The stability of long, steady, two-dimensional salt fingers

Abstract

In this paper we study the stability of long, steady, two-dimensional salt fingers. It is already known that salt fingers carrying a large enough density flux are unstable to long-wavelength internal-wave perturbations. Stern (1969) studied the mechanism of this, the collective instability, and it was studied in more detail by Holyer (1981). We extend the earlier work to include perturbations of all wavelengths, as well as long-wavelength perturbations. By applying the methods of Floquet theory to the periodic salt fingers, the growth rates of perturbations are found. For both heat-salt and salt-sugar systems the collective instability, which can be recognized by its frequency of oscillation, does not have the largest growth rate. There is a new, non-oscillatory instability, which, according to linear theory, grows faster than the collective instability. We study the instabilities that arise by using a combination of analytical and numerical methods. Further work will be necessary in order to assess the importance of these instabilities in different physical situations and to examine their development as their amplitude increases.