An Integrablemodel Forundular Bores on Shallow Water
نویسنده
چکیده
On the basis of the integrable Kaup-Boussinesq version of the shallow water equations, an analytical theory of undular bores is constructed. The problem of the decay of an initial discontinuity is considered.
منابع مشابه
Integrable Shallow-Water Equations and Undular Bores
On the basis of the integrable Kaup–Boussinesq version of the shallow-water equations, an analytical theory of undular bores is constructed. A complete classification for the problem of the decay of an initial discontinuity is made.
متن کاملJa n 20 06 Unsteady undular bores in fully nonlinear shallow - water theory
We consider unsteady undular bores for a pair of coupled equations of Boussinesq-type which contain the familiar fully nonlinear dissipationless shallow-water dynamics and the leading-order fully nonlinear dispersive terms. This system contains one horizontal space dimension and time and can be systematically derived from the full Euler equations for irrotational flows with a free surface using...
متن کاملTranscritical shallow-water flow past topography: finite-amplitude theory
We consider shallow-water flow past a broad bottom ridge, localized in the flow direction, using the framework of the forced Su–Gardner (SG) system of equations, with a primary focus on the transcritical regime when the Froude number of the oncoming flow is close to unity. These equations are an asymptotic long-wave approximation of the full Euler system, obtained without a simultaneous expansi...
متن کاملA dispersive model for undular bores
In this article, consideration is given to weak bores in free-surface flows. The energy loss in the shallow-water theory for an undular bore is thought to be due to upstream oscillations that carry away the energy lost at the front of the bore. Using a higher-order dispersive model equation, this expectation is confirmed through a quantitative study which shows that there is no energy loss if d...
متن کاملWave Breaking and the Generation of Undular Bores in an Integrable Shallow Water System
The generation of an undular bore in the vicinity of a wave-breaking point is considered for the integrable Kaup–Boussinesq (KB) shallow water system. In the framework of the Whitham modulation theory, an analytic solution of the Gurevich–Pitaevskii type of problem for a generic “cubic” breaking regime is obtained using a generalized hodograph transform, and a further reduction to a linear Eule...
متن کامل