Non-classical boundary conditions in water impact problems
Alexander Korobkin
26th November 2007

Water impact problems are of importance in many fields of ocean engineering, coastal engineering and ship hydrodynamics. The water impact is an event of short duration. However, the problems of water impact should be considered as evolutionary ones with resolution in time of both pressure distribution and structure response. Owing to uncertainty in impact conditions, 'global' theories of water impact, which rely on 'pressure - impulse' concept, were developed. Such theories are robust with respect to small variations of impact conditions but do not provide amplitudes of the impact loads. It is shown that in problems of hydroelasticity we do not need to calculate the hydrodynamic pressures, once the stresses in the structure are of main concern. A practical solution of the impact pressure problem is to estimate the pressures but not to compute their real values in uncertain impact conditions. We present several impact models, which take into account realistic conditions of impact with the help of modifications of the body boundary condition. The modified body boundary conditions are referred to as non-classical ones because they involve not only the liquid velocity over the wetted part of the body but also the hydrodynamic pressure distribution. The models are based on potential flow theory with small deformations of the liquid free surface during the impact stage. The differences between the models are due to body boundary conditions, which account for: (1) mixing processes in the impact region, (2) porosity of the body surface, (3) perforation of the body surface, (4) elastic deformations of the body surface, (5) presence of air in the impact region. These five models are reviewed with the aim to demonstrate their performance.

Asymptotic solutions for some surface tension driven inviscid flows
John Billingham
3rd December 2007

In this talk I will consider two inviscid flow problems where surface tension is important. The first is the coalescence of a bubble with a solid wall, the second is the flow driven by the acceleration of an inclined plate into a horizontal layer of fluid. Note that the second problem is a continuation of the work that David Needham presented at UEA earlier in the year.