# Mass transport for Pollard waves

## TL;DR

This paper investigates the mass-transport characteristics of Pollard's exact nonlinear water-wave solution, revealing its similarities with linear wave theory and extending understanding through higher-order Lagrangian solutions.

## Contribution

It provides a detailed analysis of Pollard's wave solution's mass transport without approximations and introduces Pollard-like solutions in higher-order Lagrangian theory.

## Key findings

- Pollard's solution shares features with linear wave theory.
- Mass transport can be characterized exactly for nonlinear waves.
- Higher-order Lagrangian solutions resemble Pollard's wave.

## 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.