## Natural convection in shallow water.(English)Zbl 1129.76049

Summary: Starting from three-dimensional Boussinesq model and taking the limit as the domain thickness tends to zero, we derive rigorously a two-dimensional model for natural convection in shallow water. The model reduces to a degenerate elliptic equation for pressure, and allows to derive an explicit formula for horizontal components of velocity and for the vertical diffusion of the vertical component. The macroscopic flow is driven by temperature variations as well as by the bottom topography.

### MSC:

 76R10 Free convection 80A20 Heat and mass transfer, heat flow (MSC2010) 86A05 Hydrology, hydrography, oceanography

### Keywords:

Boussinesq model; elliptic equation; vertical diffusion
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### References:

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