相关论文: Towards eliminating the nonlinear Kelvin wake
Lord Kelvin's result that waves behind a ship lie within a half-angle 19 deg 28' is perhaps the most famous and striking result in the field of surface waves. We solve the linear ship wave problem in the presence of a shear current of…
We study numerically the evolution of perturbed Korteweg-de Vries solitons and of well localized initial data by the Novikov-Veselov (NV) equation at different levels of the "energy" parameter $ E $. We show that as $ |E| \to \infty $, NV…
We study the 3D forced-dissipated Gross-Pitaevskii equation. We force at relatively low wave numbers, expecting to observe a direct energy cascade and a consequent power-law spectrum of the form $k^{-\alpha}$. Our numerical results show…
We explore the dynamical response of the free surface of an ultra-soft solid driven by a localized moving pressure disturbance. Experiments reveal a steady V-shaped wake analogous to a surface Mach wedge. A simple geometric argument…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
We derive a scheme by which to solve the Liouville equation perturbatively in the nonlinearity, which we apply to weakly nonlinear classical field theories. Our solution is a variant of the Prigogine diagrammatic method, and is based on an…
This paper investigates the critical quintic wave equation in a 3D bounded domain subject to locally distributed Kelvin-Voigt damping. The study tackles two major mathematical challenges: the severe loss of derivatives induced by the…
We present evidence of Kelvin excitations in space-time resolved spectra of numerical simulations of quantum turbulence. Kelvin waves are transverse and circularly polarized waves that propagate along quantized vortices, for which the…
In recent papers, denoted by MG24, MG25 in this text, we used the Korteweg-de Vries (KdV) equation and its two-dimensional extension, the Kadomtsev-Petviashvili (KP) equation to describe the evolution of wind-driven water wave packets in…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
We study the stability and dynamics of solitons in the Korteweg-de Vries (KdV) equation in the presence of noise and deterministic forcing. The noise is space-dependent and statistically translation-invariant. We show that, for small…
A forced KdV equation is derived to describe weakly nonlinear, shallow water surface wave propagation over non trivial bottom boundary condition. We show that different functional forms of bottom boundary conditions self-consistently…
We analyze theoretically and experimentally the wake behind a horizontal cylinder of diameter $d$ horizontally translated at constant velocity $U$ in a fluid rotating about the vertical axis at a rate $\Omega$. Using particle image…
The Kadomtsev-Petviashvili (KP) equation describes weakly dispersive and small amplitude waves propagating in a quasi-two dimensional situation. Recently a large variety of exact soliton solutions of the KP equation has been found and…
Kelvin waves (kelvons)--the distortion waves on vortex lines--play a key part in the relaxation of superfluid turbulence at low temperatures. We present a weak-turbulence theory of kelvons. We show that non-trivial kinetics arises only…
We consider a problem of stability of a membrane of an infinite span and a finite chord length, submerged in a uniform flow of finite depth with free surface. In the shallow water approximation, Nemtsov (1985) has shown that an…
A localised overpressure translating at a uniform speed greater than a critical value acts at the interface between two deep fluid layers with different densities. We analyse the resulting wave patterns using an initial-value problem…
We present an experimental realisation of spatial spanwise forcing in a turbulent boundary layer flow, aimed at reducing the frictional drag. The forcing is achieved by a series of spanwise running belts, running in alternating spanwise…
A new model for Korteweg and de-Vries equation (KdV) is derived. The system under study is an open channel consisting of two concentric cylinders, rotating about their vertical axis, which is tilted by slope {\tau} from the inertial…
Origin of hydrodynamical instability and turbulence in the Keplerian accretion disc as well as similar laboratory shear flows, e.g. plane Couette flow, is a long standing puzzle. These flows are linearly stable. Here we explore the…