Nonlinear acoustic wave propagation with diffusion and relaxation

Aljabali, Eman (2020) Nonlinear acoustic wave propagation with diffusion and relaxation. Doctoral thesis, University of East Anglia.

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A sonic boom is the sound associated with the pressure shock wave generated by disturbances in the atmosphere that lead to rapid increases in pressure over a short time. This research considers the propagation of the finite-amplitude plane waveform involving a balance of nonlinear steepening and other physical dissipation mechanisms. These dissipation mechanisms include the effect of viscosity and molecular relaxation associated with the vibration of polyatomic molecules. When the shock is controlled solely by thermoviscous diffusion the disturbance is governed by Burgers’ equation. A comprehensive study is undertaken with the emphasis on shock position, amplitude and thickness. This study is concerned with the applications of the combined approaches of matched asymptotic expansions, Cole-Hopf transformation, the method of characteristics, and numerical schemes such as Fourier pseudo-spectral method and the fourth-order Runge-Kutta method. The augmented Burgers’ equation is used when thermoviscosity and relaxation processes are taken into account. An asymptotic analysis of the shock profile is conducted governing the cases of one and two relaxation modes. This analysis reached a descriptive classification of the shock structure based upon the variations in relaxation parameters. The numerical schemes are adopted to simulate the propagation through the relaxing medium, and comparisons are made with the asymptotic findings. Asymptotic predications of the shock thickness, which is controlled by various physical mechanisms, are presented and compared with numerical results.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Jennifer Whitaker
Date Deposited: 27 Feb 2020 17:29
Last Modified: 27 Feb 2020 17:29

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