[MITgcm-support] Conservation of total energy for Internal Wave Simulation

[Adham El Zaher]

Hi everyone!

I am working on an internal wave simulation in a rectangular domain with no dissipation or diffusivity and with a periodic boundary condition on both ends in the x-direction, a free-slip wall at the bottom.

Theoretically, the total energy of the system is conserved and does not change with the time, but instead of that, numerically, I always get undamped oscillations (at the same frequency as this of the single wave specified in the gendata file), so there is time dependency in the numerical simulations.

I have tried several time-stepping (implicit time-stepping scheme, Crank-Nicolson scheme) and advection schemes ( 3rd order upwind scheme, 7th order one-step method) to get rid of these oscillations but unfortunately none of them worked.

 Does anyone have any idea on how to solve this problem or the reason of the presence of these oscillations, please?

Thanks in advance for all your help.

Best regards,
Zaher
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