Rhombic Patterns Near a Bicritical Point in Periodically Forced Surface Waves

TL;DR

This paper investigates how rhombic patterns form near a bicritical point in viscous fluids subjected to two-frequency vertical vibrations, highlighting conditions for their natural emergence in Faraday experiments.

Contribution

It identifies conditions under which rhombic patterns naturally occur at the primary instability in a bicritical point scenario with two-frequency forcing.

Findings

Rhombic patterns appear near the bicritical point under specific frequency ratios.

Two distinct rhombic patterns are identified as accessible in experiments.

The study links pattern selection to the ratio of driving frequencies.

Abstract

We present here a study of selection of rhombic patterns close to a bicritical point at the onset of primary surface instability in viscous fluids under two-frequency vertical vibration. Rhombic patterns appear to be natural at the primary instability in the form of a bicritical point if the ratio of driving frequencies is selected properly. We present two different patterns which may be accessible in a Faraday experiment.