The interaction between waves and currents in the nearshore zone.
thesisposted on 2018-04-04, 15:05 authored by Evans F. Osaisai
The interaction of waves and currents in the near-shore zone is an area of continuing research where interest derives in particular as a result of various environmental effects from natural phenomena such as storm surges and tsunamis. On time scales longer than that of an individual wave it is necessary to properly evaluate the interaction between waves and currents, using a consistent formulation of mass, momentum and energy within the water column. We describe the formulation of equations describing the mean current flow, driven by the radiation stress field of the waves, an equation for the mean conservation of mass, together with equations describing the conservation of wave action and the kinematics of the averaged wave field. The near-shore zone is often characterized by the presence of breaking waves, and so we develop equations to be used outside the surf zone, based on small-amplitude wave theory, and another set of equations to be used inside the surf zone, based on an empirical representation of breaking waves. Suitable matching conditions are applied at the boundary between the offshore shoaling zone and the near-shore surf zone. Both sets of equation are obtained by averaging the basic equations over the wave phase. In the shoaling zone, we supplement these equations by a simple model of sediment transport, where the bottom is allowed to move in response to the current field of the breaking waves. We use these basic equation sets to re-evaluate previous studies of wave set-up and longshore currents driven by the radiation stress field of the shoaling waves. In particular we extend previous work based on beach profiles with a linear depth dependence to more general beach profiles, including beaches with a depth dependence which varies quadratically with the onshore coordinate, and to beach profiles which approach a constant depth far offshore. We then turn to a situation where the incoming shoaling waves vary periodically in the alongshore direction, and use our basic equation sets to construct a mean current field which likewise varies periodically in the alongshore direction. The outcome, for our set of typical beach profiles, is a description of rip currents. The last part of the thesis examines .a simple model of sediment transport, induced by breaking waves in the surf zone. We show that the previous solutions for wave set-up and longshore currents now become time-dependent as the nearshore zone is eroded by the waves.
- Mathematical Sciences