The Effect of Sidewalls on Overstable Convection in a Rotating Fluid

A simple two-dimensional model is used to demonstrate some interestingeffects which arise when Chandrasekhar's (1962) theory of overstableconvection in an infinite rotating fluid layer is modified totake account of lateral walls. The aim of the investigationis to determine how sidewalls aligned with the convective rollsaffect the critical Rayleigh number and frequency of oscillationand also how the overstable eigensolutions are related to thepreviously determined stationary solutions of the equations(Daniels, 1977). For containers of large aspect ratio, L, thecritical Rayleigh number for overstability is R_o+O(L^–1)(where R_o is the value for the infinite layer) and in the neighbourhoodof this single perturbed value it is found that there is aninfinite spectrum of overstable eigenvalues with frequencieswhich differ by O(L^–1). The O(L^–1) correction toR_o is determined analytically for the case of small Prandtlnumber and rapid rotation.