Resonant surface waves and chaotic phenomena

Abstract

Surface waves in a rectangular container subjected to vertical oscillations are studied. Effects of energy dissipation along the lines of Miles (1967) and the effect of surface tension are included. Sufficient conditions, for two modes to dominate the motion, are given. The analysis is along the lines of Miles (1984a) and Holmes (1986). A complete bifurcation analysis is performed, and the modal amplitudes and phases are shown to have chaotic behaviour. This result is obtained under assumptions different from those of Holmes (1986). The conclusions regarding chaotic motions are based on a theorem of šilnikov (1970).

Simulation of sloshing motions in fixed and vertically excited containers using a 2-D inviscid σ-transformed finite difference solver

“…It has been established that there is a critical liquid depth that delineates two nonlinear regimes of the liquid free surface referred to as soft and hard spring characteristics. Gu and Sethna (1987), Gu et al (1988) and Virnig et al (1988) have examined the role of the liquid critical depth in rectangular tanks subjected to vertical sinusoidal excitation. Another important feature is that there is an excitation frequency range over which the free surface exhibits chaotic motion (Ibrahim et al, 2001).…”

Weakly nonlinear theory for oscillating wave surge converters in a channel

“…Li & Mei (2006) have developed a nonlinear theory to analyse the subharmonic resonance of trapped surface waves around a fixed cylinder while Lichter & Chen (1987) analysed the resonance of nonlinear cross-waves in a long channel. A similar subharmonic mechanism has been analysed for the so-called 'Faraday resonance': for the main contributions we refer to Miles (1984a), Holmes (1986), Gu & Sethna (1987) and Miles & Henderson (1990). Of considerable engineering interest is the case of mobile neighbouring gates to protect Venice from flooding.…”

Sloshing motions in excited tanks

“…It has been established that there is a critical liquid depth that delineates two non-linear regimes of the liquid free surface referred to as soft and hard spring characteristics. Gu and Sethna [19], Gu et al [20], Virnig et al [40] have examined the role of the liquid critical depth in rectangular tanks subjected to vertical sinusoidal excitation. Another important feature is that there is an excitation frequency range over which the free surface exhibits chaotic motion [23].…”