A family of finite area translating monopolar vortices which propagate steadily without change of shape (V states) is found for shallow flow near a finite step change in depth. Solutions are obtained numerically and are unique for a given volume and center of vorticity. Time-dependent integrations show that these vortices are robust: flows initialized with a V state remain close to the V state and flows initialized with a circular vortex shed vorticity to approach a V state. The translational velocity of the vortices is shown to be finite and, unlike that of a singular line vortex, not to increase without limit as the center of vorticity approaches the escarpment.
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.© 2005 American Institute of Physics.
2005
American Institute of Physics
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