n2/(n1²+n2²) (MOM6 n1n2). Set by ocean_hvisc_set_aniso_direction from the (n1,n2) direction vector. Default (1,0) = grid-i ⇒ n1n2 = 0 (cross terms vanish; the operator just adds kh_aniso to the tension coefficient).

CFL safety coefficient for the per-cell viscosity limiter (MOM6 HORVISC_BOUND_COEF). Consulted on the stress_tensor path and, when bound_kh is set, on the velocity-Laplacian paths too.

MOM6 BOUND_KH analogue for the velocity-Laplacian paths (scalar nu_h and the flow-aware per-face closure). When .true., the per-face harmonic viscosity is clamped to bound_coef·0.125/(dt·(idx²+idy²)) — ~0.25× the forward- Euler stability limit, matching MOM6’s Kh_Max_xx margin. Load-bearing beyond simple FE stability: the barotropic mode receives the depth-mean viscous force FROZEN over the outer step (via F_bt), and for grid-scale gravity modes with ω·dt ≳ 1 an unbounded λ·dt = ν·k²·dt ≳ 0.6 frozen force is applied with reversed phase — ANTI-damping — which exponentially pumps rim-trapped barotropic modes through the Δu corrector (the 600² Lagrangian double-gyre h-guard blow-up; e-fold ~10 outer steps). The clamp keeps λ·dt ≤ 0.5·bound_coef at every face so the corrector loop stays damped at any resolution. Default .false. ⇒ bit-identical.

When set (by configure when MEKE’s frictional source is on), the apply step fills ke_diss with the lateral-viscosity KE dissipation rate. Default off ⇒ no extra work, bit-identical.

Per-step viscous tendency at east faces, shape (nx+1, ny, nz). Filled by the compute step, consumed by the apply step.

Per-step viscous tendency at north faces, shape (nx, ny+1, nz).

True between init and destroy. Tracks GPU device attachment too — prefer this to allocated(...).

Depth-integrated KE dissipation rate by the lateral viscosity, Σ_k ρ_k h_k (u·du_visc + v·dv_visc) (kg/s³, ≤0), at T-cell centres (nx, ny). MEKE consumes it as -frcoeff·i_mass·ke_diss (the mean→eddy frictional source). Holds the most recent stage’s rate (the quantity MEKE needs is a rate, so no accumulation).

Anisotropic Laplacian viscosity magnitude (m²/s). When positive, a two-coefficient direction tensor splits the harmonic viscosity into along- and cross-direction parts. Only consulted on the stress_tensor path. Default 0 ⇒ isotropic, bit-identical. MOM6 KH_ANISO analogue (Smith & McWilliams 2003, “Anisotropic horizontal viscosity for ocean models”, Ocean Modelling 5(2), §2). Composes with the biharmonic add-on (nu_4 / smag_ah / leith_biharm) — the two are independent linear operators that sum, matching MOM6’s composition (kh_aniso inside the harmonic block, biharmonic added to the same tensor).

First-pass Laplacian buffer used by the biharmonic path — holds ∇²u_face so the second Laplacian pass (∇²(∇²u)) can read it. Same shape as du_visc. Allocated unconditionally; sits inert when nu_4 = 0.

v-face counterpart of lap_u.

Coastal lateral BC selector (shared with the lateral-mix / Coriolis kernels). .false. (free-slip) masks the corner shear stress by wet_q; .true. (no-slip) by 2 - wet_q — on the stress_tensor path AND on the velocity-Laplacian paths (scalar nu_h and the flow-aware face closures), whose corner (shear) fluxes carry the same factor. The biharmonic add-on is always free-slip (wet_q; MOM6 refuses NOSLIP with BIHARMONIC). All-wet ⇒ factor ≡ 1 ⇒ bit-identical.

Constant biharmonic horizontal viscosity (m^4/s). Scale- selective damping for stratified closed-basin runs: damps proportional to ν₄·k⁴, so it kills grid-scale baroclinic noise without bleeding into resolved scales the way a large Laplacian ν_h would. Required to keep stratified Tasman-class runs bounded past day ~10 (Laplacian-only configurations grow exponentially via parametric amplification of roundoff seeds). Numerical-stability cap: ν₄ · dt · (1/dx² + 1/dy²)² <= 1/16. Typical 2 km resolution value ~1e10 m^4/s. Composes with all of the harmonic dispatch arms, including stress_tensor — it is no longer silently disabled by it.

Constant Laplacian horizontal viscosity (m^2/s). Phase Tier-1 default is zero (kernel becomes a no-op); set positive to enable damping. Numerical-stability cap: nu_h * dt * (1/dx^2 + 1/dy^2) <= 0.5.

Thickness-weighted tension stress A_T·(du/dx−dv/dy)·h_T at T-cell centres, shape (nx, ny, nz).

Thickness-weighted shear stress A_q·(dv/dx+du/dy)·h_q·slip at Bu corners, shape (nx+1, ny+1, nz).

When true, the compute step uses the MOM6-faithful thickness-weighted stress-divergence operator diffu = (1/(h_u+h_neglect))·∇·(h·A·∇u) with a per-cell CFL viscosity limiter and wet_* coast-masking instead of the velocity Laplacian A·∇²u. Default false ⇒ bit-identical to the historical kernel. See the module header for the operator form.

Metric inverses 1/dx, 1/dy at the face.

Metric inverses 1/dx, 1/dy at the face.

