Forcing and climatology in the shallow water system

[milankl]

What is actually a reasonable warm-up / transient integration time for Speedy?

That's at the moment no straight forward to say. Most simulations I've run so far just used some initial conditions for vorticity. In that case you get a reasonably developed turbulence in 10-20 days even at higher resolution. However, that's decaying turbulence due to the lack of forcing obviously. Hence there's no actually interesting invariant measure the model converges to.

With #144 I've added some forcing for the shallow water equations, even including a seasonal cycle that you can switch on with interface_relaxation = true (default false) and control with interface_relax_time and interface_relax_amplitude.

What's happening there is that one pulls the l=1,m=0 zonal mode of the interface displacement / SSH towards something that mimicks an equatorial heating. Other modes are not affected, so you literally just dump energy into that mode. With the seasonal_cycle = true (default true) that equatorial heating moves up and down with the seasons, similar to an ITCZ but actually all the way to the tropic of cancer back to the equator and down to the tropic of capricorn and back.

My hope was to get an interesting and stable climate also in the shallow water system. But at the moment it still converges to a steady state (or one that closely follows the seasonal cycle). I probably haven't played around with it enough to get an actually nice setup that produces eddies at all resolutions with a proper energy cascade from some large scale forcing to some small scale dissipation

[milankl]

A general forcing interface for the shallow water model has been added with #327.

SpeedyWeather.jl/src/dynamics/tendencies.jl

Lines 20 to 23 in 190e646

	S,C,G,O,F = model.spectral_transform, model.constants, model.geometry, model.orography, model.forcing
	# for compatibility with other ModelSetups pressure pres = interface displacement η here
	forcing!(diagn,F,time) # = (Fᵤ, Fᵥ, Fₙ) forcing for u,v,η

Although current default is NoForcing so one would actually need to test that interface.