Nonlinear responses of sloshing based on the shallow water wave theory.

Experiments on the synchronous sloshing in suspended containers described by shallow-water theory

The synchronous interaction between a sloshing fluid and its container may take place when the motion of the container is not prescribed a priori. When a partially-filled container is suspended as a bifilar pendulum, the fluid contributes to the restoring force by its weight through the wire suspensions and may either augment or diminish the restoring force through hydrodynamic interaction with...

Nonlinear edge waves and shallow-water theory

Exact Solutions of the Nonlinear Generalized Shallow Water Wave Equation

Submitted: Nov 12, 2013; Accepted: Dec 18, 2013; Published: Dec 22, 2013 Abstract: In this article, we have employed an enhanced (G′/G)-expansion method to find the exact solutions first and then the solitary wave solutions of the nonlinear generalized shallow water wave equation. Here we have derived solitons, singular solitons and periodic wave solutions through the enhanced (G′/G)-expansion ...

Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory

We derive an asymptotic formula for the amplitude distribution in a fully nonlinear shallow-water solitary wave train which is formed as the long-time outcome of the initial-value problem for the Su-Gardner (or one-dimensional Green-Naghdi) system. Our analysis is based on the properties of the characteristics of the associated Whitham modulation system which describes an intermediate “undular ...

Analytical Solution for Nonlinear Shallow-water Wave Equations

Majority of the hodograph transform solutions of the one-dimensional nonlinear shallow-water wave equations are obtained through integral transform techniques. This approach, however, might involve evaluation of elliptic integrals, which are highly singular. Here, we couple the hodograph transform approach with the classical eigenfunction expansion method rather than integral transform techniqu...