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Zbl 1129.76049
Marušić, Sanja
Natural convection in shallow water. (English)
[J] Nonlinear Anal., Real World Appl. 8, No. 5, 1379-1389 (2007). ISSN 1468-1218

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 2000:: *76R10 Free convection
80A20 Heat and mass transfer
86A05 Hydrology, hydrography, oceanography

Keywords: Boussinesq model; elliptic equation; vertical diffusion

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