Evolution of Nonlinear Sloshing in a Tank Near Half the Fundamental Resonance

Abstract

This article describes the evolution of shallow water waves in a tank that is closed at one end and is periodically forced at half the fundamental frequency at the other end. The nonlinear response occurs at the same order as the linear response and is governed by a forced Korteweg–de Vries (K dV) equation. Unlike the corresponding problem for a gas (or the hydraulic limit), there may be nonperiodic (beating) solutions and multiple steady solutions for the same frequency. The addition of a component at the fundamental frequency to the piston input can be used to cancel the nonlinear effects and leave only the linear response in the steady state.