Tsunamis : forces on a vertical wall caused by long waves, bores, and surges on a dry bed

Abstract

The major objective of this study has been to investigate experimentally the forces and overturning moments produced by tsunamis on vertical walls. The experimental results are compared with several analytical and numerical models. Several types of waves were used in a horizontal tank including solitary waves, undular bores, turbulent bores, and surges on a dry bed. Bores produced from breaking solitary waves in a tilting wave tank were also investigated. Various measurements were made, including the incident wave celerity, the wave profile, the runup, force, overturning moment, and pressure time histories. The impact process of the bores in the tilting wave tank were recorded with high-speed movies. The wave profiles in the horizontal tank were defined using a laser induced-fluorescence system (LIF) which allows the free surface on a two-dimensional plane in the center of the wave tank to be recorded. This method was developed to measure accurately the surface elevation profile of turbulent high-speed flows which is difficult to measure reliably either with conventional flow visualization techniques or intrusive devices such as wave gages. The LIF method was also used to determine the runup on the wall. Strong vertical accelerations were shown to occur during the reflection of bores and steep solitary waves at a vertical wall. These reduced the force on the wall relative to a hydrostatic force computed from the maximum runup height on the wall. The accelerations also cause the maximum force to occur before and after the maximum runup for steep solitary waves and bores, respectively. For these cases, the maximum measured force and overturning moment were always less than computed from the maximum measured runup on the wall using hydrostatic considerations. The maximum force due to surges on a dry bed was also less than the hydrostatic force calculated from the maximum runup height on the wall. For all the dry bed cases studied, the maximum runup height on the wall was between 1.46 and 1.62 times the velocity head computed from the celerity of the incident surge. For the entire range of wave conditions of this study, the maximum relative runup occurred for a bore with a relative wave height of 1.23, and produced a runup equal to 3.8 times the velocity head computed from the wave celerity. The maximum measured water surface slopes along the front of long waves, bores, and dry bed surges were computed from the measured wave profiles. At the transition from undular bores to turbulent bores, there was a discontinuity in the maximum water surface slope where the slope increased by a factor of 2.5 to three for turbulent bores. This discontinuity corresponded with a rapid increase in the measured runup, force, and moment on the wall. The properly normalized force on a vertical wall due to the impingement of a bore on a mildly sloping beach is shown to be equivalent to the force produced by a bore of constant volume on a horizontal bed. This implies the results from the horizontal wave tank experiments can be used to estimate the loads expected from bores propagating on mild beaches with slopes ranging up to 0.02m/m. Two numerical models were compared with the experimental results. A boundary integral element model, which solves the potential flow problem subject to the full nonlinear free surface boundary conditions, predicted the loads imposed on the wall due to steep solitary waves quite well. A finite difference model of the Navier-Stokes equations was also used to simulate the reflection of solitary waves and mild turbulent bores at a vertical wall. This finite difference model predicted the solitary wave loads quite well; however, it over-predicted the steepness of the incident bore profiles and produced a force-time history with a high amplitude and short-duration peak, which was not observed in the measurements. Except for this sharp peak, the agreement of the finite difference model with the experimental results was quite reasonable.

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