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The two-dimensional problem of hydrodynamic interaction of the horizontal circular cylinders with a free-surface is investigated both analytically and numerically. The fully nonlinear initial boundary-value problem is described and a numerical solution for it is presented. The free motion of a cylinder rising towards, or moving away from the free-surface or moving horizontally is studied. The numerical calculations are compared with a simple analytic theory in which we take the low- and high-frequency limit of the added mass, and the constant added mass of the submerged cylinder in the coefficients of the equation of motion. Further numerical calculations of an initially displaced, spring-loaded cylinder undergoing slow motions are compared with a simple analytic theory in which we also take the low-frequency limit of the added mass of the submerged cylinder. The aim is to provide a useful approximate method for simulation of various offshore operations. Fully nonlinear calculations of the free-surface deformations of the initially calm water caused by forced constant velocity motion of a totally submerged circular cylinder are compared with small-time asymptotics due to Tyvand & Miloh (1995). Their analytic results, which are taken to third order5 when gravity terms first appear in the expansion, are in excellent agreement with the numerical calculations for small times, beyond which only the numerical method will give accurate results, valid until the free-surface breaks. The breaking of the surface as a result of vertical downward motion is further investigated with the aim of establishing when and how this happens, since the phenomena causes the breakdown of the numerical calculations. The free motion of a cylinder entering a free-surface, initially half-submerged in calm water and having specific gravity of 1.2 is also investigated. This motion is pursued beyond the complete submergence stage, giving rise to interesting free-surface deformations and body dynamics. This study is complemented by a further investigation involving impulsively started and forced constant motion of a cylinder entering a free-surface at various angles and Froude numbers, and is also taken beyond the complete engulfment stage. Hydrodynamic forces on the cylinder obtained for various angles at the same Froude number are compared. Also, the hydrodynamic forces for the motion in the same direction at various Froude numbers are compared.

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Thesis (Ph. D.)--University of Adelaide, 1985. / Typescript (Photocopy). Includes bibliographical references (leaf 75).

Thesis (Ph. D.)--University of Wisconsin-Madison, 1950. / Typescript with manuscript equations. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--Oregon State University, 1995. / Typescript (photocopy). Includes bibliographical references (leaves 56-58). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (Ph.D.)--Baylor University, 2006. / Includes bibliographical references (p. 53-56).

The work of this thesis was undertaken as a C.A.S.E. award project in collaboration with Rolls-Royce to examine compressible laminar boundary layers with sharp adverse pressure-gradients. Much of the work is devoted to the solution of two important particular problems. The first flow considered is that along a semi-infinite flat plate with uniform pressure when X < X0 and with the pressure for X > X0 being so chosen that the boundary layer is just on the point of separation for all X > X0. Immediately downstream of X0 there is a sharp pressure rise to which the flow reacts mainly in a thin inner sublayer; so inner and outer asymptotic expansions are derived and matched for the stream function and a function of the temperature. Throughout the thesis the ratio of the viscosity to the absolute temperature is taken to be a function of x, the distance along the wall, alone, and the Illingworth-Stewartson transformation is applied. The Prandtl number, σ, is taken to be of order unity and detailed results are presented for σ= 1 and 0.72. The second flow considered is that along a finite flat plate where the transformed external velocity U1(X) is chosen such that U1(X) = u0(-X/L)[super]ε, where O< ε <<1, is the transformed length of the plate and X represents transformed distance downstream from the trailing edge. The skin friction, position of separation and heat transfer right up to separation are determined. On the basis of these two solutions, another solution which is not presented in detail, and a solution (due to Curie) to a fourth sharp pressure gradient problem, a general Stratford-type method for computing compressible boundary layers is derived, which may be used to predict the position of separation, skin friction, heat transfer, displacement and momentum thicknesses for a compressible boundary layer with an unfavourable pressure gradient. In all this work techniques of series analysis are used to good effect. This led us to look at another boundary-layer problem in which such techniques could be used, one in which two parallel infinite disks are initially rotating with angular velocity Ω about a common axis in incompressible fluid, the appropriate Reynolds number being very large. Suddenly the angular velocity of one of the disks is reversed. A new examination of this problem is presented in the appendix to the thesis.