Related papers: A consistent phase-averaged model of the interacti…
The derivation of shallow water models from Navier-Stokes equations is revisited yielding a class of two-layer shallow water models.An improved velocity profile is proposed, based on the superposition of an ideal fluid and a viscous layer…
The interaction of surface waves with Couette-type current with uniform vorticity is a well suited problem for students approaching the theory of surface waves. The problem, although mathematically simple, contains rich physics, and is…
The currents in the ocean have a serious impact on ocean dynamics, since they affect the transport of mass and thus the distribution of salinity, nutrients and pollutants. In many physically important situations the current depends…
We examine a two-media 2-dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface with wind generated surface waves but considered bounded above by a lid by an assumption…
In this paper we consider two-dimensional, stratified, steady water waves propagating over an impermeable flat bed and with a free surface. The motion is assumed to be driven by capillarity (that is, surface tension) on the surface and a…
We investigate the weakly nonlinear dynamics of transient gravity waves at infinite depth under the influence of a shear current varying linearly with depth. An analytical solution is permitted via integration of the Euler equations.…
The refraction of surface gravity waves by currents leads to spatial modulations in the wave field and, in particular, in the significant wave height. We examine this phenomenon in the case of waves scattered by a localised current feature,…
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…
A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a…
Modeling ocean surface waves under complex ocean current conditions is of crucial importance to many naval applications. For example, traveling ships and underwater vehicles generate spatially heterogeneous currents behind them through…
A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…
Two-dimensional nonlinear gravity waves travelling in shallow water on a vertically sheared current of constant vorticity are considered. Using Euler equations, in the shallow water approximation, hyperbolic equations for the surface…
The aim of this work is to investigate the interaction of gravity-capillary waves resonantly excited by two moving disturbances along the free surface. The problem is formulated using the full Euler equations and numerical computations are…
We study dispersion properties of linear surface gravity waves propagating in an arbitrary direction atop a current profile of depth-varying magnitude using a piecewise linear approximation, and develop a robust numerical framework for…
Finite-amplitude gravity waves at the air-water interface induce net fluid and particle transport, known as Stokes drift. While this mechanism is well understood for steady waves, transport under unsteady, evolving conditions remains poorly…
This paper explores an idealized model of the ocean surface in which widely separated surface-wave packets and point vortices interact in two horizontal dimensions. We start with a Lagrangian which, in its general form, depends on the…
A model for internal interfacial waves between two layers of fluid in the presence of current and variable bottom is studied in the flat-surface approximation. Fluids are assumed to be incompressible and inviscid. Another assumption is that…
The acoustic waves generated by moving bodies and the movement of bodies by acoustic waves are central phenomena in the operation of musical instruments and in everyday's experiences like the movement of a boat on a lake by the wake…
Some data of the drift current, Ud, measured on a wavy surface of water in a laboratory and the field, are briefly described. Empirical formulas for Ud are given, and their incompleteness is noted, regarding to absence of the drift current…
Irrotational and monochromatic surface gravity waves possess a mean Lagrangian drift which transports mass and enhances mixing in the upper ocean. In the ocean, where many surface waves are present, it is commonly assumed that the mean…