Abstract
Fluid-structure interaction is a well-known and complicated problem. Its formulation requires simplifications in modelling, and usually the presence of gravity is one aspect which is neglected, especially in violent impact. In this thesis we account for the influence of gravity on two physically different but mathematically similar two-dimensional flows. First (in Chapters 2{4), sloshing impact of a standing wave on the lid of a rigid tank, and second (in Chapter 5), impact of a rigid blunt body entering water which is initially at rest. Chapter 1 presents the motivation, literature, aim and structure of the thesis. In Chapter 2, gravity is neglected and model equations are solved analytically, in particular the linearised hydrodynamic problem with and without the lid using the Wagner approximation, time and coordinate stretching, and displacement potential. Chapter 3, introduces gravity into the formulation and the model is solved semi-analytically to determine its influence on the width of the wetted region and on the pressure distribution on the lid during impact. We numerically find the effect of gravity on the moving contact points, hydrodynamic pressure, and surface elevation in Chapter 4. Chapter 5 studies the influence of gravity on the impact of a blunt body entering vertically with a constant speed into an initially at water. All problems are formulated and solved within the Wagner model. In both problems we found visible effects of gravity on the positions of moving contact points after the early stage of impact. Gravity shortens the size of the wetted region. Consequently, the velocities of the contact points are decreased by gravity. The effect of gravity on the surface elevation is shown for both problems. Negative hydrodynamic pressures and forces are found during the sloshing impact stage when gravity is neglected. Numerically, it was found that gravity decreases the hydrodynamic pressure on the lid of the tank. Similarly the hydrodynamic pressure is found to be decreased by gravity in the water-entry problem. Also in the water-entry problem it is shown that gravity increases both the thickness and the mass flux into the spray jets. Also the total energy (potential and kinetic) of the system, and the work done by the body on the fluid are decreased by gravity.