Upper bound on the solute flux in doubly diffusive convection

Abstract

The properties of doubly diffusive convection of large amplitude are investigated using the upper bounding method. The specific problem treated is the thermohaline instability in a horizontal layer of fluid containing temperature and solute concentration increasing in the direction opposite to that of gravity. For large values of the solute and thermal Rayleigh numbers, R and Ra, a boundary-layer analysis is used to calculate an upper bound on the solute flux. This upper bound is found to be f*(R/Ra)Ra11/8, where the function f* is a monotonically increasing function of R/Ra. Thus, for large values of Ra, the solute flux may be very large even when R/Ra is only slightly in excess of unity.