Unsteady free-surface waves generated by bodies in a viscous fluid
Abstract of thesis entitled
UNSTEADY FREE-SURFACE WAVES GENERATED BY BODIES IN A VISCOUS FLUID
for the degree of Doctor of Philosophy
at The University of Hong Kong
in December 2002
The interaction of laminar flows with free-surface waves generated by submerged bodies in an incompressible viscous fluid of infinite depth is investigated analytically. The analysis is based on the linearized Navier-Stokes equations for disturbed flows. The kinematic and dynamic boundary conditions are linearized for the small-amplitude free-surface waves, and the initial values of the flow are taken to be those of the steady-state cases. The submerged bodies are mathematically represented by fundamental singularities of viscous flows.
In the first part of this thesis, the fundamental solutions for the singular Stokes and Oseen flows in an unbounded fluid are derived in a universal form which involves the Hamiltonian, Hessian, and Laplacian operators, and elementary functions. The new solutions for singular unsteady flows can be theoretically applied to construct solutions for general unsteady flows.
In the second part, the interaction of unsteady low-Reynolds-number flows with a free surface is investigated analytically. The disturbed flows, generated
by submerged bodies moving vertically downwards away from the surface of the fluid, are governed by the unsteady Stokes equations. The submerged body is modeled as a Stokeslet with a vertical component. The asymptotic representations for free-surface waves produced by the instantaneous and oscillating Stokeslets are derived for large time with a fixed distance-to-time ratio.
In the third part, the interaction of unsteady far wakes with a free surface is investigated analytically. The disturbed flows generated by submerged bodies moving horizontally beneath the free surface of the fluid are governed by the unsteady Oseen equations. The submerged body is modeled as an Oseenlet with horizontal and vertical components corresponding respectively to the drag and lift exerted on the body. The asymptotic representations are derived for the far-field free-surface waves produced by two-dimensional suddenly starting, suddenly stopping, and oscillating Oseenlets, and by three-dimensional suddenly starting and suddenly stopping Oseenlets.
The results obtained show analytically the effects of unsteadiness, viscosity, and submergence on the waves generated. It is found that the unsteady waves generated by a body consist of steady-state and transient responses. As time tends to infinity, the transient waves vanish due to the presence of a viscous decay factor. Thus, an ultimate steady state can be attained. It is demonstrated that the non-physical behavior predicted by the potential-flow theory disappears with the application of the present viscous theory.
School:The University of Hong Kong
School Location:China - Hong Kong SAR
Source Type:Master's Thesis
Keywords:viscous flow navier stokes equations fluid mechanics waves
Date of Publication:01/01/2003