ON THE STABILITY OF VERTICAL DOUBLE-DIFFUSIVE INTERFACES - PART 3 - CYLINDRICAL INTERFACE

This is the final part of a three-part study of the stability of verti cally oriented double-diffusive interfaces having an imposed vertical stable temperature gradient. In this study, flow is forced within a fl uid of infinite extent by a prescribed excess of compositionally buoya nt material within a circular cylindrical interface. Compositional dif fusivity is ignored while thermal diffusivity and viscosity are finite . The instability of the interface is determined by quantifying the ex ponential growth rate of a harmonic deflection of infinitesimal amplit ude. Attention is focused on the zonal wavenumber of the fastest growi ng mode. The interface is found to be unstable for some wavenumber for all values of the Prandtl number and interface radius. The zonal wave number of the fastest growing mode increases roughly linearly with int erface radius, except for small values of the Prandtl number (< 0.065) . For small and moderate values of the radius, the preferred mode is e ither axisymmetric or has zonal wavenumber of 1, representing a helica l instability. The growth rate of the fastest-growing mode is largest for interfaces having radii of from 2 to 3 salt-finger lengths.