Flux boundary condition with two components

[EavenW]

New to the ecosystem. I have a u* at the surface that I am trying to impart as a flux boundary condition, but the experiment requires that it rotates as a function of time.
Can this be done as a 2D flux or does it need to be an @inline = @inbounds function?

Thanks

[ali-ramadhan]

Hi @EavenW hope it wasn't too hard to get started (the documentation needs some more work, sorry about that).

Not totally sure what you mean by a flux boundary condition with two components (sounds like the u and v velocity fields might be further coupled via this boundary condition?).

Sounds like you're trying to impose a (time-dependent?) surface flux boundary condition which can be done a few different ways.

• If it's independent of time then imposing a flux BC with a 2D array is one option.
• If it's time-dependent then imposing the flux BC as a function is probably the way to go. The function signature for boundary conditions is f(i, j, grid, t, U, C, params) so the boundary condition can depend on time t, the velocity fields U = (u, v, w) and any tracer quantity in C.
• If you can write your surface flux BC as a function of only (x, y, t) then a BoundaryFunction can simplify the setup a little. I just realized this isn't showing up in the documentation but the docstring in the file I linked to has an example of how to use it.

PS: Not sure which version you're running but we've been making some improvements to the user interface lately which may break certain things if you upgrade to v0.21 or v0.22. Please don't hesitate to ping us if you have any questions or if something isn't working. We're more than happy to help.

[ali-ramadhan]

PS²: @EavenW if you're at the Ocean Sciences 2020 meeting and have some simulations in mind that you're trying to set up you should try to meet up with @glwagner!

[glwagner]

Hi @EavenW, yes, you have to specify the x- and y- components of a momentum flux vector separately on u and v.

Because each flux component is a function of time, you should use our BoundaryFunction wrapper for each component cf @ali-ramadhan comment above.

Thanks for the question — keep them coming!

[glwagner]

@EavenW here is some code for you:

using Oceananigans
using Oceananigans.Fields

f = 1e-4 # [s⁻¹] Coriolis parameter

# Use 'const' so boundary functions work on the GPU.
const ω = 2π/f  # [s] Inertial period
const u★ = 0.01 # [m s⁻¹], friction velocity

# fluxes *kinematic* because they are applied to the velocity field. 
x_momentum_flux(x, y, t) = u★^2 * cos(ω * t)
y_momentum_flux(x, y, t) = u★^2 * sin(ω * t)

τˣ = BoundaryFunction{:z, Face, Cell}(x_momentum_flux)
τʸ = BoundaryFunction{:z, Cell, Face}(y_momentum_flux)

u_boundary_condition = HorizontallyPeriodicBCs(top=BoundaryCondition(Flux, τˣ))
v_boundary_condition = HorizontallyPeriodicBCs(top=BoundaryCondition(Flux, τʸ))

As @ali-ramadhan we are redesigning this API this week. So expect changes very soon if you keep Oceananigans updated. We think the API will become clearer and easier to use. This code is young so we certainly appreciate comments and criticism that will help us make the code easier-to-use.

I just noticed that the docstring defined inside the struct does not print at the REPL, so here it is:

    """
        BoundaryFunction{B, X1, X2}(func)
    A wrapper for user-defined boundary condition functions on the
    boundary specified by symbol `B` and at location `(X1, X2)`.

    Example
    =======
    julia> using Oceananigans: BoundaryCondition, BoundaryFunction, Flux, Cell

    julia> top_tracer_flux = BoundaryFunction{:z, Cell, Cell}((x, y, t) -> cos(2π*x) * cos(t))
    (::BoundaryFunction{:z,Cell,Cell,getfield(Main, Symbol("##7#8"))}) (generic function with 1 method)

    julia> top_tracer_bc = BoundaryCondition(Flux, top_tracer_flux);
    """

[EavenW]

Thank you so much! This clears up a lot about how to communicate the boundary conditions. And yes, I'll be at OSM albeit presenting something completely different.