Dispersive and non-dispersive nonlinear long wave transformations: Numerical and experimental results

TL;DR

This paper reviews the historical development of models for long water waves, emphasizing the role of dispersion in wave propagation and run-up, supported by numerical and experimental results.

Contribution

It provides a comparative analysis of dispersive and non-dispersive models for long wave transformations, highlighting their respective applicability to tsunami wave prediction.

Findings

Wave dispersion significantly affects wave propagation and transformation.

Maximum run-up height is less sensitive to dispersion effects.

Non-dispersive models are sufficient for estimating run-up height.

Abstract

The description of gravity waves propagating on the water surface is considered from a historical point of view, with specific emphasis on the development of a theoretical framework and equations of motion for long waves in shallow water. This provides the foundation for a subsequent discussion about tsunami wave propagation and run-up on a sloping beach, and in particular the role of wave dispersion for this problem. Wave tank experiments show that wave dispersion can play a significant role for the propagation and wave transformation of wave signals that include some higher frequency components. However, the maximum run-up height is less sensitive to dispersive effects, suggesting that run-up height can be adequately calculated by use of non-dispersive model equations.