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 l ayer of quiescent fluid. We use a combination of analytical and numerical t echniques to obtain for the first time a detailed description of the margin al stability curves for the onset of oscillatory convection. We perform a c omprehensive asymptotic analysis of the marginal curves in the limits of bo th long-wave and short-wave perturbations and present the results of numeri cal calculations which illustrate the effect of varying the problem paramet ers on the marginal curves and hence on the critical Marangoni number, freq uency of oscillation and wavenumber for the onset of convection.