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Dear All,

Is it possible to simulate basin scale internal wave using telemac 3d. I am setting up the problem in a prismatic channel. T

The water motion in the channel is caused by gradient in density only. I want to switch off both advection and diffusion and only have density gradient term active.

Somewhat similar problem is solved in the paper, "Validation of numerical shallow water models for stratified seiches" by Eliason D. E. and Bourgeois A. J., International Journal for Numerical Methods in Fluids, Vol, 24, 771-786, 1997



Best regards,
Sumit

Hello Sumit,

It was never tried, to my knowledge. As a solution of Navier-Stokes equations I would say it should work, I just wonder whether the Boussinesq approximation for buoyancy terms could be hindering us.

With best regards,

Jean-Michel Hervouet

Hi JMH,

The way I am setting up this problem is as follows

a) The fluid is assumed to be immiscible and channel is having no bottom friction.
b) Temperature(Density) gradient is prescribed in horizontal and vertical direction.
c) The advection terms are not considered, consequently we have an analytical solution and the motion essentially develops only in X-Z plane. No temp. gradient in Y direction.

Because of the above consideration momentum equation reduces to to sum of inertia and density gradient term in X direction.

For temp. transport it is recommended to consider dS/dt + wdS/dZ = 0.0, as rest of the terms are of lower order.

My problem is, where should I look in the code in order just to have density/buoyancy (no diffusion, no advection) term in x-momentum equation?

As regards to temp. transport, I am of the opinion I can model wdS/dZ term as a reaction term, what do you think?

All your guidance and help is immensely appreciated.

Kind regards,
Sumit

Hello Sumit,

As the mesh will move with the internal waves, you need to have advection for relocalization. Then you cannot cancel U and V and not W, otherwise you will spoil mass-conservation. So you probably have to cancel U, V and W, and then you treat your velocity w as an extra velocity, like we do with the settling velocity equation, which is treated so far in the diffusion. In this case we take a conservative form and the problem of having div(U)=0 then vanishes. So your equation should not be dS/dt + wdS/dZ = 0.0 but dS/dt + d(wS)/dZ = 0.0.
What we do so far for the settling velocity is an upwind implicit scheme (see in CVDF3D). Another variant based on finite volumes is prepared at HR-Wallingford.

With best regards,

Jean-Michel Hervouet