Abstract
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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
