# Mathematical modelling of overwash on low freeboard bodies by water waves

**Program:** Doctor of Philosophy (PhD)**Supervisor:** Dr Luke Bennetts - Senior Research Fellow**School:** Mathematical Sciences**Campus:** North Terrace

In this project, a simplified mathematical model for the overwash of low freeboard bodies will be developed. Overwash is the process where surface-gravity water waves wash water over the surface of an otherwise unsubmerged body.

The investigation is motivated by wave-tank experiments on the interaction between waves and floating elastic plates - the canonical model for the interaction between waves and sea ice. These experiments have found that when overwash occurs it dissipates energy and perturbs the surrounding water waves. This is not accounted for in existing models of waves interacting with floating elastic plates because they do not include the overwash process.

The objective of this investigation is to develop a theoretical model of overwash that can predict the water on the body and surrounding waves accurately. Two overwash problems are considered: Overwash of a thin floating elastic plate, and overwash of a step (a vertical wall with at upper surface). Both of these problems are modelled using two spatial dimensions (one length and one depth), and the overwash is created by monochromatic water waves.

The overwashed floating plate problem is investigated because of its relevance to these experiments and the interaction of waves and sea ice. The overwashed step problem is investigated because its relative simplicity allows for a more direct investigation into the overwash phenomenon. In each problem the mathematical model uses the nonlinear shallow-water equations to model the overwashed water and linear potential flow theory to model the motion of the surrounding waves. The models force the overwash by assuming it has a negligible impact on the surrounding waves, and then correct the surrounding waves using an energy conservation method.

The model for the floating elastic plate is compared to experiments and good agreement is found in terms of the prediction of the overwash and surrounding waves. Similarly, the model for the step is compared to a computational fluid dynamics model and good agreement is found in terms of the prediction of the overwash and surrounding waves.

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