On the double-diffusive layer formation in the vertical annulus driven by radial thermal and salinity gradients

Abstract

We employ the Chebyshev tau-qz algorithm developed by Straughan and co-workers (1996, 2013) to investigate the stability of the double-diffusive convection in a vertical annulus, in which the inner cylinder maintains cold and fresh and the outer cylinder warm and salty. Results show that the double-diffusive layer may form through a successive generation of vortices induced by the interaction between the radial thermal and salinity gradients. The competition of the two gradients leads to three different types of double-diffusive instabilities: thermal, salt-finger, and diffusive. The axisymmetric mode is generally the most unstable, and its instability enhances when the annular gap width is larger. The non-axisymmetric mode becomes more stable for the annulus with a larger gap width, and its stability enhances when the mode has a smaller azimuthal wavelength. Finally, we show through a simulated experiment that the HDDL thickness is of a scale about the gap width.