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dc.contributor.authorZhen, Cui
dc.date.accessioned2014-06-30T09:48:52Z
dc.date.issued2014-03-25
dc.description.abstractIn 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.en_GB
dc.identifier.urihttp://hdl.handle.net/10871/15119
dc.language.isoenen_GB
dc.publisherUniversity of Exeteren_GB
dc.subjectFluid Dynamicsen_GB
dc.subjectMicroorganism Swimmingen_GB
dc.subjectCompletenessen_GB
dc.subjectInertial Modesen_GB
dc.subjectPrecessing Cylinderen_GB
dc.titleA Study of Three Fluid Dynamical Problemsen_GB
dc.typeThesis or dissertationen_GB
dc.date.available2014-06-30T09:48:52Z
dc.contributor.advisorKeke, Zhang
dc.publisher.departmentMathematicsen_GB
dc.type.degreetitlePhD in Mathematicsen_GB
dc.type.qualificationlevelDoctoralen_GB
dc.type.qualificationnamePhDen_GB


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