Wave impacts on rectangular structures

Abstract

There is a good deal of uncertainty and sensitivity in the results for wave impact. In a practical situation, many parameters such as the wave climate will not be known with any accuracy especially the frequency and severity of wave breaking. Even if the wave spectrum is known, this is usually recorded offshore, requiring same sort of (linear) transfer function to estimate the wave climate at the seawall. What is more, the higher spectral moments will generally be unknown. Wave breaking, according to linear wave theory, is known to depend on the wave spectrum, see Srokosz (1986) and Greenhow (1989). Not only is the wave climate unknown, but the aeration of the water will also be subject to uncertainty. This affects rather dramatically the speed of sound in the water/bubble mixture and hence the value of the acoustic pressure that acts as a maximum cutoff for pressure calculated by any incompressible model. The results are also highly sensitive to the angle of alignment of the wave front and seawall. Here we consider the worst case scenario of perfect alignment. Given the above, it seems sensible to exploit the simple pressure impulse model used in this thesis. Thus Cooker (1990) proposed using the pressure impulse P(x, y) that is the time integral of the pressure over the duration of the impact. This results in a simplified, but much more stable, model of wave impact on the coastal structures, and forms the basis of this thesis, as follows: Chapter 1 is an overview about this topic, a brief summary of the work which will follow and a summary of the contribution of this thesis. Chapter 2 gives a literature review of wave impact, theoretically and experimentally. The topics covered include total impulse, moment impulse and overtopping. A summary of the present state of the theory and Cooker’s model is also presented in Chapter 2. In Chapter 3 and Chapter 4, we extend the work of Greenhow (2006). He studied the berm and ditch problems, see Chapter 3, and the missing block problem in Chapter 4, and solved the problems by using a basis function method. I solve these problems in nondimensionlised variables by using a hybrid collocation method in Chapter 3 and by using the same method as Greenhow (2006) in Chapter 4. The works are extended by calculating the total impulse and moment impulse, and the maximum pressure arising from the wave impact for each problem. These quantities will be very helpful from a practical point of view for engineers and designers of seawalls. The mathematical equations governing the fluid motion and its boundary conditions are presented. The deck problem together with the mathematical formulation and boundary conditions for the problem is presented in Chapters 5 and 6 by using a hybrid collocation method. For this case, the basis function method fails due to hyperbolic terms in these formulations growing exponentially. The formulations also include a secular term, not present in Cooker’s formulation. For Chapter 5, the wave hits the wall in a horizontal direction and for Chapter 6, the wave hits beneath the deck in a vertical direction. These problems are important for offshore structures where providing adequate freeboard for decks contributes very significantly to the cost of the structure. Chapter 7 looks at what happens when we have a vertical baffle. The mathematical formulation and the boundary conditions for four cases of baffles which have different positions are presented in this chapter. We use a basis function method to solve the mathematical formulation, and total impulse and moment impulse are investigated for each problem. These problems are not, perhaps, very relevant to coastal structures. However, they are pertinent to wave impacts in sloshing tanks where baffles are used to detune the natural tank frequencies away from environmental driving frequencies (e.g ship roll due to wave action) and to damp the oscillations by shedding vortices. They also provide useful information for the design of oscillating water column wave energy devices. Finally, conclusions from the research and recommendations for future work are presented in Chapter 8.