On the stability of vertical double-diffusive interfaces. Part 1. A single plane interface

This is the first part of a three-part study of the stability of vertically oriented double-diffusive interfaces having an imposed vertical stable temperature gradient. Flow is forced by a prescribed jump of composition across the interfaces. Compositional diffusivity is ignored, while thermal diffusivity and viscosity are finite. In this first part, basic-state solutions are presented and discussed for three configurations a single plane interface, two parallel interfaces and a circular cylindrical interface. The stability of a single plane interface is then analysed. It is shown that the presence of the compositional jump gives rise to a new type of three-dimensional instability which occurs for any non-zero forcing. This is in contrast to the thermally driven flow adjacent to a rigid wall, which is unstable only for a finite value of the forcing and results in the growth of a two-dimensional perturbation.