Water entry and related problems
In this thesis we formalize, reconcile and generalize some existing mathematical models for deep- and shallow-water entry at small and zero deadrise angles for normal and oblique impact velocities. Our method throughout is to exploit the existence of one or more small parameters via the method of matched asymptotic expansions. In the first chapter we describe some motivating solid-fluid impact events, summarize the literature on which this thesis builds and discuss our main modelling assumptions. In Chapter 2, the small-deadrise-angle deep-water entry model is systematically derived, a new expression for the first-order force on the body is found and the slender body limit of an exact three-dimensional solution is used to discuss the validity of strip theory. In Chapter 3, the small-deadrise-angle shallow-water entry model is systematically derived. The deep water Wagner and shallow water Korobkin theories are reconciled. New models and analytic results for the three-dimensional case are presented. In Chapter 4, models for the impact of a flat-bottomed body on deep- and shallow-water are reviewed and conjectures are made concerning their reconciliation. In Chapter 5, the theories of Chapters 2, 3 and 4 are used as building blocks to formulate and analyse some conjectured models for oblique shallow water impacts at small and zero deadrise angles. In the final chapter the main results are summarized and directions for further work indicated.