Preprint Article Version 1 This version is not peer-reviewed

Evidence of Landau Damping in a Fluid Coupled with an Anharmonic Lattice

Version 1 : Received: 13 November 2018 / Approved: 15 November 2018 / Online: 15 November 2018 (05:43:52 CET)

How to cite: Ludu, A.; Padilla, E.; Mazumder, M.A.Q. Evidence of Landau Damping in a Fluid Coupled with an Anharmonic Lattice. Preprints 2018, 2018110345 (doi: 10.20944/preprints201811.0345.v1). Ludu, A.; Padilla, E.; Mazumder, M.A.Q. Evidence of Landau Damping in a Fluid Coupled with an Anharmonic Lattice. Preprints 2018, 2018110345 (doi: 10.20944/preprints201811.0345.v1).

Abstract

The Landau damping effect was observed in collisionless plasma, as a microscopic resonant mechanism between electromagnetic radiation and the collective modes. In this paper we demonstrate the occurrence of the Landau damping at macroscopic scale in the interaction between water waves and anharmonic lattice of magnetic buoys. By coupling the Navier-Stokes equations for incompressible fluid with the nonlinear dynamics of an anharmonic magnetic lattice we obtain a resonant transfer of momentum and energy between the two systems. The velocity of the flow is obtained in the Stokes approximation with Basset type of drag force. The dynamics of the buoys is calculated in the surfactant approximation for a specific frequency, then we use Fourier analysis to obtain the general time variable interaction. After involving an integral Dirichlet transform we obtain the time dependent expression of the drag force, the interaction waves-lattice with a new term in the form of a Caputo fractional derivative. We compare the results of the model with experiments performed in a wave tank with free floating magnetic buoys under the action of small amplitude gravitational waves. This configuration can be applied in studies for the attenuation with resonant damping of rogue waves, storms or tsunamis.

Subject Areas

Landau damping; resonant transfer; anharmonic lattice; nonlinear waves; collective modes; gravity waves; Stokes flow; Basset drag force; surfactant approximation; fractional derivative; anharmonic

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