Related papers: A Didactic Approach to Linear Waves in the Ocean
The complexity of real-world geophysical systems is often compounded by the fact that the observed measurements depend on hidden variables. These latent variables include unresolved small scales and/or rapidly evolving processes, partially…
We study the waves at the interface between two thin horizontal layers of immiscible liquids subject to high-frequency tangential vibrations. Nonlinear governing equations are derived for the cases of two- and three-dimensional flows and…
Revealing the ongoing changes in ocean dynamics and their impact on marine ecosystems requires the joint analysis of multiple variables. Yet, global observational records only cover a few decades, posing a challenge in the separation of…
We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed…
Linear and weakly nonlinear stability analyses of an externally shear-imposed, gravity-driven falling film over a uniformly heated wavy substrate are studied. The longwave asymptotic expansion technique is utilized to formulate a single…
We formulate a model of the two-way interactions between surface gravity waves and ocean currents. The model couples the transport of wave action in the four-dimensional (horizontal) position--wavevector phase space with the…
Dynamical systems theory approach has been successfully used in physical oceanography for the last two decades to study mixing and transport of water masses in the ocean. The basic theoretical ideas have been borrowed from the phenomenon of…
Diffraction of elastic waves is considered for a system consisting of two parallel arrays of thin (subwavelength) cylinders that are arranged periodically. The embedding media supports waves with all polarizations, one longitudinal and two…
Internal gravity waves are an essential feature of stratified media, such as oceans and atmospheres. To investigate their dynamics, we perform simulations of the forced-dissipated kinetic equation describing the evolution of the energy…
There are two distinct regimes commonly used to model traveling waves in stratified water: continuous stratification, where the density is smooth throughout the fluid, and layer-wise continuous stratification, where the fluid consists of…
We present our study on the emergent states of two interacting nonlinear systems with differing dynamical time scales. We find that the inability of the interacting systems to fall in step leads to difference in phase as well as change in…
Chen et al. (Eur. J. Mech. B/Fluids 78, pp. 88-105, 2019) recently proposed a two-dimensional continuum model for linear gravity waves propagating in ice-covered seas. It is based on a two-layer formulation where the ice cover is viewed as…
We introduce the notion of asymptotic integrability into the theory of nonlinear wave equations. It means that the Hamiltonian structure of equations describing propagation of high-frequency wave packets is preserved by hydrodynamic…
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…
In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane…
High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points…
A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a…
The problem of reconstructing non-harmonic internal gravity wave packets generated by a source moving in a stratified ocean is considered. The uniform asymptotic form of the internal gravity waves field generated by a source moving above…
In the study on nonlinear wave-wave processes in an ionosphere and a magnetosphere usually the main attention is paid to investigation of plasma turbulence at well developed stage, when the wide spectrum of plasma wave is present. On the…
We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any…