friction.py

from veros.core.operators import numpy as npx

from veros import veros_kernel, KernelOutput
from veros.variables import allocate
from veros.core import numerics, utilities
from veros.core.operators import update, update_add, at


@veros_kernel
def isoneutral_friction(state):
    """
    vertical friction using TEM formalism for eddy driven velocity
    """
    vs = state.variables
    settings = state.settings

    flux_top = allocate(state.dimensions, ("xt", "yt", "zt"))
    delta, a_tri, b_tri, c_tri = (allocate(state.dimensions, ("xt", "yt", "zt"))[1:-2, 1:-2, :] for _ in range(4))

    if settings.enable_implicit_vert_friction:
        aloc = vs.u[:, :, :, vs.taup1]
    else:
        aloc = vs.u[:, :, :, vs.tau]

    # implicit vertical friction of zonal momentum by GM
    ks = npx.maximum(vs.kbot[1:-2, 1:-2], vs.kbot[2:-1, 1:-2])
    _, water_mask, edge_mask = utilities.create_water_masks(ks, settings.nz)

    fxa = 0.5 * (vs.kappa_gm[1:-2, 1:-2, :] + vs.kappa_gm[2:-1, 1:-2, :])
    delta = update(
        delta,
        at[:, :, :-1],
        settings.dt_mom
        / vs.dzw[npx.newaxis, npx.newaxis, :-1]
        * fxa[:, :, :-1]
        * vs.maskU[1:-2, 1:-2, 1:]
        * vs.maskU[1:-2, 1:-2, :-1],
    )
    delta = update(delta, at[..., -1], 0.0)
    a_tri = update(a_tri, at[:, :, 1:], -delta[:, :, :-1] / vs.dzt[npx.newaxis, npx.newaxis, 1:])
    b_tri_edge = 1 + delta / vs.dzt[npx.newaxis, npx.newaxis, :]
    b_tri = update(
        b_tri,
        at[:, :, 1:-1],
        1
        + delta[:, :, 1:-1] / vs.dzt[npx.newaxis, npx.newaxis, 1:-1]
        + delta[:, :, :-2] / vs.dzt[npx.newaxis, npx.newaxis, 1:-1],
    )
    b_tri = update(b_tri, at[:, :, -1], 1 + delta[:, :, -2] / vs.dzt[-1])
    c_tri = update(c_tri, at[...], -delta / vs.dzt[npx.newaxis, npx.newaxis, :])

    sol = utilities.solve_implicit(
        a_tri, b_tri, c_tri, aloc[1:-2, 1:-2, :], water_mask, b_edge=b_tri_edge, edge_mask=edge_mask
    )
    vs.u = update(vs.u, at[1:-2, 1:-2, :, vs.taup1], npx.where(water_mask, sol, vs.u[1:-2, 1:-2, :, vs.taup1]))
    vs.du_mix = update_add(
        vs.du_mix,
        at[1:-2, 1:-2, :],
        (vs.u[1:-2, 1:-2, :, vs.taup1] - aloc[1:-2, 1:-2, :]) / settings.dt_mom * water_mask,
    )

    if settings.enable_conserve_energy:
        # diagnose dissipation
        diss = allocate(state.dimensions, ("xt", "yt", "zt"))
        fxa = 0.5 * (vs.kappa_gm[1:-2, 1:-2, :-1] + vs.kappa_gm[2:-1, 1:-2, :-1])
        flux_top = update(
            flux_top,
            at[1:-2, 1:-2, :-1],
            fxa
            * (vs.u[1:-2, 1:-2, 1:, vs.taup1] - vs.u[1:-2, 1:-2, :-1, vs.taup1])
            / vs.dzw[npx.newaxis, npx.newaxis, :-1]
            * vs.maskU[1:-2, 1:-2, 1:]
            * vs.maskU[1:-2, 1:-2, :-1],
        )
        diss = update(
            diss,
            at[1:-2, 1:-2, :-1],
            (vs.u[1:-2, 1:-2, 1:, vs.tau] - vs.u[1:-2, 1:-2, :-1, vs.tau])
            * flux_top[1:-2, 1:-2, :-1]
            / vs.dzw[npx.newaxis, npx.newaxis, :-1],
        )
        diss = update(diss, at[:, :, -1], 0.0)
        diss = numerics.ugrid_to_tgrid(state, diss)
        vs.K_diss_gm = diss

    if settings.enable_implicit_vert_friction:
        aloc = vs.v[:, :, :, vs.taup1]
    else:
        aloc = vs.v[:, :, :, vs.tau]

