Related papers: Steady water waves with multiple critical layers: …
In this article, we mainly investigate the properties of vertical velocity v for two dimensional steady water waves over a flat bed. Firstly we prove the existence of the inflection point for each streamline, then we find the behavior of v…
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…
We consider steady surface waves in an infinitely deep two--dimensional ideal fluid with potential flow, focusing on high-amplitude waves near the steepest wave with a 120 degree corner at the crest. The stability of these solutions with…
We investigate hydrodynamic fluctuations in a 2D granular fluid excited by a vibrating base and in the presence of gravity, focusing on the transverse velocity modes. Since the system is inhomogeneous, we measure fluctuations in horizontal…
We investigate the linearized hydrodynamic equations of interacting self-propelled particles in two dimensional space. It is found that the small perturbations of density and polarization fields satisfy the hyperbolic partial differential…
We provide analytic solutions of the nonlinear differential equation system describing the particle paths below small-amplitude periodic gravity waves travelling on a constant vorticity current. We show that these paths are not closed…
In oceans, multiple energetic inertia-gravity waves often coexist in a region. In this paper, we study the stability of two coexisting plane inertia-gravity waves (hereafter, primary waves), with the same frequencies ($\omega_1$) and…
In this paper, we study two-dimensional traveling waves in finite-depth water that are acted upon solely by gravity. We prove that, for any supercritical Froude number (non-dimensionalized wave speed), there exists a continuous…
Waves with constant vorticity and electrohydrodynamics flows are two topics in fluid dynamics that have attracted much attention from scientists for both the mathematical challenge and their industrial applications. The coupling of electric…
Rotating waves are a fascinating feature of a wide array of complex systems, particularly those arising in the study of many chemical and biological processes. With many rigorous mathematical investigations of rotating waves relying on the…
We study travelling waves on a two--dimensional lattice with linear and nonlinear coupling between nearest particles and a periodic nonlinear substrate potential. Such a discrete system can model molecules adsorbed on a substrate crystal…
A previously unknown instability creates space-filling lattices of 3D vortices in linearly-stable, rotating, stratified shear flows. The instability starts from an easily-excited critical layer. The layer intensifies by drawing energy from…
We study large traveling surface waves within a two-dimensional finite depth, free boundary, homogeneous, incompressible and viscous fluid governed by Darcy's law. The fluid is bound by a gravitational force to a flat rigid bottom and meets…
In this work, we study the nonlinear traveling waves in density stratified fluids with depth varying shear currents. Beginning the formulation of the water-wave problem due to [1], we extend the work of [4] and [18] to examine the interface…
The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output…
We study the long time evolution of internal waves in two dimensional subcritical channels with flat horizontal ends. We show the leading profiles of solutions are the outgoing solutions to the stationary equations. This is done by showing…
In this paper we consider fundamental processes of the disturbance and propagation of internal gravity waves in the ocean modeled as a vertically stratified, horizontally non-uniform, and non-stationary medium. We develop asymptotic methods…
We numerically study the scattering coefficients of linear water waves on stationary flows above a localized obstacle. We compare the scattering on trans- and subcritical flows, and then focus on the latter which have been used in recent…
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…
The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…