# Instability of a horizontal water half-cylinder under vertical vibration

## TL;DR

This study experimentally investigates the behavior of a water half-cylinder on a vibrating plate, revealing the excitation of non-axisymmetric stationary waves and providing a linear theory that matches observed dispersion relations.

## Contribution

It introduces experimental results on parametrically driven waves in a water half-cylinder and develops a linear theory to explain the observed wave phenomena.

## Key findings

- Stationary waves are excited above a critical forcing amplitude.
- Non-axisymmetric subharmonic waves differ from classical axisymmetric waves.
- Linear theory accurately predicts dispersion relations.

## Abstract

We present the results of an experimental investigation on parametrically driven waves in a water half-cylinder on a rigid horizontal plate, which is sinusoidally vibrated in the vertical direction. As the forcing amplitude is raised above a critical value, stationary waves are excited in the water half-cylinder. Parametrically excited subharmonic waves are non-axisymmetricand qualitatively different from the axisymmetric Savart-Plateau-Rayleigh waves in a vertical liquid cylinder or jet. Depending on the driving frequency, stationary waves of different azimuthal wave numbers are excited. A linear theory is also supplemented, which captures the observed dispersion relations quantitatively.