Vertically Driven Waves: Energy Transfer Between Gravity Waves Revisited

TL;DR

This paper revisits the mechanism of energy transfer from large to small gravity waves, emphasizing the dominant role of vertical acceleration and exploring its relation to wave instability phenomena.

Contribution

It provides a detailed analysis of vertical acceleration-driven energy transfer and establishes new limits on small wave stability, linking to Benjamin-Feir instability.

Findings

Vertical acceleration significantly enhances energy transfer between waves.

Exponential growth rates for energy transfer are quantified.

Limits on small wave stability under large wave accelerations are derived.

Abstract

We investigate the energy transfer from large waves to small ones through vertical acceleration and demonstrate that this is a much larger effect than that of the potential energy changes of the small waves moving over the larger ones. Rates of exponential growth for this process are given and limits on the stable size of small waves in the horizontal accelerations from the larger ones are derived. We discuss the possibility of this being a manifestation of the Benjamin-Feir instability.