Page, MA; Johnson, ER; (2008) On steady linear diffusion-driven flow. J FLUID MECH , 606 433 - 443. 10.1017/S002211200800178X.

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Abstract

Wunsch (1970) and Phillips (1970) (Deep-Sea Res. vol. 17, pp. 293, 435) showed that a temperature flux condition on a sloping non-slip surface in a stratified fluid can generate a slow steady upward flow along a thin 'buoyancy layer'. Their analysis is extended here to the more-general case of steady flow in a contained fluid where buoyancy layers may expel or entrain fluid from their outer edge. A compatibility condition that relates the mass flux and temperature gradient along that edge is derived, and this allows the fluid recirculation and temperature perturbation to be determined in the broader-scale 'outer flow' region. The analysis applies when the Wunsch-Phillips parameter R is small, in the linear case for which the density variations are dominated by a constant vertical gradient.

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