The interaction of laminar far wake with a free surface

The interaction of laminar far wake with a free surface

陳德儀(Tak-yee Chan)

香港大學/Doctor of Philosophy/Mechanical Engineering/博士(1997年)

並列摘要

(Uncorrected OCR)
Abstract of thesis entitled
THE INTERACTION OF LAMINAR FAR WAKE WITH A FREE SURFACE
submitted by
Andy Tak-yee Chan
for the degree of Doctor of Philosophy
at The University of Hong Kong
in December 1996
The various properties of viscous singularities and their laminar far-wake interactions with a free surface are investigated. In the first part of this work, the image system of an Oseenlet with respect to a horizontal no-slip boundary is derived. It is found that the image system consists of a negative Oseenlet located at the mirror image point plus a distribution of vertical Oseen doublet at the horizontal boundary.
The unsteady low-Reynolds-number flow of an incompressible viscous fluid past a singular forcelet is investigated analytically. New fundamental three-dimensional solutions for a concentrated impulsive force are derived for the unsteady Stokes and Oseen equations. These elementary solutions can be used as fundamental Green� functions to obtain solutions for flow over singularities with any time-dependent nature. These fundamental singularities are employed to construct some known solutions to demonstrate their validity and usefulness in solving unsteady problems governed by the Stokes and Oseen equations.
In the second part of this work, the wave disturbances caused by the uniform translatory motion of a submerged body moving parallel to the free surface of a viscous fluid are investigated analytically. The submerged body is idealized as an Oseenlet or an Oseen doublet, and exact solutions in closed integral forms are obtained. Based on these exact solutions, asymptotic representations of the wave amplitude for large Reynolds numbers at large distances downstream of the body are derived for both infinite and finite water depth. In both cases, the solutions show that the wave patterns possess many properties similar to the inviscid Kelvin ship wave pattern. The results also show explicitly the effect of viscous decay, water depth and submergence on the wave amplitude and phase of the surface waves thus created.
The third part of the thesis deals with the generation of ripples in viscous fluid by the downward vertical motion of a submerged body. We again model the object by an Oseenlet or an Oseen doublet moving vertically downwards away from the free surface. The solutions derived demonstrate clearly the effect of viscous decay on the wave amplitude of ripples.

並列關鍵字

Hydrodynamics - Impulse and resistance. ； Wakes (Fluid dynamics) ； Water waves.