Hi All,
I have a question about determining the time-step size. For example, my grid has a uniform 5 m spacing in both xi and eta directions. The water depth is about 2000 m. The CFL condition for 2-D advection equation is
Cdt/dx<1/2. Assuming C is the shallow water wave phase speed C = sqrt(gH) ~ 140 m/s. Substituting C into the CFL condition gives dt < 0.02 s. I am wondering if this is the right way to determine the time-step size in the barotropic mode. If so, how do I determine the baroclinic time-step size for here?
Many thanks!
Guangyu
how to determine the right time step size
Re: how to determine the right time step size
Yes, that's a good guess for barotropic timestep. If the timestep ratio is 10-20, then you try that and see what happens. ROMS will report Courant numbers during initialization - and a lot more besides. Best is to just make some guesses and see what you get, then adjust as needed.
Re: how to determine the right time step size
Hi Kate. Thanks again for the prompt reply. When you say the time-step ratio is 10 to 20, do you mean the baroclinic time-step is 10 to 20 times the baroclinic time step? If this is true, I am curious to know why a much less stringent time-step size requirement is allowed for the baroclinic mode. Is this because the waves in the baroclinic mode (e.g., internal waves) are propagating at a much slower speed than shallow water surface waves?kate wrote:Yes, that's a good guess for barotropic timestep. If the timestep ratio is 10-20, then you try that and see what happens. ROMS will report Courant numbers during initialization - and a lot more besides. Best is to just make some guesses and see what you get, then adjust as needed.
Also, do you think ROMS can resolve the flow structure as fine as 5 m (the grid spacing of my simulation)? Do you think the hydrostatic assumption will hold up on such a small scale?
Re: how to determine the right time step size
Yes, the baroclinic waves are slower. The 3-D timestep is more costly than the 2-D timestep. The purpose of the time splitting is to save computer time - otherwise you compute everything at the barotropic timestep limit.
Yes, ROMS can model things at 5 m resolution. It has successfully simulated a laboratory tank with smaller scales. Is your flow hydrostatic? That I can't answer.
Yes, ROMS can model things at 5 m resolution. It has successfully simulated a laboratory tank with smaller scales. Is your flow hydrostatic? That I can't answer.
Re: how to determine the right time step size
I see. Now I know why two time steps are needed.kate wrote:Yes, the baroclinic waves are slower. The 3-D timestep is more costly than the 2-D timestep. The purpose of the time splitting is to save computer time - otherwise you compute everything at the barotropic timestep limit.
Yes, ROMS can model things at 5 m resolution. It has successfully simulated a laboratory tank with smaller scales. Is your flow hydrostatic? That I can't answer.
Actually I don't quite know the answer to your question. I am trying to use ROMS to do a simple simulation of the flow field generated by sloshing tidal currents over a mid-ocean ridge segment. I want to see what kind of small scale currents can be generated in this simple setting. The model domain is a 2 km by 2 km box and the water depth is about 2000 m. I learnt that for the hydrostatic assumption to be valid, the horizontal scale of the flow has to be larger than the vertical flow. In my case, the length of the model domain is the same as the water column thickness. Therefore, the hydrostatic assumption may not be valid. The magnitude of the tidal currents is up to 10 cm/s and I am not sure how strong a vertical flow can be generated from the interaction of the horizontal currents with the rough bottom topography.
I am hoping you can provide some insightful thoughts on this.