The time-dependent motion of water waves with a parametrically-defined free surface is mapped to a fixed time-independent rectangle by an arbitrary transformation. The emphasis is on the general properties of transformations. Special cases are algebraic transformations based on transfinite interpolation, conformal mappings, and transformations generated by nonlinear elliptic PDEs. The aim is to...

We present measurements of the complete spatiotemporal Fourier spectrum of Faraday waves. The Faraday waves are generated at the interface of two immiscible index matched liquids of different density. By use of a light absorption technique we are able to determine the bifurcation scenario from the flat surface to the patterned state for each complex spatial and temporal Fourier component separa...

This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady surface waves propagating in shallow water. We consider the (fully nonlinear, weakly dispersive) Serre–Green–Naghdi equations with surface tension, because it provides a tractable model that, in the same time, is not...

A space-time discontinuous Galerkin (DG) finite element method for nonlinear water waves in an inviscid and incompressible fluid is presented. The space-time DG method results in a conservative numerical discretization on time dependent deforming meshes which follow the free surface evolution. The dispersion and dissipation errors of the scheme are investigated and the algorithm is demonstrated...

Emission of compressional acoustic waves at the second harmonic frequency (second harmonic generation, SHG) is possible from rough surfaces undergoing oscillatory shear in liquids. This nonlinear response is a consequence of the inertial term in the Navier-Stokes equation. On a corrugated surface, the streamlines of the sheared liquid are not strictly parallel to the surface, leading to variati...

We study the growth of small-scale inhomogeneities of the density of particles floating in weakly nonlinear, small-amplitude, surface waves. Despite the amplitude smallness, the accumulated effect of the long-time evolution may produce strongly inhomogeneous distribution of the floaters: density fluctuations grow exponentially with a small but finite exponent. We show that the exponent is of si...

This paper concerns a development of a new efficient numerical model for the short term prediction of evolving weakly nonlinear ocean surface waves. By extending the works of West et al. 1 and Choi, and utilizing the fact that waves in the ocean tend to travel primarily in one direction, this new numerical model is derived based on additional assumption of a weak transverse dependence. The mode...

We describe a way to generate subdiffraction light spots that can be moved over a surface without resorting to near-field manipulation, nonlinear effects, or negative index materials. We use a periodically patterned substrate that converted efficiently, through scattering, the impinging propagative waves into evanescent ones. Then we optimize the wave front of the incident propagative beam so t...

Mountain gravity wave theories often neglect the observationnal evidence that the large scale winds can become very small near the earth surface. This common shortcoming is related to the fact that mountain waves have a critical level near the surface in this case, making the problem extremely involved. We briefly expose here how Lott (2016) circumvents this difficulty and derive a theory where...

The linear and nonlinear processes in ferromagnetic films at low temperatures (T ≪ Tc) are studied in a microscopic theory. Both the long-range magnetic dipole-dipole and the Heisenberg exchange interactions to nearest and next-nearest neighbors are included. The results obtained for the linearized spin-wave spectrum are compared with previous macroscopic theories. For ultrathin films (or for l...