Corner waves downstream from a partially submerged vertical plate

Resumo

In this dissertation, the high-Reynolds-number flow near the corner of a vertical at plate partially submerged across an uniform stream has been studied using a combination of experimental, numerical and analytical tools. In this configuration, a three dimensional wave forms at the corner of the plate which evolves downstream in a similar way as a time-evolving two dimensional plunging or spilling breaker, depending the occurrence of one or the other type of breaker on the flow conditions. Experiments have been performed submerging a flat plate perpendicular to the free stream in the test section of a recirculating water channel. Experimental results show that the formation and the initial development of the wave is nearly unaffected by the presence of the channel walls and bottom even when their distance to the corner, where the wave originates, is of the order of the size of the wave itself. This is a remarkable observation, that suggests that the formation of the corner wave is a local process in a sense that it is only influenced by the characteristics of the velocity field very near the corner. Moreover, it has been observed that the jet formed when the corner wave adopts the plunging breaker configuration follows a nearly ballistic trajectory, has is the case in two-dimensional unsteady plunging breakers. Theoretical analysis shows that, taking advantage of the slender nature of the flow, the 3D steady problem can be transformed into a two dimensional unsteady one using the so called 2D+T approximation. Together with the high Reynolds number of the flow, the 2D+T approximation makes the problem amenable to be simulated numerically using a Boundary Element Method (BEM). Moreover, a pressure-impulse asymptotic analysis of the flow near the origin of the corner wave has been performed in order to describe the initial evolution of the wave and to clarify the physical mechanisms that lead to its formation. The analysis shows that the flow near the corner exhibits a self similar behavior at short times. The problem considered in this dissertation is of interest in naval hydrodynamics as well as oceanography. Indeed, the flow resembles to the one found at the dry stern of high-speed surface vessels. The similarities between the waves formed in the wake of such ships and our laboratory breakers will be investigated. This experiment also shares many features with deep water waves in the ocean, and thus it will be applied to the study of their breaking process. A criterion for the transition between overturning laboratory waves and spilling ones is proposed. ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------