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.

Keywords:

• Geophysical waves
• linear waves
• particle trajectory
• mean velocity
• mass transport
• exact and explicit solution
• waves in rotating fluid
• deep-water waves

AMS Classifications:

• Primary: 35Q35
• Secondary: 76B15
• 86A05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Mateusz Kluczek acknowledges gratefully the support of the Science Foundation Ireland (SFI) research Grant 13/CDA/2117.