Influence of non-Boussinesq effects on patterns in salt-finger convection

Abstract

The influence of non-Boussinesq effects on the quadratic coefficient of the amplitude equations for patterns that are doubly periodic with respect to the hexagonal lattice is discussed. The vertical length scale is assumed to be long compared with the horizontal. Within this approximation, we consider a variety of non-Boussinesq effects including the dependence of the fluid properties on temperature and salinity and the nonlinearity of the basic temperature and salinity profiles. We include some numerical calculations for the latter case. Oceanic data show a pronounced nonlinearity of the basic temperature profile. Our calculations, however, show this effect to be small, and, moreover, the dominant contribution in this case is not covered by our asymptotic "thin finger" analysis. The reasons for this are discussed. A nonlinear salinity profile, on the other hand, produces a much stronger effect, and our analysis seems to be applicable to this case.