Potential instability related to explicit treatment of Coriolis for C-grid

[JFLemieux73]

Although we have not seen any problems so far, it is possible the current forward Euler for time-stepping the momentum equation is unstable.

We should investigate the use of another approach such as leap-frog.

[dupontf]

An Euler-forward temporal scheme for inertial oscillations is

$$u^{n+1}-u^{n} + i f \Delta_t u^{n} = 0$$

and its dispersion relation yields

$$| e^{i \omega \Delta_t} | = | 1 + i f \Delta_t | >= 1$$

and thus, $\omega$ must have an imaginary part which allows for growing amplitude, therefore the scheme is unconditionally unstable.

[JFLemieux73]

Thanks Fred. Could you do the same thing but adding the water stress?

[JFLemieux73]

See comments from Martin Losch about this in this issue:

#941