The onset of oscillatory Marangoni convection in a semi-infinitely deep layer of fluid

In this paper we use classical linear stability theory to analyse the onset of thermocapillary-driven Marangoni convection in a semi-infinitely deep layer of quiescent fluid. We use a combination of analytical and numerical techniques to obtain for the first time a detailed description of the marginal stability curves for the onset of oscillatory convection. We perform a comprehensive asymptotic analysis of the marginal curves in the limits of both long-wave and short-wave perturbations and present the results of numerical calculations which illustrate the effect of varying the problem parameters on the marginal curves and hence on the critical Marangoni number, frequency of oscillation and wavenumber for the onset of convection.