Dimensions of FrictWork and GMWork

[iangrooms]

I'm working on a stochastic backscatter with a rate that is proportional to the horizontal viscous dissipation rate and/or the GM work. My goal is to get a value A with the same units as velocity-squared over dt such that A equals the frictional KE dissipation rate within a layer (where KE has units of (length / time)**2). For GM I need A to equal the depth-average GM work rate.

In MOM_thickness_diffuse.F90 the variable GMWork is declared as having units of watts per meter squared. It is then computed here. I think that I need to take Work_h (aka GMWork) and divide by GV%Rho0 * (h_tot + h_neglect), but I am not 100% sure. My uncertainty about GMWork is entirely due to the seemingly different nature of FrictWork as described below.

In MOM_hor_visc.F90 the variable FrictWork is declared as having units of watts per meter squared. It is then computed here. (Evidently this computation is not completely correct on a curvilinear grid - see #1366 - but the units are not the problem.) By analogy to GMWork (they both have the same units) I might divide FrictWork by GV%Rho0 * (h(i,j,k) + h_neglect). But when I look at the way that FrictWork is computed, this seems incorrect. The layer thickness is never used in the computation of FrictWork; rather, it is a product of viscous coefficients and derivatives of velocity. This also seems suspicious since the depth integral FrictWorkIntz is computed on this line by just summing up FrictWork without making any reference to layer depths. So just by looking at how FrictWork is computed, and ignoring the declaration that says watts per meter squared, I am guessing that the correct approach is to just divide FrictWork by GV%H_to_RZ, which should produce a quantity with the same units as velocity squared over dt. But the values I produce in this way seem overly large, so I am not sure this is correct.

I would appreciate guidance on how to correctly convert the energy dissipation rates FrictWork and GMWork into quantities with units of velocity squared over dt.