Vertical Stewartson layers in a stratified flow
Abstract
The slow, steady, stratified flow past an obstacle is well known to be characterized by a long upstream wake. Coriolis forces of very small relative magnitude shorten that feature markedly by allowing vertical motion of the fluid ahead of an obstacle via Ekman pumping rather than by small viscous forces acting through the interior of the fluid. Foster (1979) found that such a flow past any obstacle is characterized by an upstream eigenfunction if the fluid is nondiffusive; here we take the Prandtl number to be order one, and a similar upstream eigenfunction appears. The perhaps surprising thing here is that the vertical shear layers in this flow are the familiar Stewartson layers of homogeneous rotating flow theory. The results are valid so long as the Rossby number is large compared to the Ekman number, E, but small compared to Esuper0.75.
 Publication:

Quarterly Journal of Mechanics and Applied Mathematics
 Pub Date:
 November 1979
 Bibcode:
 1979QJMAM..32..339F
 Keywords:

 Flow Geometry;
 Fluid Mechanics;
 Shear Layers;
 Stratified Flow;
 Boundary Layer Transition;
 Coriolis Effect;
 Eigenvalues;
 Steady Flow;
 Upstream;
 Fluid Mechanics and Heat Transfer