Theoretical Model for Faraday Waves with Multiple-Frequency Forcing

TL;DR

This paper introduces a generalized Swift-Hohenberg model to analyze Faraday wave patterns driven by dual-frequency forcing, capturing various symmetric patterns observed experimentally.

Contribution

It presents a theoretical model extending the Swift-Hohenberg equation to describe complex Faraday wave patterns with multiple unstable length scales.

Findings

Model reproduces steady-state patterns with multiple symmetries.

Captures both periodic and quasiperiodic patterns.

Aligns with recent experimental observations.

Abstract

A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a fluid driven by a linear combination of two frequencies. The model exhibits steady-state solutions with two-, four-, six-, and twelve-fold symmetric patterns, similar to the periodic and quasiperiodic patterns observed in recent experiments.