Related papers: Modeling shallow water waves
We presented numerical simulation of long waves, interacting with arrays of emergent cylinders inside regularly spaced patches, representing discontinues patchy coastal vegetation. We employed the fully nonlinear and weakly dispersive…
In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models were formally derived in the literature. The idea, coming from G.…
The general equations of motion for ocean dynamics are presented and the waves supported by the (inviscid, unforced) linearized system with respect to a state of rest are derived. The linearized dynamics sustains one zero frequency mode…
We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is…
We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equations which combine the dispersion relation of water waves and the nonlinear shallow water equations, and which generalize the Whitham…
We propose a shallow water model which combines the dispersion relation of water waves and the Boussinesq equations, and which extends the Whitham equation to permit bidirectional propagation. We establish that its sufficiently small,…
The fully nonlinear and weakly dispersive Green-Naghdi model for shallow water waves of large amplitude is studied. The original model is first recast under a new formulation more suitable for numerical resolution. An hybrid finite volume…
In 1982, Marshall P. Tulin published a report proposing a framework for reducing the equations for gravity waves generated by moving bodies into a single nonlinear differential equation solvable in closed form [Proc. 14th Symp. on Naval…
The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying…
Recent theoretical progress using multiscale asymptotic analysis has revealed various possible regimes of stratified turbulence. Notably, buoyancy transport can either be dominated by advection or diffusion, depending on the effective…
In this paper, we discuss the incorporation of dynamic subgrid scale (SGS) models in the lattice-Boltzmann method (LBM) for large-eddy simulation (LES) of turbulent flows. The use of a dynamic procedure, which involves sampling or…
Turbulence and large-scale waves in the tropical region are studied using the spherical shallow water equations. With mesoscale vorticity forcing, both moist and dry systems show kinetic energy scaling that is dominated by rotational modes,…
The simulation of long, nonlinear dispersive waves in bounded domains usually requires the use of slip-wall boundary conditions. Boussinesq systems appearing in the literature are generally not well-posed when such boundary conditions are…
We develop a weakly nonlinear model to study the spatiotemporal manifestation and the dynamical behavior of surface waves in the presence of an underlying interfacial solitary wave in a two-layer fluid system. We show that interfacial…
The objective of this three-part work is to formulate and rigorously analyse a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled surface…
In this article, we derive a viscous Boussinesq system for surface water waves from Navier-Stokes equations. We use neither the irrotationality assumption, nor the Zakharov-Craig-Sulem formulation. During the derivation, we find the bottom…
Our aim is to study the effect of a continuous prescribed density variation on the propagation of ocean waves. More precisely, we derive KdV-type shallow water model equations for unidirectional flows along the Equator from the full…
This paper presents a novel methodology for the direct numerical modeling and simulation of turbulent flows. The kinetic model equation is firstly extended to turbulent flow with the account of coupled evolution of kinetic, thermal, and…
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 development of turbulence closure models, parametrizing the influence of small non-resolved scales on the dynamics of large resolved ones, is an outstanding theoretical challenge with vast applicative relevance. We present a closure,…