Length-distorted Physical Models for Tsunami Engineering

Tsunamis are earthquake induced waves which can have catastrophic consequences when reaching the shoreline. The wave height of Tsunamis in the open sea rarely exceeds 2 m, their length reaches 10 km or more even in shallow water. Due to shoaling effects, wave heights in shallow water increase. The water masses thrown onto land, and the subsequent flooding can extend several kilometres inland.

Physical modelling is a design tool often employed in tsunami engineering. Short wave trains or solitary waves are employed to simulate tsunami waves. With the restricted length of wave tanks, (usually in the 20 to 50 m), the length of the wave crest is limited to several meters. This means, that with typical scales of 1:25 to 1:50 the water volume transported by the wave crest is small compared to (a) the water volume transported by a scaled tsunami and (b) with the area on land which is susceptible to flooding.

At Southampton University, the concept of length distorted models was developed. The length scale of the coastal topography was increased from 1:50 of the original model to 1:500, making the effective wave crest 10 times longer. Scaling was analysed both in respect to velocity, and breaker number. Physical model tests of an idealised scenario were conducted with an undistorted (length distorted) model with a 1:10 (1:100) slope, a 2000 (200) mm foreshore and a 1:20 (1:2) slope at the end of the plateau. It was found that the results were dramatically different. In the undistorted model, initial flood depths ranged from 0.7H (shoreline) to 0.25 H (H = wave height at shoreline). Wave velocities reduced from 4.0 sqrt(g·H) at the shoreline to near zero at the end of the flood plain (2.00 m). Backflow velocities were very low. In the distorted model, the flood depth was 0.7 H during the inflow. The backflow created a seaward traveling bore, with a velocity of 0.5 sqrt (g·H) and an increased water depth of 1.43 H. A theoretical model was developed for this scenario.

The results indicated that the quantitative and qualitative effect of tsunami waves is a function of the relative volume of wave and flood area. Length distorted models appear to be an attractive possibility to replicate these conditions.