Spatially periodic temperature modulation of a compressible fluid

A spatially periodic temperature modulation is gradually applied at the lower boundary of a layer of compressible fluid. The temperature from the lower wall diffuses into the layer and induces various convection patterns. As the amplitude of the temperature modulation is increased, non-linear effects, including those due to the inclusion of compressibility, become more prominent. An accurate numerical scheme is developed to capture the full time-dependent behaviour here. Spectral methods will be used throughout this work to provide accurate representations of the various solution components and allow for the efficient implementation of a variety of boundary conditions.

Three different types of modulation are considered, namely a pure cosine as well as rounded triangle and rounded square profiles, where the latter two of these have applications in various physical situations. Interest lies in how the nature of the convection and temperature diffusion change as the amplitude of these modulations is increased. Both no-slip and slip conditions will be implemented on the upper and lower boundaries of the layer and the differences between the two will be considered for selected cases.