Experimental Study of Parametric Autoresonance in Faraday Waves

Parametric autoresonance in Faraday waves.

We develop a theory of parametric excitation of weakly nonlinear standing gravity waves in a tank, which is under vertical vibrations with a slowly time-dependent ("chirped") vibration frequency. We show that, by using a negative chirp, one can excite a steadily growing wave via parametric autoresonance. The method of averaging is employed to derive the governing equations for the primary mode....

Autoresonance of coupled nonlinear waves

Adiabatic passage of weakly coupled nonlinear waves with space-time varying parameters through resonance is investigated. Slow evolution equations describing this wave interaction problem are obtained via Whitham’s averaged variational principle. Autoresonant solutions of these equations are found and, locally, comprise adiabatically varying quasiuniform wave train solutions of the decoupled pr...

FAR Faraday Waves

Pattern Selection in Faraday Waves

We present a systematic nonlinear theory of pattern selection for parametric surface waves (Faraday waves), not restricted to fluids of low viscosity. A standing wave amplitude equation is derived from the Navier-Stokes equation that is of gradient form. The associated Lyapunov function is calculated for different regular patterns to determine the selected pattern near threshold as a function o...

On Faraday waves

The standing waves of frequency wand wavenumber k that are induced on the surface of a liquid of depth d that is subjected to the vertical displacement a, cos 2wt are determined on the assumptions t1mt: the effects of lateral boundaries are negligible: £ = ka, tanh kd ~ 1 and 0 < £-0 = 0(0'), where 0 is the linear damping ratio of a free wave of frequency w; the ""wes form a square pattern (whi...