Control of spatiotemporal disorder in parametrically excited surface waves

Area of Science:

• Nonlinear dynamics
• Fluid mechanics
• Wave phenomena

Background:

• Parametrically excited surface waves exhibit complex nonlinear states.
• A disordered state arises from competing nonlinearities near a bicritical point.

Purpose of the Study:

• To investigate the stabilization of disordered nonlinear wave states.
• To explore the role of external control in selecting specific nonlinear states.

Main Methods:

• Experimental study of interacting surface waves.
• Application of open-loop control using a third frequency excitation.
• Analysis of temporal and spatial symmetries of selected states.

Main Results:

• A disordered spatio-temporal state was identified.
• Open-loop control rapidly stabilized this disordered state into various nonlinear states.
• The symmetry of the third excitation frequency dictated the symmetry of the selected nonlinear state.
• Rapid switching between different nonlinear states was achieved.

Conclusions:

• Open-loop control offers an effective method for stabilizing complex nonlinear wave dynamics.
• External frequency excitation provides a means to select and control the symmetry of nonlinear states.
• This technique facilitates rapid transitions between distinct nonlinear dynamical behaviors.