Amplitude Equations for Hexagonal Patterns of Convection in Non-Boussinesq Fluids
Hexagonal patterns can be observed in a fluid heated from below, mainly in three situations: 1) when the upper surface has a temperature-dependent surface tension (Bénard-Marangoni convection)1, 2) when its transport coefficients vary with the temperature (non-Boussinesq convection)2 and 3) under a modulated heating.3 Convective patterns can be described by means of the so-called amplitude equations, that are obtained either from the hydrodynamic equations 4or simply from symmetry arguments.5 This system of equations is simpler than the hydrodynamic nonlinear equation and it is easily simulated in computers.6
KeywordsNusselt Number Rayleigh Number Hydrodynamic Equation Normalize Nusselt Number Critical Rayleigh Number
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