CFL safety coefficient (this%bound_coef).

Reciprocal time step 1/dt.

Metric inverses 1/dx, 1/dy at the face.

Metric inverses 1/dx, 1/dy at the face.

CFL safety coefficient (this%bound_coef).

Reciprocal time step 1/dt.

.false. ⇒ leave the apply on queue 1 without syncing (batched).

Bu-corner wet mask (free-slip corner factor, as in the ungated pass).

Per-layer 0/1 u-face open mask (metrics%open_u).

Per-layer 0/1 v-face open mask (metrics%open_v).

Bu-corner wet mask (metrics%wet_q). BOTH chained Laplacians mask their corner (shear) fluxes by it – free-slip, MOM6 sh_xy = mask2dBu·(...) for Del2u and str_xy·mask2dBu for the biharmonic stress. Unmasked, the zero stored at a land face read as a Dirichlet-0 wall and the k^4 operator rang against it at every staircase step. Always free-slip: MOM6 refuses NOSLIP with BIHARMONIC. All-wet corner => factor 1 => bit-identical.

Per-layer 0/1 u-face open mask (&vcoord_nml zfixed_closed_faces). ABSENT (the default path) => the loops below are textually the ones this routine has always run => bit-identical. PRESENT => see hvisc_biharm_lap_closed: in BOTH chained Laplacians every face-to-face difference carries open(a)*open(b), so a closed face-layer is a free-slip (Neumann/mirror) boundary of the stencil exactly as a land corner is under wet_q, and receives zero tendency.

v-face twin. Present iff open_u is.

Bu-corner wet mask (metrics%wet_q). BOTH chained Laplacians mask their corner (shear) fluxes by it – free-slip, MOM6 sh_xy = mask2dBu·(...) for Del2u and str_xy·mask2dBu for the biharmonic stress. Unmasked, the zero stored at a land face read as a Dirichlet-0 wall and the k^4 operator rang against it at every staircase step. Always free-slip: MOM6 refuses NOSLIP with BIHARMONIC. All-wet corner => factor 1 => bit-identical.

Per-layer 0/1 u-face open mask (&vcoord_nml zfixed_closed_faces). ABSENT (the default path) => the loops below are textually the ones this routine has always run => bit-identical. PRESENT => see hvisc_biharm_lap_closed: in BOTH chained Laplacians every face-to-face difference carries open(a)*open(b), so a closed face-layer is a free-slip (Neumann/mirror) boundary of the stencil exactly as a land corner is under wet_q, and receives zero tendency.

v-face twin. Present iff open_u is.

Bu-corner wet mask (metrics%wet_q). Each corner (shear) flux of the velocity Laplacian is scaled by the slip factor (1 - 2·ns)·wet_q + 2·ns – the same C1 factor the Smagorinsky strain, the Coriolis corner vorticity and the stress-tensor path use (MOM6 sh_xy = mask2dBu·(dvdx+dudy) free-slip, (2-mask2dBu) no-slip). Free-slip: a land corner carries NO shear flux, so the zero stored at a land face never acts as a Dirichlet-0 wall. All-wet corner => factor 1 => bit-identical.

1 = no-slip (&ocean_hvisc_nml no_slip), 0 = free-slip.

Per-layer 0/1 u-face open mask (&vcoord_nml zfixed_closed_faces). ABSENT (the default path) => the interior loops below are textually the ones this routine has always run => bit-identical.

v-face twin. Present iff open_u is.

Bu-corner wet mask (metrics%wet_q). Each corner (shear) flux of the velocity Laplacian is scaled by the slip factor (1 - 2·ns)·wet_q + 2·ns – the same C1 factor the Smagorinsky strain, the Coriolis corner vorticity and the stress-tensor path use (MOM6 sh_xy = mask2dBu·(dvdx+dudy) free-slip, (2-mask2dBu) no-slip). Free-slip: a land corner carries NO shear flux, so the zero stored at a land face never acts as a Dirichlet-0 wall. All-wet corner => factor 1 => bit-identical.

1 = no-slip (&ocean_hvisc_nml no_slip), 0 = free-slip.

Per-layer 0/1 u-face open mask (&vcoord_nml zfixed_closed_faces) — the FREE-SLIP closure of a z-level partial step. See hvisc_compute_face_impl’s open_u docstring for the full argument; ABSENT (the default path) ⇒ the loops below are textually unchanged ⇒ bit-identical.

v-face twin. Present iff open_u is.

Velocity/thickness source arrays — the prognostic components on the historical path, the u_av time-mean family under split_scheme = "pred_corr" (MOM6 evaluates horizontal_viscosity on u_av/h_av).

Velocity/thickness source arrays — the prognostic components on the historical path, the u_av time-mean family under split_scheme = "pred_corr" (MOM6 evaluates horizontal_viscosity on u_av/h_av).

Velocity/thickness source arrays — the prognostic components on the historical path, the u_av time-mean family under split_scheme = "pred_corr" (MOM6 evaluates horizontal_viscosity on u_av/h_av).

Outer (or RK2-stage) time step. Required when this%stress_tensor is true (drives the per-cell CFL viscosity limiter) and whenever a biharmonic add-on is active (drives its own per-face CFL clamp) — the velocity- Laplacian dispatch itself does not consume it, but the biharmonic block reached from every dispatch arm does. Omitting it defaults the biharmonic clamp to dt_local = 1 (a huge, effectively-inactive bound); the caller is responsible for CFL in that case.