Liu, J; (2017) Shallow-water skimming, skipping and rebound problems. Doctoral thesis , UCL (University College London).

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Abstract

The subject of water-entry related problems has a wide range of applications in industries and natural sciences. In this thesis we study the dynamics of a solid body slamming, skimming, rebounding or sinking in shallow water. We reconcile and extend some existing mathematical models, primarily by exploiting the existence of one or more small parameters via the method of asymptotic expansions, as well as deriving new models of interest. This thesis begins by providing an overview of the existing solid-liquid impact and skimming modelling; reviews of relevant literatures as well as some key modelling assumptions used throughout the thesis are introduced. The problem of a thin object skimming on a layer of shallow water is analysed in Chapter 2 and 3. A model that describes such an object’s motion from its moment of water impact to eventual exit (or sinking) is introduced. Asymptotic behaviours of the object based on its mass, moment of inertia as well various water entry profiles are studied, yielding results in qualitative agreement with physical experiments. We subsequently shift our modelling effort from that of a thin body to one with non-negligible thickness in Chapter 4 and 5. In such case the unknown position of the object’s trailing separation edge, as well as its surface curvature pose additional modelling complexities. Chapter 4 focuses on analysing flows in a small region enclosing the object’s trailing separation edge; analytical as well as numerical solutions of the flow in this region are presented. Chapter 5 models the complete transition cycle of water entry to water exit for a blunt body. A three-phase planing model is presented based on the presence of a weak adverse pressure gradient at the trailing edge. In Chapter 6 we investigate the phenomenon of a thin object that first undergoes a skimming motion and is subsequently subject to flooding over its upper surface. Numerous conditions are investigated to establish whether such an object is able to re-emerge from water or sink to the flow bed. We conclude this thesis with summaries of our main results and possible directions of further research.

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