NonhydrostaticModel: Boundary Conditions

[parfenyev]

Hello everyone!

I would like to do a 2D simulation in a non-hydrostatic model in the (x, z) plane, where the x-direction is periodic and the z-direction is opposite to the gravity acceleration. As a pumping, I would like to set the vertical velocity at the lower boundary. Is it possible? In the documentation I have found that ValueBoundaryCondition shouldn't be used on a wall-normal velocity component. It would also be interesting to know what these restrictions are related to.

[jagoosw]

Hi @parfenyev

You can use OpenBoundaryCondition to set wall-normal velocity components.

The difference between wall normal velocities and other boundaries is that velocities live on the component normal face of the cell so are on the boundary, where as every thing else lives at cell centers so when a boundary value is specified the halo value has to be computed, where as open boundaries directly sets the boundary value.

These pages in the documentation might help to visulise.

[parfenyev]

Hi @jagoosw

Thank you for your responce. Do you have an example of implementation? Below is the code where I set the horizontal velocity value at the boundary. What should I change in it to be able to set the vertical velocity in the similar way?

using Oceananigans, Oceananigans.Units, CUDA, Printf, Statistics

Lx = 1.517388
Lz = 0.43
N = 1.56605

grid = RectilinearGrid(GPU(), 
    size=(512, 512), x=(0, Lx), z=(0, Lz),
    topology=(Periodic, Flat, Bounded))

B_bg(x, z, t, N) = N^2 * z
B = BackgroundField(B_bg, parameters=N)

@inline velocity_x(x, t) = 0.05*sin(16π*x/1.517388)*sin(0.43*t);
bottom_velocity_bc = ValueBoundaryCondition(velocity_x)
x_vel_bcs = FieldBoundaryConditions(bottom = bottom_velocity_bc)

model = NonhydrostaticModel(; grid, 
                            advection = Centered(order=4),
                            closure = ScalarDiffusivity(ν=1.004e-6, κ=1.5e-7),
                            tracers = :b,
                            buoyancy = BuoyancyTracer(),
                            background_fields = (; b=B),
                            boundary_conditions = (u=x_vel_bcs, ))

set!(model, u=0, w=0, b=0)

[glwagner]

It's something like

using Oceananigans.BoundaryConditions: PerturbationAdvectionOpenBoundaryCondition
bottom_w_bc = PerturbationAdvectionOpenBoundaryCondition(velocity_w)
w_vel_bcs = FieldBoundaryConditions(bottom = bottom_w_bc)

I believe the docstring for PerturbationAdvectionOpenBoundaryCondition has some information too.

[parfenyev]

Thank you, I will try. Where can I find documentation about OpenBoundaryCondition or PerturbationAdvectionOpenBoundaryCondition? Searching the site does not provide any useful information.

I also have a question about the boundary condition for the buoyancy field b. Am I right that the standard no-flux BC mean that $wb + \kappa \partial_z b = 0$ at the boundary and this condition can be applied at non-zero normal to the boundary velocity w? Or is it just $\partial_z b = 0$? It is not clear, since documentation assumes that normal to the boundary velocity should be zero.

[glwagner]

To see the docstring, open a REPL, write using Oceananigans, press ? to activate help mode, and then type

help?> Oceananigans.BoundaryConditions.PerturbationAdvectionOpenBoundaryCondition

this will print the docstring. you can also try Oceananigans.BoundaryConditions.PerturbationAdvection (which is suggested by that docstring). Same for all other docstrings.

(I believe that all exported functions are automatically added to online docs, but non-exported functions are not.)

You're right: FluxBoundaryCondition(nothing) only has the effect of setting the gradient to zero (and therefore the diffusive fluxes). It does not set the total flux to zero. Since open boundary conditions are becoming more and more used, we should consider whether we should change this behavior (or maybe just update the documentation to be more clear about this).