A two-dimensional model for deep-water waves on a background vortex Flow #

Emanuele Zuccoli, Ed Brambley, Dwight Barkley

11:30 Wednesday in 3E11.

Part of the Applied fluid dynamics session.

Abstract #

In this talk we consider surface water waves interacting with a mean horizontal flow, such as a spinning vortex.
We will present the derivation of a two-dimensional system of equations for surface water waves interacting with a background flow in the deep water limit. In particular, this formulation does not neglect the mean free surface deformation, and is valid for any arbitrary (horizontally varying) background flow. The need to reduce the set of equations from three spatial dimensions to two is dictated both by analytical as well as numerical reasons. The novelty in our derivation is the introduction of a closure boundary condition imposed along the base free surface, and is valid only for surface gravity waves. We justify the validity of our closure boundary condition by means of numerical results and comparisons with full three-dimensional calculations for the case of a single Lamb–Oseen vortex flow. We will then show results obtained by considering other types of vortex profiles.