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The Westervelt equation describes the propagation of pressure waves in continuous nonlinear and, eventually, diffusive media. The classical framework of this equation corresponds to fluid dynamics theory. This work seeks to connect this…
In this Part 2 we study further experimental properties of two-layer exchange flows in a stratified inclined duct (SID), which are turbulent, strongly-stratified, shear-driven, and continuously-forced. We analyse the same state-of-the-art…
We study a 2D potential flow of an ideal fluid with a free surface with decaying conditions at infinity. By using the conformal variables approach, we study a particular solution of Euler equations having a pair of square-root branch points…
Direct phase-resolved simulations are performed to investigate the propagation and scattering of nonlinear ocean waves in fragmented sea ice. The numerical model solves the full time-dependent equations for nonlinear potential flow coupled…
An incremental wave superimposed on a pre-deformed hyper-elastic material perceives an elastic media with the instantaneous modulus of the current material. This offers a new route with a broadband feature to control elastic waves by…
In this paper, we are interested in studying the modulational dynamics of interfacial waves rising buoyantly along a conduit of a viscous liquid. Formally, the behavior of modulated periodic waves on large space and time scales may be…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…
This paper develops a mathematical framework for interpreting observations of solar inertial waves in an idealized setting. Under the assumption of purely toroidal linear waves on the sphere, the stream function of the flow satisfies a…
The electromagnetic modes and the resonances of homogeneous, finite size, two-dimensional bodies are examined in the frequency domain by a rigorous full wave approach based on an integro-differential formulation of the electromagnetic…
In this article, we introduce a moving-frame approach to the geophysical equation of two-dimensional uniformly stratified rotational fluid in oceans and find a family of exact solutions containing ten arbitrary parameter functions.
We investigate the behavior of the solutions of the ray equation in isotropic media. We discuss local and global transversals and wavefronts and give examples of rays without wavefronts.
A central mechanism of linearised two dimensional shear instability can be described in terms of a nonlinear, action-at-a-distance, phase-locking resonance between two vorticity waves which propagate counter to their local mean flow as well…
Wrinkling instabilities of thin elastic sheets can be used to generate periodic structures over a wide range of length scales. Viscosity of the thin elastic sheet or its surrounding medium has been shown to be responsible for dynamic…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
In this paper we construct periodic capillarity-gravity water waves with a piecewise constant vorticity distribution. They describe water waves traveling on superposed linearly sheared currents that have different vorticities. This is…
We theoretically investigate the interplay between magnetohydrodynamic (MHD) waves and shear flows in a partially ionized solar plasma, focusing on the energy exchange mediated by the flow and the transformation between wave modes. We…
Wave propagation in one-dimensional heterogeneous bistable media is studied using the Schl\"ogl model as a representative example. Starting from the analytically known traveling wave solution for the homogeneous medium, infinitely extended,…
Refraction is the predominant mechanism causing spatially inhomogeneous surface gravity wave fields. However, the complex interplay between depth- and current-induced wave refraction remains poorly understood. Assuming weak currents and…
In this study, a new set of fifth-order Stokes wave solutions, incorporating the effects of a linear shear current, is derived by utilizing the perturbation method originally proposed for pure waves that was recently published. The present…