open TELEMAC-MASCARET The mathematically superior suite of solvers

Just curious: how does Telemac-3d solve for vertical velocity when the flow is stratified, but assumed hydrostatic? I'm guessing the buoyancy term (\rho'/\rho_0)*g is calculated from an equation of state and then used to get the vertical gradient in pressure perturbation p' (difference from hydrostatic condition due to buoyancy effects), i.e., dp'/dz=-\rho'g. I'm assuming this pressure perturbation then feeds into the lateral momentum equations and that, finally, the vertical velocity is calculated in the continuity step. Does anyone know if this is correct?

Thanks,
Ben

Hello,

Actually the buoyancy terms are computed with a Boussinesq approximation, which makes that they appear only in the horizontal equations of momentum. Then the vertical velocity is computed with the continuity equation. This is the classical way, which gives the so-called barotropic and baroclinic buoyancy terms. The drawback of this approach is that the vertical velocity copes for all the errors. We are studying other approaches. Another one is under investigation in subroutine preadv.f if you set OPT_TRID = 3 instead of 2. In this option the 3 velocities are simultaneously corrected to get the continuity. However it happens in this case that the vertical velocity is still the more impacted, because of the aspect ratio that tends to give more importance to links between points on a vertical. So this is still an open problem.

With best regards,

Jean-Michel Hervouet

Thanks, Jean-Michel. Do you know of a good reference that describes the classic method that results in barotropic and baroclinic buoyancy terms under the Boussinesq approximation?

Regards,
Ben

Hello,

In my book it is page 143 to 146. The reference I give is Bijvelds M.: numerical modelling of estuarine flow over steep topography. Communication on Hydraulic and Geotechnical Engineering, TU Delft Faculty of Civil Engineering Report 01-2. March 2001.

Regards,

JMH