Faraday Instabilities

Yu, Rui

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Faraday Instabilities

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The shape of a liquid's surface is determined by both the body force and surface force of the liquid. In this report, the body force is solely from the gravitational force. The surface force is generated from the movement of an elastic interface between the solid and liquid. To obtain the shape of the surface, both asymptotic analysis and numerical approaches are used in this report. The asymptotic analysis is applied on the potential flow. The initial conditions are chosen to be the function of the shape of the interface between the solid and liquid and the free stream velocity far away from the interface. The time dependent contributions from the fluid system are also considered. The initial condition changes according to the function of the calculated velocity potential. The numerical approach includes two parts: calculation the velocity potential and a formalism of the change of the system as time evolves. For the first part, two idealized vertical boundaries are utilized to give a unique solution of the Laplace equation. The boundary conditions are determined as the flow under linear viscosity. For the second part, the flow is first assumed to be a potential flow, and a boundary layer is considered to make the no-slip condition valid and to give a more precise approximation for the shear stress.

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