We study the generation of surface waves on water as a bifurcation phenomenon. For a critical wind-speed there appear traveling wave solutions. While linear waves do not transport mass (in the mean), nonlinear effects create a shear-flow and result in a net mass transport in the direction of the wind. We derive an asymptotic formula for the average tangential velocity along the free surface. Nu...

Interacting surface waves, parametrically excited by two commensurate frequencies, yield a number of nonlinear states. Near the system's bicritical point, a state, highly disordered in space and time, results from competition between nonlinear states. Experimentally, this disordered state can be rapidly stabilized to a variety of nonlinear states via open-loop control with a small-amplitude thi...

We present a new numerical method to simulate the time evolution of axisymmetric nonlinear waves on the surface of a ferrofluid jet. It is based on the reduction of this problem to a lower-dimensional computation involving surface variables alone. To do so, we describe the associated Dirichlet–Neumann operator in terms of a Taylor series expansion where each term can be efficiently computed by ...

In problems of dispersive wave propagation governed by two distinct restoring-force mechanisms, the phase speed of linear sinusoidal wavetrains may feature a minimum, cmin, at non-zero wavenumber, kmin. Examples include waves on the surface of a liquid in the presence of both gravity and surface tension, flexural waves on a floating ice sheet, in which case capillarity is replaced by the flexur...

A time domain method is presented for analyzing simultaneous measurements of pressure and the horizontal components of velocity obtained beneath irregular multidirectional wave fields. This new method differs from the usual linear directional analyses applied to PUV data in two important aspects. First, the essential nonlinearity of the measured waves is not sacrificed to achieve a solution. Th...

The wind blowing over sea surface generates tiny wind waves. They develop with time and space absorbing wind energy, and become huge wind waves usually referred to ocean surface waves. The wind waves cause not only serious sea disasters but also take important roles in the local and global climate changes by affecting the fluxes of momentum, heat and gases (e.g. CO2) through the air-sea boundar...

In this paper we investigate the effect of a prescribed superficial shear stress on the generation and structure of roll waves developing from infinitesimal disturbances on the surface of a power-law fluid layer flowing down an incline. The unsteady equations of motion are depth integrated according to the von Kármán momentum integral method to obtain a non-homogeneous system of nonlinear hyper...

We develop a new methodology for the numerical modeling of nonlinear free surface waves, caused by an advancing free surface disturbance, based on combining Lagrangian and Eulerian, or pseudoLagrangian, methods for the time updating of free surface geometry and motion. We solve potential flow equations with a threedimensional (3D) higher-order Boundary Element Method (BEM; Grilli et al., 2000, ...

Consider a uniform train of surface waves with a two-dimensional, bi-periodic surface pattern, propagating on deep water. One approximate model of the evolution of these waves is a pair of coupled nonlinear Schrödinger equations, which neglects any dissipation of the waves. We show that in this model, such a wave train is linearly unstable to small perturbations in the initial data, because of ...

Crack front waves are nonlinear localized waves that propagate along the leading edge of a crack. They are generated by both the interaction of a crack with a localized material inhomogeneity and the intrinsic formation of microbranches. Front waves are shown to transport energy, generate surface structure, and lead to localized velocity fluctuations. Their existence locally imparts inertia, wh...