AbstractsMathematics

The aim of this thesis is to investigate the problem of a rigid plate, inclined at an angle α ∈(0,1/2π) the horizontal, accelerating uniformly from rest into or away from a semi-infinite expanse of inviscid, incompressible fluid. This work generalized that of Needham, Chamberlain, and Billingham\(^1\), by considering the case of negative plate accelerations. We use the method of matched asymptotic expansions to investigate the asymptotic structure of the solution to the free surface evolution problem as t→0\(^+\), paying particular attention to the innermost asymptotic region encompassing the initial interaction between the fluid free surface and the inclined accelerating plate. \(^1\) Needham et al. The initial development of a jet caused by fluid, body and free surface interaction. The Quarterly Journal of Mechanics and Applied Mathematics. 61(4):581-614, 2008.