In this paper a Godunov-type projection method for computing approximate solutions of the zero Froude number (incompressible) shallow water equations is presented. It is second-order accurate and locally conserves height (mass) and momentum. To enforce the underlying divergence constraint on the velocity field, the predicted numerical fluxes, computed with a standard second order method for hyp...

Consideration is given to slow interfacial dynamics in a two-layer system of viscous fluids of comparable density. The fluid flow is governed by the two-dimensional Navier–Stokes equations where it is assumed that the inertial terms can be disregarded. A numerical methodology is presented which allows the study of the dynamics in the nonlinear regime. The numerical method is based on rewriting ...

A hydraulic jump is a flow singularity characterised by a significant amount of air entrainment in the shear zone. The air is entrapped at the jump toe that is a discontinuity between the impinging flow and the roller. The impingement point is a source of air bubbles, as well as a source of vorticity. Herein the convective transport of air bubbles in the jump roller is re-visited. Some analytic...

A forced Korteweg–de Vries (fKdV) equation can be used to model the surface wave of a twodimensional water flow over a bump when the upstream Froude number is near one. The fKdV model typically has four types of solutions: sub-critical cnoidal waves, sub-critical hydraulic fall, transcritical upstream soliton radiation, and supercritical multiple solitary waves. This paper provides a numerical ...

This paper provides a theoretical description of the 3-dimensional flow produced by a surface pressure distribution moving in a channel at speeds such that the Froude number based on depth is near 1. The transient flow begins in a fully 3-dimensional manner, then focuses away from the distribution, due to the side walls, into predominantly 2-dimensional "solitary" or "cnoidal" waves. Two sets o...

The flow generated by a sphere descending uniformly in a linearly stratified diffusive fluid is investigated numerically for different Reynolds (Re) and Froude (F ) numbers. The parameters used for the simulations were 10 ≤ Re ≤ 10 and 10 ≤ F ≤ 10, keeping the Schmidt number, Sc (= 700, typical of sea water) fixed. The results demonstrate drag dependence on viscosity and stratification, suggest...

In previous work, we investigated two-dimensional steady gravity-capillary waves generated by a localized pressure distribution moving with constant speed U in water of finite depth h . Localized solitary waves can only exist in subcritical flows where the Froude number F = U/(gh) < 1 , and were found using a combination of numerical simulations of the fully nonlinear inviscid, irrotational equ...

We consider the Euler equations describing nonlinear waves on the free surface of a twodimensional inviscid, irrotational fluid layer of finite depth. For large surface tension, Bond number larger than 1=3, and Froude number close to 1, the system possesses a one-parameter family of small-amplitude, traveling solitary wave solutions. We show that these solitary waves are spectrally stable with ...