相关论文: Instability of large solitary water waves

We derive analytical formulas for the wake and wave drag of a disturbance moving arbitrarily at the air-water interface. We show that, provided a constant velocity is reached in finite time, the unsteady surface displacement converges to…

We present a method to prove nonlinear instability of solitary waves in dispersive models. Two examples are analyzed: we prove the nonlinear long time instability of the KdV solitary wave (with respect to periodic transverse perturbations)…

A mechanism of excitation of the large-scale inertial waves in a rotating inhomogeneous turbulence due to an excitation of a large-scale instability is found. This instability is caused by a combined effect of the inhomogeneity of the…

We investigate the existence of solitary gravity waves traversing a two-dimensional body of water that is bounded below by a flat impenetrable ocean bed and above by a free surface of constant pressure. Our main interest is constructing…

The study of the Euler equations in flows with constant vorticity has piqued the curiosity of a considerable number of researchers over the years. Much research has been conducted on this subject under the assumption of steady flow. In this…

We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…

The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional…

Observations show that maximally-steep breaking water wave crest speeds are much slower than expected. We report a wave-crest slowdown mechanism generic to unsteady propagating deep water wave groups. Our fully nonlinear computations show…

Here we show that there exist internal gravity waves that are inherently unstable, that is, they cannot exist in nature for a long time. The instability mechanism is a one-way (irreversible) harmonic-generation resonance that permanently…

We present a large-amplitude existence theory for two-dimensional solitary waves propagating through a two layer body of water. The domain of the fluid is bounded below by an impermeable flat ocean floor and above by a free boundary at…

We obtain the most general matrix criterion for stability and instability of multi-component solitary waves considering a system of $N$ incoherently coupled nonlinear Schrodinger equations. Soliton stability is studied as a constrained…

The $2$D Benney-Luke equation is an isotropic model which describes long water waves of small amplitude in $3$D whereas the KP-II equation is a unidirectional model for long waves with slow variation in the transverse direction. In the case…

We study the motion of an interface between two irrotational, incompressible fluids, with elastic bending forces present; this is the hydroelastic wave problem. We prove a global bifurcation theorem for the existence of families of…

This paper presents a comprehensive analysis of two-dimensional water waves characterized by a significant adverse constant vorticity over flows without stagnation points. Surprisingly, we discover qualitative distinctions between this…

This paper investigates the stability of traveling wave solutions to the free boundary Euler equations with a submerged point vortex. We prove that sufficiently small-amplitude waves with small enough vortex strength are conditionally…

Integral constraints on the linear instability of stratified parallel flow with planar shear at an arbitrary angle to the vertical are derived using the analytical approach of Miles and Howard, for perturbations with 2D spatial structure,…

Coherent structures, such as solitary waves, appear in many physical problems, including fluid mechanics, optics, quantum physics, and plasma physics. A less studied setting is found in geophysics, where highly viscous fluids couple to…

We determine the modulational stability of standing waves with small group velocity in quasi-onedimensional systems slightly above the threshold of a supercritical Hopf bifurcation. The stability limits are given by two different…

The wave instability acts in astrophysical plasmas to redistribute energy and momentum in the absence of frequent collisions. There are many different types of waves, and it is important to quantify the wave energy density and growth rate…

This paper sheds new light on the stability properties of solitary wave solutions associated with models of Korteweg-de Vries and Benjamin\&Bona\&Mahoney type, when the dispersion is very lower. Via an approach of compactness, analyticity…