Dear Colleagues, I am developing an analytical model for computing the internal wave celerity in a linearly density stratified fluid in a circular cross-section channel, i.e. in a bounded domain. The solution for a rectangular cross-section channel is given in Baines, 1997 (see the attached pdf for the complete reference). I have used some results by Yih (1980) referred to a full circle cross section. These results map the circle into a rectangular domain and found a solution in terms of Mathieu functions. The results by Yih did not give the dispersion relation of the waves, but it is straightforward to evaluate such a dispersion relation, at least for the long wave approximation, see the attached pdf. A further step is to consider a half-circle cross section with a lid at the top, since my experiments are in a circular cross-section channel half filled. To tackle the problem, I have used the same transformation used by Yih, but changing the rectangular domain (see after eq.25 in the attached pdf). Then the same expression in terms of Mathieu functions for the full filled circle is recovered and with further computations I obtain the same dispersion relation already obtained for the full circle. This is somehow disturbing me, in the sense that it seems that in the long wave approximation the internal wave celerity assumes the same value for the full circle and for the half circle cross-section channel. I would appreciate your comments on this point. Thanks Sandro
Hello Mr Longo
I think you can use Navier Stokes equation with an anisotropic turbulence model, you can also use volume of fluid transport equation for each immiscible phase if you have multiphase situation in your model. then apply them in a circular boundary condition.
Dear Mr Mirabi,
thank you for your suggestion. However, I was looking for an analytical solution, similar to that depicted in the script attached to my question. In addition, I am interested primarily in internal waves in a fluid at rest, so no turbulence is involved.
Sincerely
Sandro
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