Two-dimensional oscillatory convection in a gravitationally modulated fluid layer

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Abstract
A Galerkin method is used to study the two-dimensional modes of oscillatory convection in a gravitationally modulated fluid layer with rigid, isothermal boundaries heated either from below or from above. Nonlinear solutions are obtained for dimensionless frequencies ω (frequency is made non-dimensional with the timescale d2/κ where d is the depth of the fluid layer and κ is the thermal diffusivity) in the range 100–3000, dimensionless accelerations ε (εg is the amplitude of the externally imposed oscillatory vertical acceleration and g is the constant vertical acceleration of gravity) in the range of 1–104, and Prandtl numbers P in the range 0.71 (air) to 7 (water). The problem of convective onset is explored for a broader range of parameters than heretofore considered, including Prandtl numbers between 0.71 and 50. Both synchronous and subharmonic modes of convection are identified and it is found that finite-amplitude synchronous convection can be unstable to subharmonic modes.