# Remarks on bernoulli constants, gauge conditions and phase velocities in the context of water waves

## TL;DR

This paper clarifies the definitions of Bernoulli constants, gauge conditions, and phase velocities in water wave theory, addressing common ambiguities and confusion in the literature.

## Contribution

It provides explicit clarifications of fundamental concepts in water wave analysis, improving understanding and consistency in the field.

## Key findings

- Clarification of gauge conditions for velocity potential
- Explicit definitions of Bernoulli constant and phase velocities
- Reduction of ambiguities in water wave literature

## Abstract

This short note is about the gauge condition for the velocity potential, the definitions of the Bernoulli constant and of the velocity speeds in the context of water waves. These definitions are often implicit and thus the source of confusion in the literature. This