Irrotational, two-dimensional Surface waves in fluids

TL;DR

This paper derives equations for irrotational surface waves in fluids, introduces a shallow water approximation for varying bottoms, and establishes a conserved norm crucial for wave quantization and black hole analog models.

Contribution

It provides a new derivation of wave equations in irrotational fluids, including a conserved norm for quantization and applications in analog gravity models.

Findings

Derived wave equations in velocity potential coordinates

Established a conserved norm for surface waves

Presented a shallow water approximation for varying bottom topography

Abstract

The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying bottom topography. Most importantly, the conserved norm for the surface waves is derived, important for quantisation of these waves and their use in analog models for black holes.