相关论文: Near-critical reflection of internal waves

The paper deals with the 2D gravity-capillary water waves equations in their Hamiltonian formulation, addressing the question of the nonlinear interaction of a plane wave with its reflection off a vertical wall. The main result is the…

This paper presents the second-order perturbation theory of the Navier-Stokes equations for free surface flows, with the wave amplitude considered as the perturbation parameter. Gravity-capillary surface waves in incompressible viscous…

Spiral waves in excitable media possess both wave-like and particle-like properties. When resonantly forced (forced at the spiral rotation frequency) spiral cores travel along straight trajectories, but may reflect from medium boundaries.…

This article is devoted to the proof of the well-posedness of a model describing waves propagating in shallow water in horizontal dimension $d=2$ and in the presence of a fixed partially immersed object. We first show that this…

Dispersive averaging effects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this…

The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of…

We study the defocusing energy-critical nonlinear wave equation in four dimensions. Our main result proves the stability of the scattering mechanism under random pertubations of the initial data. The random pertubation is defined through a…

This study investigates nonlinear gravity waves in the compressible atmosphere from the Earth's surface to the deep atmosphere. These waves are effectively described by Grimshaw's dissipative modulation equations which provide the basis for…

People have been familiar with the phenomenon of wave refraction for several centuries. Recently, a novel type of refraction, i.e., negative refraction, where both incident and refractory lines locate on the same side of the normal line,…

The problem of existence of stable nonlinear groups of gravity waves in deep water is revised by means of laboratory and numerical simulations with the focus on intense waves. Wave groups with steepness up to $A_{cr} \omega_m^2 /g \approx…

The problem of propagating nonlinear acoustic waves is considered; the solution to which, both with and without damping, having been obtained to-date starting from the Navier-Stokes-Duhem equations together with the continuity and thermal…

Two-dimensional periodic surface waves propagating under the combined influence of gravity and surface tension on water of finite depth are considered. Within the framework of small-amplitude waves, we find the exact solutions of the…

We prove decay estimates for solutions to non-isotropic linear systems of wave equations. The defining feature of these estimates is that they depend only on the commutation properties of the system with the scaling vector field. As…

We construct a simple analytic model for wall-bounded turbulence, containing only four adjustable parameters. Two of these parameters characterize the viscous dissipation of the components of the Reynolds stress-tensor and other two…

A problem of finding the linear theory satisfaction limits in propagation of the internal gravity waves is considered. It is evident that internal gravity waves excitation, propagation in actual practice is highly nonlinear phenomenon.…

The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…

Weakly-nonlinear waves in a layered waveguide with an imperfect interface (soft bonding between the layers) can be modelled using coupled Boussinesq equations. We assume that the materials of the layers have close mechanical properties, in…

The propagation of nonlinear waves in one dimensional space, unsteady and compressible flow in Darcy-type porous media is analyzed. It is assumed that the weak discontinuity propagate long the characteristic path using the characteristics…

This paper is concerned with the inflow problem for the one-dimensional compressible Navier-Stokes equations. For such a problem, F. M. Huang, A. Matsumura and X. D. Shi showed that there exists viscous shock wave solution to the inflow…

In this paper we address the stability of resonantly forced density waves in dense planetary rings. Already by Goldreich & Tremaine (1978) it has been argued that density waves might be unstable, depending on the relationship between the…