A note on boundary layers and wakes in rotating fluids
The flow induced by the two-dimensional line vortex moving in a rotating fluid is discussed. The governing vorticity equation is linearized adopting the Oseen approximation.
First, the problem is considered on a constantf-plane. The solution shows that the Stewartson E1/4 layer is transformed into the Oseen wake as the role of the advection becomes important.
Second, the problem is considered on aΒ-plane. When the line vortex moves westward, the solution shows a pattern of Rossby lee waves decaying downstream of the vortex and alternating flows far upstream. When the line vortex moves eastward, the inviscid solution shows definite alternating jets downstream. In a viscous case, however, the jets become less definite and identical with the above mentioned alternating flows in the far field. Far upstream, there are no disturbances because of the special propagation characteristics of Rossby waves.
KeywordsVortex Boundary Layer Vorticity Advection Propagation Characteristic
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- Greenspan, H.P. (1968): The Theory of Rotating Fluids. Cambridge University Press, Cambridge, 328 pp.Google Scholar
- Janowitz, G. S. (1968): On wakes in stratified fluids. J. Fluid Mech.,33, 417–432.Google Scholar
- Lighthill, M.J. (1967): On waves generated in dispersive systems by travelling forcing effects, with applications to the dynamics of rotating fluids. J. Fluid Mech.,27, 725–752.Google Scholar
- Martin, S. andR. R. Long (1968): The slow motion of a flat plate in a viscous stratified fluid. J. Fluid Mech.,31, 669–688.Google Scholar
- Nitani, H. (1975): Variation of the Kuroshio south of Japan. J. Oceanogr. Soc. Japan,31, 154–173.Google Scholar
- Rosenhead, L. ed. (1963): Laminar Boundary Layers. Oxford University Press, Oxford, 687 pp.Google Scholar
- Turner, J.S. (1973): Buoyancy Effects in Fluids. Cambridge University Press, Cambridge, 367 pp.Google Scholar
- Yamagata, T. (1974): How does the ocean respond to the withdrawal of water from a watergate located at the eastern boundary on a beta-plane? J. Oceanogr. Soc. Japan,30, 282–288.Google Scholar