Related papers: Nonlinear wave interaction in coastal and open sea…
Holm (Proc. Roy. Soc 2015) introduced a variational framework for stochastically parametrising unresolved scales of hydrodynamic motion. This variational framework preserves fundamental features of fluid dynamics, such as Kelvin's…
The interaction between small-scale waves and a larger-scale flow can be described by a multi-scale theory that forms the basis for a new class of parameterizations of subgrid-scale gravity waves (GW) in weather and climate models. The…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
We derive scaling laws for the steady spectrum of wind excited waves, assuming two inviscid fluids (air and water) and no surface tension, an approximation valid at large speeds. In this limit there exists an unique (small) dimensionless…
We investigate the dynamics of localized solutions of the relativistic cold fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed…
The Riemann problem of one dimensional shallow water equations with discontinuous topography has been constructed recently. The elementary waves include shock waves, rarefaction waves, and the stationary wave. The stationary wave appears…
In this paper we introduce models of short wave-long wave interactions in the relativistic setting. In this context the nonlinear Schr\"odinger equation is no longer adequate for describing short waves and is replaced by a nonlinear Dirac…
Effects of wave-wave interactions on ocean swell are studied. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation at long times up to $10^6$ seconds are presented. Basic…
We complete a full classification of non-degenerate traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under (piecewise) smooth perturbations. A striking feature of our analysis is…
The Hamiltonian formulation of the water wave problem due to Zakharov, and the reduced Zakharov equation derived therefrom, have great utility in understanding and modelling water waves. Here we set out to review the cubic Zakharov equation…
Weak interactions of solitary waves in the generalized nonlinear Schr\"{o}dinger equations are studied. It is first shown that these interactions exhibit similar fractal dependence on initial conditions for different nonlinearities. Then by…
The general equations of motion for ocean dynamics are presented and the waves supported by the (inviscid, unforced) linearized system with respect to a state of rest are derived. The linearized dynamics sustains one zero frequency mode…
We provide a rigorous justification of various kinetic regimes exhibited by the nonlinear Schr\"{o}dinger equation with an additive stochastic forcing and a viscous dissipation. The importance of such damped-driven models stems from their…
In this paper we give a general account of Wave Interaction Theory which by now consists of two parts: kinetic wave turbulence theory (WTT), using a statistical description of wave interactions, and the D-model recently introduced in…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…
Weakly nonlinear internal wave-wave interaction is a key mechanism that cascades energy from large to small scales, leading to ocean turbulence and mixing. Oceans typically have a non-uniform density stratification profile; moreover,…
We study a nonlinear Schr\"odinger equation with logarithmic nonlinearity on a star graph $\mathcal{G}$. At the vertex an interaction occurs described by a boundary condition of delta type with strength $\alpha\in \mathbb{R}$. We…
It is shown that the generalized discrete nonlinear Schr\"odinger equation can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or the fifth-order KdV equations, depending on values of the parameters. In dispersionless…
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…
During the past decades the study of strongly interacting fluids experienced a tremendous progress. In the relativistic heavy ion accelerators, specially the RHIC and LHC colliders, it became possible to study not only fluids made of…