Volume 135, Number 3, August 2021
|Number of page(s)||6|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||14 October 2021|
Anisotropy in Faraday instabilities of a shallow conducting fluid
Department of Applied Mathematics, University of Waterloo - Waterloo, ON, Canada, N2L 3G1
Received: 27 May 2021
Accepted: 23 July 2021
In this work, we study the impact of temporally varying gravity on an idealized shallow conducting fluid with a free surface. We formulate the problem in terms of the shallow magnetohydrodynamic (SMHD) equations which allows the study of the resulting anisotropy in the context of a Faraday instability. We simplify the linear stability problem into a Mathieu equation by assuming gravity is periodic in time. Using the existing theory of Mathieu's equation, we find that anisotropy occurs, with wave vectors parallel to the imposed magnetic field stabilized. We describe the regions of instability in wave number space.
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