Low-Reynolds-number diffusion-driven flow around a horizontal cylinder

Abstract

Diffusion-driven flow occurs when any insulated sloping surface is in contact with a quiescent stratified and viscous fluid. This startling fluid motion is generally very slow, and is caused by a hydrostatic pressure imbalance due to bending of isotherms near the surface. In contrast to previous studies of the phenomenon, the low-Reynolds-number case is considered here, for which the induced steady motion is influenced by viscous and density diffusion over a much larger length scale than the size of the insulated object. The relevant linear equations of steady two-dimensional motion in a linearly stratified fluid are solved for a circular cylinder using a matched two-region approach that yields analytical solutions for the streamfunction and the density variations both close to and far from the object. The exact analytical expressions for the solutions in the ‘outer-flow region’ are new, and after matching enable accurate solutions to be evaluated easily at any point. Similar qualitative behaviour is expected under similar conditions near isolated objects of other shapes, including for a sphere. Implications for multiple objects are also discussed.