Related papers: Wave Triad with Forcings as a Nambu System
A self-consistent, thermodynamic approach is employed to derive the wave energy of a magnetohydrodynamic system within the harmonic approximation and to obtain the familiar dispersion relation from the resulting equation of motion. The…
We propose a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial value problems. The key idea is to represent each conservation law or dissipation inequality by means…
The propagation of wave disturbances over a vertically oscillating liquid may form standing waves, known as Faraday waves. Here we present an alternative description of the generation and evolution of Faraday waves by nonlinear resonant…
Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type. The advantage of…
The dynamics of spatiotemporal patterns in oscillatory reaction-diffusion systems subject to periodic forcing with a spatially random forcing amplitude field are investigated. Quenched disorder is studied using the resonantly forced complex…
Generalized Navier-Stokes (GNS) equations describing three-dimensional (3D) active fluids with flow-dependent spectral forcing have been shown to possess numerical solutions that can sustain significant energy transfer to larger scales by…
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted…
We explore the near-resonant interaction of inertial waves with geostrophic modes in rotating fluids via numerical and theoretical analysis. When a single inertial wave is imposed, we find that some geostrophic modes are unstable above a…
In this paper, using multiple scale analysis we derive a generalized mathematical model for amplitude evolution, and for calculating the energy exchange in resonant and near-resonant global triads consisting of weakly nonlinear internal…
This study aims to explore the complex interactions between an internal solitary wave and an external force using the Benjamin-Ono equation as the theoretical framework. The investigation encompasses both asymptotic and numerical…
A fluid system is derived to describe electrostatic magnetized plasma turbulence at scales somewhat larger than the Larmor radius of a given species. It is related to the Hasegawa- Mima equation, but does not conserve enstrophy, and, as a…
A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…
Ocean motions at frequencies of the internal wave band are generally associated with freely propagating waves that are supported by stable vertical stratification in density. Previous analyses of yearlong current observations from the Bay…
Three-wave interactions form the basis of our understanding of many pattern forming systems because they encapsulate the most basic nonlinear interactions. In problems with two comparable length scales, it is possible for two waves of the…
We regard the Cauchy problem for a particular Whitham-Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. The system can be seen as a weak nonlocal dispersive perturbation of the shallow water system. The…
Interaction between atmospheric mid-latitude flow and wind-driven ocean circulation is studied coupling two idealized low-order spectral models. The barotropic Charney-DeVore model with three components simulates a bimodal mid-latitude…
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,…
In the high persistence regime of non-inertial active Brownian particles (ABP), polarization becomes a relevant dynamical field. Based on a recently proposed kinetic description for ABP, we derive Navier-Stokes-like equations for the…
One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose internal wave attractors in the large amplitude regime as a unique…
Starting from the classical formulation of the weak turbulence theory in a density stratified fluid, we derive a simplified version of the kinetic equation of internal gravity wave turbulence. This equation allows us to uncover scaling laws…