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Reflection and Refraction of Finite Amplitude Acoustic Waves at a Fluid- Fluid Interface

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Doctoral thesis

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A theoretical investigation is presented of the nonlinear effects in reflection and refraction of plane finite-amplitude acoustic waves at an initially plane interface between two lossless fluids. In the first part, the terms in the equations of motion for a homogeneous, thermoviscous fluid with a single relaxation mechanism are rank ordered to determine the most important nonlinear and dissipation terms. The equations are then combined to form a general wave equation that includes the most important effects of nonlinearity and dissipation. In the second part, the terms in the boundary conditions between two lossless fluids are rank ordered to include the most important nonlinear effects. Subject to these boundary conditions, a solution of the lossless form of the aforementioned wave equation is obtained by way of second order perturbation expansion. The lossless form of the wave equation and the lossless boundary conditions are expanded, and the O epsilon and O epsilon- sq systems are solved in terms of a modified velocity potential. The analysis is performed for oblique incidence, and the boundary condition at the source is arbitrary. Effects examined include the finite displacement of the interface and the variation of the direction of the normal to the interface, both of which are caused by the motion of the interface as it responds to the incident sound. In the third part, two different modified forms of Snells law for the special case of simple wave flow are derived one by matching the trace velocities at the interface and one by matching the variation of the pressure along the interface. It is shown, however, that to Oepsilon-sq, both reduce to ordinary Snells law and a condition necessary for simple wave flow.

Subject Categories:

  • Acoustics
  • Fluid Mechanics

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