A Study of Three Fluid Dynamical Problems
Zhen, Cui
Date: 25 March 2014
Publisher
University of Exeter
Degree Title
PhD in Mathematics
Abstract
In this thesis, three fluid dynamical problems are studied.
First in chapter 2 we investigate, via both theoretical and experimental
methods, the swimming motion of a magnetotactic bacterium having the
shape of a prolate spheroid in a viscous liquid under the influence of an
imposed magnetic field. The emphasis of the study is ...
In this thesis, three fluid dynamical problems are studied.
First in chapter 2 we investigate, via both theoretical and experimental
methods, the swimming motion of a magnetotactic bacterium having the
shape of a prolate spheroid in a viscous liquid under the influence of an
imposed magnetic field. The emphasis of the study is placed on how
the shape of the non-spherical magnetotactic bacterium, marked by the
size of its eccentricity, affects the pattern of its swimming motion. It is
revealed that the pattern/speed of a swimming spheroidal magnetotactic
bacterium is highly sensitive not only to the direction of its magnetic
moment but also to its shape.
Secondly, an important unanswered mathematical question in the theory
of rotating fluids has been the completeness of the inviscid eigenfunctions
which are usually referred to as inertial waves or inertial modes. In chapter
3 we provide for the first time a mathematical proof for the completeness
of the inertial modes in a rotating annular channel by establishing
the completeness relation, or Parseval’s equality, for any piecewise continuous,
differentiable velocity of an incompressible fluid.
Thirdly, in chapter 4 we investigate, through both asymptotic analysis
and direct numerical simulation, precessionally driven flow of a homogeneous
fluid confined in a fluid-filled circular cylinder that rotates rapidly
about its symmetry axis and precesses about a different axis that is fixed
in space. A particular emphasis is placed on the spherical-like cylinder
whose diameter is nearly the same as its length. An asymptotic analytical
solution in closed form is derived in the mantle frame of reference for
describing weakly precessing flow in the spherical-like cylinder at asymptotically
small Ekman numbers. We also construct a three-dimensional
finite element model, which is checked against the asymptotic solution,
in attempting to elucidate the structure of the nonlinear flow.
Doctoral Theses
Doctoral College
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