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.
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