Overtopping and Run-up Hazards Induced by Solitary Waves and Bores

Abstract

Solitary waves are wave forms that consist of a single wave, rather than waves that form part of a series of regular waves or random waves, the latter being typical of ocean wind and swell waves. A solitary wave that propagates with constant form has a unique shape for a given water depth and height, but in general, single waves of arbitrary shape are referred to as solitary waves. Single waves that have broken can be regarded as solitary bores. While the exact solitary wave shape has long been used to represent tsunami, Madsen et al. (2008) show that this is not likely to be usually the case and more complex wave shapes result. However, tsunami waves often closely resemble a solitary wave type and such waves still form the basis of most tsunami modelling. Tsunami are generated by impulsive geophysical events on ocean bed, and take the form of long waves with small steepness in the open ocean (Synolakis and Bernard, 2006). As witnessed in the 2004 Indian Ocean Tsunami, at the shore, the leading waves of a tsunami may steepen sufficiently to break and form very long surf bores. The impact of tsunami bores may be very different to that from non-breaking or standing solitary waves, and this may require different disaster management strategies and evacuation plans, particularly when considering the initial impact and first few minutes after the wave arrival. Hall and Watts (1953) provided the first study of such waves with later laboratory studies of bore run-up providing further details on the speed of the run-up in comparison to theory (Yeh, 1991). In addition to tsunami, inundation of coastal zones by overwash is a major flooding hazard in many regions. In this instance, the overwash may be a result of run-up and overtopping on the sub-aerial beach, or as a result of overwash from waves in shallow water as the tide level inundates a barrier. In these cases, the overwash may be driven by surf zone bores or long wave surges that arise from wave groups in the shallow water or surf zone. The leading part of the long wave surge typically exhibits a solitary wave shape, as shown by Baldock (2006) and Nielsen and Baldock (2010). This overland flow in the run-up zone on beaches is frequently termed swash, and comprises an uprush (landward) and backwash (seaward) phase. This work considers these issues, and presents the results of recent laboratory experiments measuring the overtopping flows from solitary waves and long bores. The results are discussed in the context of recent run-up theory, and used to further verify that theory for application to long bores, solitary waves and potentially initial tsunami impact. In addition, using the recent solutions, some estimates of the fluid forces, maximum inundation depths and the potential human safety hazard arising during the run-up are presented. This chapter is organised as follows: section 2 provides an overview of previous work on tsunami, overwash, and overtopping of wave-run-up, together with an outline of the model for bore run-up (Shen and Meyer, 1963; Peregrine and Williams, 2001; Guard and Baldock, 2007). Section 3 describes the experimental setup, data collection and wave conditions in the experiments. Results and comparisons with the Guard and Baldock (2007) model are presented in section 4. Application of the model to derive flow forces and a hazard assessment in the run-up zone are discussed in section 5, with final conclusions in section 6. Copyright © 2011 InTech