Surface stresses at wrong time step in zdftke/zdfgls

[jchanut]

Context

Gls and tke vertical mixing schemes are discretized in time thanks to backward Euler time stepping (over rdt), but shifted one time step in the past. Hence turbulent quantities are integrated from "kstep-1" to "kstep" leapfrog time steps. This leads to "now" diffusivities/viscosities at kstep. However, surface stresses are obtained from taum which is the surface stress module at kstep+0.5. It should be taken one step in the past at kstep-0.5. I encountered some instabilities due to that.
There is a similar problem with bottom stresses, taub being computed from "now" bottom friction parameter. This is mitigated by now velocities entering the stress which is in agreement with implicit bottom friction.

Analysis

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Fix

Would be far better if tke/gls schemes would be integrated from now to after time steps. Then taum would be at the right time step and this would greatly simplify interaction with AGRIF. Sticking with the current implementation, simply recomputing squared surface velocity scales from before stresses could solve the problem.

This said, and in contrary with what is stated in the documentation, I don't think that mixing a backward Euler time stepping over rdt with backward Euler time stepping over 2 rdt does give the correct energetic transfer (through vertical shear) from momentum equations to TKE/GLS schemes.

[smasson]

Wontfix in the leap-frog environment