Oscillations of a Fluid in a Channel

In this work we investigate the motion of a viscous, incompressible fluid contained in an uncovered three-dimensional rectangular channel. The upper surface changes with the motion of the fluid, so we deal with a free boundary problem. We consider small perturbations of a uniform flow with a flat free surface. We include the effect of the surface tension; the external forces are gravity, and the wind force which acts on the free boundary. The motion of the fluid in the channel is governed by the Navier-Stokes equations. We consider the system to be periodic in the direction of the length of the channel. Technically, we identify the inflow boundary with the outflow boundary of the channel and then we consider the second spatial variable belonging to the circle S¹. In order to obtain a well-posed model, we have to prescribe the value of the dynamic contact angle between the walls and the free boundary and we choose it to be \frac{π}{2}. As boundary conditions, we consider that the walls are impenetrable together with a perfect slip condition, and a no slip condition for the bottom. The main aim of this paper is to analyse the qualitative behavior of the flow (oscillations of periodic solutions) using tools of bifurcation theory. In order to do this we need fundamental facts of existence and regularity of solutions, spectral analysis of the linear system connected with the free boundary value problem taking into account the underlying symmetries, and techniques of equivariant Hopf bifurcation theorem.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Heidelberg

Year

2003

Author dc:creator

• Bodea, Simina

Contributors dc:contributor

• Jäger, Willi,

Repository record source_url

http://www.ub.uni-heidelberg.de/archiv/3753

OAI identifier oai:identifier

oai:archiv.ub.uni-heidelberg.de:3753