Journal of Nonlinear Mathematical Physics

Volume 15, Issue Supplement 2, August 2008

Water waves

Supplement reflecting the results of the water waves program organised by the Hamilton Mathematics Institute, Trinity College Dublin, Ireland.

Adrian Constantin, Robin Stanley Johnson
Pages: 58 - 73
In this note we describe the underlying principles — and pitfalls — of the process of non-dimensionalising and scaling the equations that model the classical problem in water waves. In particular, we introduce the two fundamental parameters (associated with amplitude and with wave length) and show how...
David Henry
Pages: 87 - 95
We present a simple approach showing that Gerstner’s flow is dynamically possible: each particle moves on a circle, but the particles never collide and fill out the entire region below the surface wave.