Coupled instabilities drive quasiperiodic order-disorder transitions in Faraday waves

TL;DR

This study experimentally investigates how coupled instabilities cause quasiperiodic transitions between ordered and disordered states in Faraday wave patterns, revealing a generic mechanism for quasiperiodicity in nonlinear systems.

Contribution

It uncovers the coupling between amplitude modulation and oscillatory instabilities as a driver for quasiperiodic order-disorder transitions in Faraday waves.

Findings

Long-wave amplitude modulation instability triggers defect formation.

Dislocation appearance dampens amplitude modulations, restoring order.

The coupling of instabilities leads to quasiperiodic pattern transitions.

Abstract

We present an experimental study of quasiperiodic transitions between a highly ordered square-lattice pattern and a disordered, defect-riddled state, in a circular Faraday system. We show that the transition is driven initially by a long-wave amplitude modulation instability, which excites the oscillatory transition phase instability, leading to the formation of dislocations in the Faraday lattice. The appearance of dislocations damps amplitude modulations, which prevents further defects from being created and allows the system to relax back to its ordered state. The process then repeats itself in a quasiperiodic manner. Our experiments reveal a surprising coupling between two distinct instabilities in the Faraday system, and suggest that such coupling may provide a generic mechanism for quasiperiodicity in nonlinear driven dissipative systems.