Interfacial and internal waves generated by a submerged prolate spheroid

Westlake, Paul Charles (1997) Interfacial and internal waves generated by a submerged prolate spheroid. University of Southampton, Doctoral Thesis.

Abstract

The fluid disturbance created by a body moving in a stratified fluid is theoretically investigated. In part I velocity potential solutions are derived for an arbitrary shaped body moving horizontally in a fluid system consisting of two or three discrete layers. In each layer, the fluid is assumed to be incompressible, inviscid and irrotational. The boundary conditions on the free surface and interfaces are linearised and a radiation condition imposed. Expressions for the far field free surface and interface waves systems are derived. A three dimensional extension of Lagally's theorem is used to obtain the wave resistance experienced by the body. Ekman's dead water effect is demonstrated at low body speeds. This is a very simplified model not fully representing the physical characteristics of the fluid disturbance but it does provide insight into the interaction between the body and the fluid layers.

In part II, the constant density assumptions and potential theory are not retained and rotational characteristics are introduced into the fluid model. From the equations of motion an integral equation is formed from which fundamental equations can be defined. The definition of the fundamental equations permits the integral equation to simplify significantly. Rayleigh damping is incorporated into the fluid model and successfully produces outgoing wave behaviour only. Under the assumption that the fluid has a constant Brunt-Vaisala frequency analytic solutions are obtained. These solutions display characteristics associated with the generation and propagation of internal waves. When these solutions are distributed over an arbitrary shaped body the fluid disturbance can be obtained.

The analytic slender body solution derived from the integral equation permits the rapid calculation of the fluid disturbance throughout the fluid domain. It is shown that on the fluid's surface the apex angle correctly responds to variations in forward speed and stratification. Calculations through the body's wake demonstrate the formation and propagation of the experimentally observed St Andrews cross.

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