"sharp corners" in the energy-time plot of Rayleigh Benard

[Jack]

Hi Dedalus Users, 

I added an analysis task in the example script rayleigh_benard.py for plotting the energy of the system versus time (rb_test1.py, plot_rb_energy.py). The curve in the profile is very smooth (energy_rb30.png). 

However, when I change the boundary conditions to be the "stress-free" ones(rbsf0_test.py, plot_rbsf_energy.py), I get a rough curve with sharp corner in several places .

I made iter smaller in 

analysis_RB = solver.evaluator.add_file_handler(filename2, iter=10)

analysis_RB.add_task("integ(u*u + w*w + b*b)", name="norm2")

and got similar result with those "sharp corners".

Does anyone know a possible reason for this? 

Best,

Jack

[geoff]

My guess is that this is somewhat “physical”. 

Not that the spikes are supposed to be there. But that the system is less stable with the different boundary conditions. This is actually to be expected. The Reynolds number of the flow should be roughly 

Re ~ sqrt( Ra / Rac ) 

The critical Rayleigh number for stress-free boundaries is lower than for no-slip. ~650 vs 1700. This means that a stress-free simulation will be a little more difficult than no-slip. This might be fixed with a small safety factor in the tilmestep. Or it might need a bit more resolution. 

I would try both options and see if things improve. 

-Geoff 

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<rb_test1.py><energy_rb30.png><plot_rb_energy.py><energy_rbsf30.png><energy_rbsf30a.png><plot_rbsf_energy.py><rbsf0_test.py>

[geoff]

PS: and there’s a small chance that the spikes are fully physical; i.e. the flow has some kind of extreme even more often with stress-free boundaries. I doubt this is the case. But you’ll find out if you run a more-resolved simulation and they don’t go away, and the solutions seem to make sense during the intermittent events. 

[Jack]

Geoffrey, 

Thanks for this! I raised the number of modes to be 512x128 (with the safety number remains as it was) and the spikes disappeared for up to a simulation time of 30s. I'm not very sure though if it would appear or not if the time is longer, say, 200s. 

I will try a longer time later.

Jack