Related papers: Wave topology brought to the coast

We study the effects of an uneven bottom on the internal wave propagation in the presence of stratification and underlying non-uniform currents. Thus, the presented models incorporate vorticity (wave-current interactions), geophysical…

The truncated Korteweg-De Vries (TKdV) system, a shallow-water wave model with Hamiltonian structure that exhibits weakly turbulent dynamics, has been found to accurately predict the anomalous wave statistics observed in recent laboratory…

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…

Long linear wave transformation in the basin of varying depth is studied for a case of a convex bottom profile in the framework of one-dimensional shallow water equation. The existence of travelling wave solutions in this geometry and the…

A Kolmogorov-type cascade of Kelvin waves--the distortion waves on vortex lines--plays a key part in the relaxation of superfluid turbulence at low temperatures. We propose an efficient numeric scheme for simulating the Kelvin wave cascade…

Wave turbulence is by nature a multiple time scale problem for which there is a natural asymptotic closure. The main result of this analytical theory is the kinetic equation that describes the long-time statistical behaviour of such…

Recent laboratory experiments of Bolles et al. (2019) demonstrate that an abrupt change in bottom topography can trigger anomalous statistics in randomized surface waves. Motivated by these observations, Majda et al. (2019) developed a…

A domain wall separating two different topological phases of the same crystal can support the propagation of backscattering-immune guided waves. In valley-Hall and quantum-Hall crystal waveguides, this property stems from symmetry…

An alternative way for the derivation of the new KdV-type equation is presented. The equation contains terms depending on the bottom topography (there are six new terms in all, three of which are caused by the unevenness of the bottom). It…

This work studies the problem of predicting the loads and motions induced by wave systems on a ship in forward motion (seakeeping). Assuming that the hull is rigid, the motion of the ship is described by the equations of rigid body…

In the context of topological insulators, the shallow-water model was recently shown to exhibit an anomalous bulk-edge correspondence. For the model with a boundary, the parameter space involves both longitudinal momentum and boundary…

We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom…

The article considers implications of tilt symmetry (symmetry with respect to tilting of the coordinate axis with respect to which vortex motion is studied) in the non-linear dynamics of Kelvin waves. The conclusion is that although the…

Energy transmission over long distances by waves is a key mechanism for many natural processes. This possibility arises when an inhomogeneous medium is arranged in such a manner that it enables a certain type of wave to propagate with…

The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…

On the basis of recently proposed scenario of the transformation of the Kolmogorov cascade into the Kelvin-wave cascade, we develop a theory of low-temperature cutoff. The theory predicts a specific behavior of the quantized vortex line…

Inertial waves in convective regions of stars exhibit topological properties linked to a Chern number of 1. The first of these is a unique, unidirectional, prograde oscillation mode within the cavity, which propagates at arbitrarily low…

The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…

The problem about a body in a three dimensional infinite channel is considered in the framework of the theory of linear water-waves. The body has a rough surface characterized by a small parameter $\epsilon>0$ while the distance of the body…

From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, new theories state that transitions between extreme waves are allowed. However, these have never been experimentally observed…