The general motion of a pair of point vortices of arbitrary circulations in two-dimensional ideal shallow water near topography in the form of rectilinear step is found using Hamiltonian techniques. Paths are determined by the constants of motion: energy, linear impulse, and circulation. The behavior of vortex patches in the same geometry is computed using contour dynamics. Comparisons of point vortex and patch trajectories are found to be close provided the vortex patch centroids are sufficiently far away from the escarpment. For special values of the constants of motion, vortex pairs that propagate steadily parallel to the escarpment without deformation are found (that is, vortex pair equilibrium states) and exist even when the circulation of each vortex has the same sign.

Topics
Bioacoustics of amphibians, Equilibrium thermodynamics, Hamiltonian mechanics, Newtonian mechanics, Rigid body dynamics, Depth profiling techniques, Geometrical optics, Eddies, Turbulent flows, Vortex dynamics
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© 2007 American Institute of Physics.
2007
American Institute of Physics
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