The instability of Stokes waves, steady propagating waves on the surface of an ideal fluid of
infinite depth, is a fundamental problem in the field of nonlinear science. The dominant …

Free surface flows occur frequently in our daily lives and many natural or industrial settings.
Our understanding of such flows has grown tremendously with progress in mathematical …

We review recent progress on the long-time regularity of solutions of the Cauchy problem for
the water waves equations, in two and three dimensions. We begin by introducing the free …

The paper fully answers a long standing open question concerning the stability/instability of
pure gravity periodic traveling water waves—called Stokes waves—at the critical Whitham …

Bathymetry is an important factor affecting wave propagation in coastal environments but is
often challenging to measure in practice. We propose a method for inferring coastal …

Periodic equatorial water flows from a Hamiltonian perspective - ScienceDirect Skip to main
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Recent work has given rise to a novel and simple numerical technique for solving elliptic
boundary value problems formulated in convex polygons in two dimensions. The method …

This document is an announcement and preview of a memoir whose full version is available
on the Open Math Notes repository of the American Mathematical Society (OMN …

Recently, the authors presented two numerical studies for capturing the flow structure
beneath water waves (Nachbin and Ribeiro-Junior 2014 Disc. Cont. Dyn. Syst. A 34, 3135 …

For wave tank, coastal and oceanic applications, a fully nonlinear Variational Boussinesq
model with optimized dispersion is derived and a simple Finite Element implementation is …