Horizon effects with surface waves on moving water

TL;DR

This paper explores complex horizon effects experienced by gravity-capillary surface waves on moving water, highlighting phenomena like wave blocking, negative co-moving frequency, and the Hawking effect within an analogue gravity framework.

Contribution

It provides a comprehensive analysis of horizon effects for gravity-capillary waves, including analytical results in the deep water/short wavelength regime, and connects wave dynamics to thermodynamic analogies.

Findings

Multiple horizons can exist for a single wave frequency.

Wave blocking and Hawking-like effects are observed in surface wave propagation.

Analytical results are derived for the deep water/short wavelength case.

Abstract

Surface waves on a stationary flow of water are considered, in a linear model that includes the surface tension of the fluid. The resulting gravity-capillary waves experience a rich array of horizon effects when propagating against the flow. In some cases three horizons (points where the group velocity of the wave reverses) exist for waves with a single laboratory frequency. Some of these effects are familiar in fluid mechanics under the name of wave blocking, but other aspects, in particular waves with negative co-moving frequency and the Hawking effect, were overlooked until surface waves were investigated as examples of analogue gravity [Sch\"utzhold R and Unruh W G 2002 Phys. Rev. D 66 044019]. A comprehensive presentation of the various horizon effects for gravity-capillary waves is given, with emphasis on the deep water/short wavelength case kh>>1 where many analytical results can be derived. A similarity of the state space of the waves to that of a thermodynamic system is pointed out.