Related papers: Shallow water models for stratified equatorial flo…
Diffusion-driven flow is a boundary layer flow arising from the interplay of gravity and diffusion in density-stratified fluids when a gravitational field is non-parallel to an impermeable solid boundary. This study investigates…
This paper is devoted to study the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the…
A novel geometric method is applied to the problem of describing traveling wave solutions of the generalized Korteweg--de Vries (gKdV) equation in the form $$ u_t + u_{xxx} + a(u)u_x = 0, $$ where $a(u)$ is a smooth function characterizing…
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…
In this work an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave solutions expressible in terms of quasi-periodic…
Partially invariant solution to (2+1)D shallow water equation is constructed and investigated. The solution describes an extension of a stripe, bounded by linear source and drain of fluid. Realizations of smooth flow and of hydraulic jump…
We use a Hamiltonian normal form approach to study the dynamics of the water wave problem in the small amplitude long wave regime (KdV regime). If $\mu$ is the small parameter corresponding to the inverse of the wave length, we show that…
Spatially-explicit estimates of population density, together with appropriate estimates of uncertainty, are required in many management contexts. Density Surface Models (DSMs) are a two-stage approach for estimating spatially-varying…
We present experimental and computational studies of the propagation of internal waves in a stratified fluid with an exponential density profile that models the deep ocean. The buoyancy frequency profile $N(z)$ (proportional to the square…
The mild-slope equation and its various modifications aim to model, with varying degrees of success, linear water wave propagation over sloping or undulating seabed topography. However, despite multiple modifications and attempted…
We suggested a one-fluid model of a turbulent dilute suspension which accounts for the ``two-way'' fluid-particle interactions by $k$-dependent effective density of suspension and additional damping term in the Navier-Stokes equation. We…
The authors of the paper "The third-order perturbed Korteweg-de Vries equation for shallow water waves with a non-flat bottom" [1] claim that they have derived the full third order perturbed KdV equation for the case of uneven bottom. We…
The gravity-driven spreading of one fluid in contact with another fluid is of key importance to a range of topics. To describe these phenomena, the two-layer shallow-water equations is commonly employed. When one layer is significantly…
In this paper we use the short-wavelength instability approach to derive an instability threshold for exact trapped equatorial waves propagating eastwards in the presence of an underlying current.
The KdV equation models the propagation of long waves in dispersive media, while the NLS equation models the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves. A system that couples the two equations to model…
This paper considers the propagation of shallow-water solitary and nonlinear periodic waves over a gradual slope with bottom friction in the framework of a variable-coefficient Korteweg-de Vries equation. We use the Whitham averaging…
We consider travelling internal waves in a two-layer fluid with linear shear currents from the viewpoint of the extended Korteweg-de Vries (eKdV) equation derived from a strongly-nonlinear long-wave model. Using an asymptotic…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
We present a review of the normal form theory for weakly dispersive nonlinear wave equations where the leading order phenomena can be described by the KdV equation. This is an infinite dimensional extension of the well-known…