    # implicit vertical friction of zonal momentum by GM
    ks = npx.maximum(vs.kbot[1:-2, 1:-2], vs.kbot[1:-2, 2:-1])
    _, water_mask, edge_mask = utilities.create_water_masks(ks, settings.nz)

    fxa = 0.5 * (vs.kappa_gm[1:-2, 1:-2, :] + vs.kappa_gm[1:-2, 2:-1, :])
    delta = update(
        delta,
        at[:, :, :-1],
        settings.dt_mom
        / vs.dzw[npx.newaxis, npx.newaxis, :-1]
        * fxa[:, :, :-1]
        * vs.maskV[1:-2, 1:-2, 1:]
        * vs.maskV[1:-2, 1:-2, :-1],
    )
    delta = update(delta, at[..., -1], 0.0)
    a_tri = update(a_tri, at[:, :, 1:], -delta[:, :, :-1] / vs.dzt[npx.newaxis, npx.newaxis, 1:])
    b_tri_edge = 1 + delta / vs.dzt[npx.newaxis, npx.newaxis, :]
    b_tri = update(
        b_tri,
        at[:, :, 1:-1],
        1
        + delta[:, :, 1:-1] / vs.dzt[npx.newaxis, npx.newaxis, 1:-1]
        + delta[:, :, :-2] / vs.dzt[npx.newaxis, npx.newaxis, 1:-1],
    )
    b_tri = update(b_tri, at[:, :, -1], 1 + delta[:, :, -2] / vs.dzt[-1])
    c_tri = update(c_tri, at[...], -delta / vs.dzt[npx.newaxis, npx.newaxis, :])

    sol = utilities.solve_implicit(
        a_tri, b_tri, c_tri, aloc[1:-2, 1:-2, :], water_mask, b_edge=b_tri_edge, edge_mask=edge_mask
    )
    vs.v = update(vs.v, at[1:-2, 1:-2, :, vs.taup1], npx.where(water_mask, sol, vs.v[1:-2, 1:-2, :, vs.taup1]))
    vs.dv_mix = update_add(
        vs.dv_mix,
        at[1:-2, 1:-2, :],
        (vs.v[1:-2, 1:-2, :, vs.taup1] - aloc[1:-2, 1:-2, :]) / settings.dt_mom * water_mask,
    )

    if settings.enable_conserve_energy:
        # diagnose dissipation
        diss = allocate(state.dimensions, ("xt", "yt", "zt"))
        fxa = 0.5 * (vs.kappa_gm[1:-2, 1:-2, :-1] + vs.kappa_gm[1:-2, 2:-1, :-1])
        flux_top = update(
            flux_top,
            at[1:-2, 1:-2, :-1],
            fxa
            * (vs.v[1:-2, 1:-2, 1:, vs.taup1] - vs.v[1:-2, 1:-2, :-1, vs.taup1])
            / vs.dzw[npx.newaxis, npx.newaxis, :-1]
            * vs.maskV[1:-2, 1:-2, 1:]
            * vs.maskV[1:-2, 1:-2, :-1],
        )
        diss = update(
            diss,
            at[1:-2, 1:-2, :-1],
            (vs.v[1:-2, 1:-2, 1:, vs.tau] - vs.v[1:-2, 1:-2, :-1, vs.tau])
            * flux_top[1:-2, 1:-2, :-1]
            / vs.dzw[npx.newaxis, npx.newaxis, :-1],
        )
        diss = update(diss, at[:, :, -1], 0.0)
        diss = numerics.vgrid_to_tgrid(state, diss)
        vs.K_diss_gm = vs.K_diss_gm + diss

    return KernelOutput(u=vs.u, v=vs.v, du_mix=vs.du_mix, dv_mix=vs.dv_mix, K_diss_gm=vs.K_diss_gm)