Wave Instability in Finite Depths

Abstract

Waves in finite-depth and shallow water represent an important and challenging research topic, both from practical and academic perspective. Most of practical applications related to the ocean are conducted in coastal areas, but most of research attention has been dedicated to the surface waves in deep water. Shallow areas are effectively a different physical environment, where wave kinematics change, waves become steeper and consequently more nonlinear but less or non-dispersive, and as a result their nonlinear behaviors change dramatically, waves directly interact with the bottom, in a number of different ways, and most importantly release their energy and momentum through intensive and extensive breaking. In the paper, modulational instability in finite depths will be discussed. This mechanism is regarded responsible for rogue waves, and hence extreme wave heights in deep water. Extreme wave heights are a key design criterion for the ocean industry, including shallow environments too. It is believed, however, that wave breaking rather than wave instabilities is the primary mechanism that controls the maximum possible wave height in depth-limited environments. Here, data of the LoWish JIP will be used in order to identify the criteria for transition from modulational instability being active in the deep-water environments to being suppressed in the shallow waters.