Numerical instability at edge of slope

[dcherian]

Hi all,

I'm having trouble with what looks like a numerical instability that starts in the vertical velocity field.

My setup consists of an idealized flat bottom shelf + slope at the southern end of a beta-plane channel with a west to east (along-isobath) barotropic inflow (2cm/s). There is an anticyclonic eddy in the channel that moves southwards towards the topography since it is on the beta plane. The southern boundary (i.e. the coast) is closed and the remaining three are open. I have sponge layers along all open boundaries. The boundary conditions are

• * Shc or RadNud for 2D momentum
  * Che for free surface
  * RadNud for 3D momentum
  * RadNud on tracers at the western (inflow boundary) and Rad everywhere else
  * VolCons is not enabled
  * RADIATION_2D is enabled

For dx=dy=1.5km, the rx0 (Beckmann & Haidvogel no.) is 0.09, rx1 (Haney no.) is 6. My stretching parameters are Vtransform = 2, Vstretching=4, theta_s = 1, theta_b = 1, Tcline = 500. Shelfbreak depth is 75m, max. water depth is 1100m. max. dz = 40m, number of vertical levels = 30.

The instability happens at the edge of the continental slope (where the vertical levels are stretched more) but not over the flat bottom region. For this case, bottom slope = 0.02, N = 3e-3, f = 5e-5 i.e., a slope Burger number of 1.2. The trouble is

• * results in vertical velocity growing with time to O(10^-4) m/s. I haven't run it long enough to see if it results in blow up eventually.
  * Similar patterns are seen in u,v,rho also. magnitude of noise is O(1cm/s) in u.
  * Independent of where the eddy is in the domain. It is seen at locations pretty far away from the eddy.
  * Has a wavelength of 10-15km in the horizontal = 9-10 grid points. So, my horizontal viscosity is not effective at killing it.
  * Has a time period of 20 inertial periods
  * Looks like grid-scale noise in the vertical (see figure).
  * It is always seen where the vertical grid spacing is maximum. Changing the stretching parameters only makes it appear at different depth levels in the vertical i.e., wherever the dz is large.
  * At a horizontal resolution dx=dy=1.5, Doubling the number of vertical levels to 60 delays the onset of instability by approx. 1.5 times but it still appears at a time where I'm interested in the dynamics.
  * Increasing horizontal resolution to dx=dy=1km doesn't change it by much.

I think increasing the vertical resolution even more might help by delaying the onset further but I would like to avoid the additional computational expense. I have TS_MPDATA, UV_C3HADVECTION, UV_C4VADVECTION, UV_VIS4, MIX_GEO_TS, MIX_GEO_UV, DJ_GRADPS enabled.

Have any of you seen anything like this before? Any suggestions on what might be causing it or what might help mitigate it?

Thanks,

Deepak

[austinctodd]

Hey Deepak,

What are your initial conditions? In particular, what are your temperature and salinity fields? Have you tried running without any forcing at all?

One suggestion is to run with flat isopycnals and without forcing of any kind and see if significant velocities are still being generated along the slope. If this is the case, your problem may be with the vertical stretching you've chosen, leading to errors with the horizontal pressure gradient.

Austin

[dcherian]

Hi Austin,

My background state is just flat isopycnals, N2 = constant.

You are right, I see the same trouble with no forcing and flat isopycnals. Increasing the number of vertical levels reduces the growth rate, but then increasing N2 increases the growth rate quite dramatically.

I've played with the stretching some, but all that seems to do is move the noise to wherever the dz spacing is maximum.

Deepak