Mass transport for Pollard waves

Abstract

We provide an in-depth exploration of the mass-transport properties of Pollard's exact solution for a zonally-propagating surface water-wave in infinite depth. Without resorting to approximations we discuss the Eulerian mass transport of this fully nonlinear, Lagrangian solution. We show that it has many commonalities with the linear, Eulerian wave-theory, and also find Pollard-like solutions in the first and second order Lagrangian theory.