On the stability of vertical double-diffusive interfaces. Part 3. Cylindrical interface

Abstract

This is the final part of a three-part study of the stability of vertically oriented double-diffusive interfaces having an imposed vertical stable temperature gradient. In this study, flow is forced within a fluid of infinite extent by a prescribed excess of compositionally buoyant material within a circular cylindrical interface. Compositional diffusivity is ignored while thermal diffusivity and viscosity are finite. The instability of the interface is determined by quantifying the exponential growth rate of a harmonic deflection of infinitesimal amplitude. Attention is focused on the zonal wavenumber of the fastest growing mode.

The interface is found to be unstable for some wavenumber for all values of the Prandtl number and interface radius. The zonal wavenumber of the fastest growing mode increases roughly linearly with interface radius, except for small values of the Prandtl number (<0.065). For small and moderate values of the radius, the preferred mode is either axisymmetric or has zonal wavenumber of 1, representing a helical instability. The growth rate of the fastest-growing mode is largest for interfaces having radii of from 2 to 3 salt-finger lengths.