Abstract
We present the experimental analysis of the instabilities generated on a large drop of liquid metal by a time-dependent magnetic field. The study is done exploring the range of tiny values of the control parameter (the ratio between the Lorentz forces and inertia) avoiding nonlinear effects. Two different instabilities break the symmetries generating spatial patterns that appear without a threshold for some specific frequencies (up to the experimental precision) and have been observed for parameter values two orders of magnitude lower than in previously published experiments [J. Fluid Mech. 239, 383 (1992)JFLSA70022-112010.1017/S0022112092004452]. One of the instabilities corresponds to a boundary condition oscillation that generates surface waves and breaks the azimuthal symmetry. The other corresponds to a parametric forcing through a modulation of the Lorentz force. The competition between these two mechanisms produces time-dependent patterns near codimension-2 points.
Highlights
The existence of nonlinear effects and instabilities is a key point on the dynamics of many natural, industrial, and even social processes [1]
Many different configurations have been analyzed: small containers shaken by vertical vibration [2], droplets driven by ultrasounds [3], small convective problems [4,5], colloidal droplets with electrical fields [6], or liquid metals with electric [7] or magnetic [8,9,10,11,12,13,14,15] fields
This last configuration is a particular case of a discipline, magnetohydrodynamics (MHD) [16], that studies the interaction between conducting fluids and magnetic fields and that is involved in a broad variety of fields: biophysics [17], crystal growth [18], metallurgy [19], heat transfer [20], geo- and astrophysics [21], plasma physics [22], and electrolysis [23]
Summary
The existence of nonlinear effects and instabilities is a key point on the dynamics of many natural, industrial, and even social processes [1]. Many different configurations have been analyzed: small containers shaken by vertical vibration [2], droplets driven by ultrasounds [3], small convective problems [4,5], colloidal droplets with electrical fields [6], or liquid metals with electric [7] or magnetic [8,9,10,11,12,13,14,15] fields. Other instabilities where no external currents are involved were neglected, pure MHD instabilities without a threshold have been proposed but in a different context [10] In this last case all the experiments up to now were done in a strongly nonlinear regime [8,9,11,12,13,14,15], a common feature of many of the examples cited above
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