New tsunami runup relationships based on long wave experiments

- Reproduction of long elevated and depressed waves in a large scale laboratory.
- Experimental investigation of wavelength and potential energy.
- Application of complete regression analysis to empirical observations.
- Presence of two different runup regimes, for long and very long waves.

Tsunami are propagating waves characterized by long wavelengths and large amplitudes close to the shore. They may also have a profile characterised by a large trough preceding the positive wave. These waves are destructive, causing severe damage to structures and human casualties when they reach coastal areas (e.g., Indian Ocean, 2004; Japan, 2011). Runup is a local characteristic of a wave flow inland and this measure, easily identifiable in the field, is extensively used as an indicator of tsunami inundation and impact on the coast.In this paper, an innovative large scale experimental programme is applied to develop runup equations for long propagating waves. A pneumatic generator with a controlled valve system, capable of exchanging large volumes of water with the propagation flume is used. This novel generation system allows waves to be generated that have much larger wavelengths than those experimentally reproduced to date. Moreover, it enables leading depressed waves to be stably generated and analysed for the first time.To analyse the influence of wavelength and wave shape on runup, the experimental data was partitioned into groups classified by wave period T/Tb (where Tb is the travel time of a linear wave along the length of the beach) and wave shape (elevated or N-waves). In this paper, elevated waves refer to waves of translation having a single positive elevation above mean water level, and N-waves refer to waves of translation comprising both a negative elevation (below mean water level) and a positive elevation. Dimensional analysis (using experimentally determined wavelength, potential energy and wave amplitudes) was applied to identify correlated measures. A statistical analysis was used to determine a power law relationship between runup and measures of the waveform, and to test the significance of the power law hypothesis. The experimental results show how both the wavelength and wave shape influence the runup distance. For TTb<1, the runup is seen to scale as R∼a, while for TTb>1, it scales as R∼a.