1 degree idealized ocean basin simulation. Spin-up problems: Checkerboard grid patterns emerge and stick around

[connerlester]

I want to ask about how to properly spin up ocean scale simulations and avoid checkbaord patterns and other possible instabilities when eddies and other small/fast scale dynamics aren't resolved.

This simulation is effectively like a WenoNeverworld.jl sim but with no channel or scotia ridge:

I am running an idealized ocean 1 degree resolution simulation in a closed box with walls that slope up to zero depth from a flat ocean depth of -4000 m (slope width ~ 4 degrees). The box goes from -70 to 70 degrees in lat and 0 to 60 lon and uses lat/lon coords and spherical coriolis. It transports buoancy with simple parabolic surface relaxation (forcing amplitude = 0.01 m/s^2, relaxation time scale = 10 days). The surface has an idealized cos(3pi y/Ly) wind stress. I am also transporting TKE (:e) for vertical diffusion, CATKEVerticalDiffusivity(), and I am also using an eddy closure IsopycnalSkewSymmetricDiffusivity(κ_skew=1e3, κ_symmetric=1e3).

Right now the simulation starts from zero flow everywhere and initial buoyancy profile reflecting the forcing (taken from WenoNeverworld). The simulation starts and equatorial flow bands form. As time goes on the flow bands produce waves parallel to the equator across the domain. Over time the wavelengths get smaller and smaller until they reach the grid size (1 degree) then checkerboarding seems to happen---noticable around 100 days. In the output plots below I have the dt = 10 min (quickly reached by the TimeStepWizard(cfl = 0.5, max_Δt = 10minutes, max_change = 1.01) from an initial dt = 30 s)

**My question is how should I go about running such a large scale coarse resolution simulation to avoid checkerboarding and other grid scale artifacts/instabilities?

When running a coarse resolution WenoNeverworld simulation what is your initial spin-up process?**

I want to spin up the sim and have it be stable enough to greatly increase the time step (>~30 min ?). I want to run this sim for order 1K years to study long time scale ocean circulation. (Please let me know if oceananigans is not build to handle such long timescale modeling).

Here are some output plots to show you what I am talking about:

Day 0:

Day 1:

Day 5:

Day 10:

Day 30:

Day 70:

Day 100:

I now increased the dt to 20 min...
Day 110:

Day 120:

[simone-silvestri]

Hello @connerlester, what is your numerical setup (i.e. timestepper, advection schemes, free surface) and your closures (i.e. viscous dissipation)?
You can maybe paste a snippet of the model constructor here.
It might be that you have not provided enough dissipation to remove grid-scale artifacts and these eventually pop up as noise in your simulation.
At one degree, 30 minutes should be more than enough to run the simulation.

[connerlester]

Here is my full setup:

model = HydrostaticFreeSurfaceModel(;grid ,boundary_conditions, 
                                        tracers = (:b,:e),
                                        buoyancy = BuoyancyTracer(),
                                        coriolis = HydrostaticSphericalCoriolis(),
                                        free_surface = SplitExplicitFreeSurface(grid; cfl = 0.75),
                                        momentum_advection = WENOVectorInvariant(order=3),
                                        tracer_advection = WENO(order=3),             #for b only, e has no advection
                                        timestepper = :SplitRungeKutta3,
                                        closure = (IsopycnalSkewSymmetricDiffusivity(κ_skew=1e3, κ_symmetric=1e3),
                                                          CATKEVerticalDiffusivity()),
                                        )