Abstract
The aim of the present paper is to examine the effect of the vertical quasiperiodic oscillations on the stability of the free surface of an ideal horizontal liquid layer. The quasiperiodic motion considered here is characterized by two incommensurate frequencies ω1 and ω2. The governing system of equations is reduced to a quasiperiodic Mathieu equation. In this situation, using the harmonic balance method developed by Rand et al. [10, 11] and Hill’s determinants, we determine the marginal stability curves. We show that the quasiperiodic excitation produces a stabilizing or a estabilizing effect and is strongly depending on the ratio of the frequencies.
Highlights
The aim of the present paper is to examine the effect of the vertical quasiperiodic oscillations on the stability of the free surface of an ideal horizontal liquid layer
The Faraday instability is a parametric generation of standing waves on the free surface of a liquid subjected to vertical vibrations
The linear stability analysis of the Faraday instability on an arbitrarily deep layer of a viscous fluid has been performed by Kumar and Tuckerman [8] and a discussion on the mechanism of the wave number selection in the Faraday instability on high−viscous fluids have been done by Kumar [9]
Summary
The Faraday instability is a parametric generation of standing waves on the free surface of a liquid subjected to vertical vibrations. This phenomenon has been studied by Faraday [1]. The problem was investigated by Matthiessen [2, 3]. He has found in his experiment that the vibrations were synchronous. A detailed experimental study of the various patterns on a viscous fluid has been performed by Edwards and Fauve [7] who have used oscillations with one frequency as well as oscillations with two frequency.
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