Excitation of Faraday-like body waves in vibrated living earthworms

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...

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....

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...

Hysteretic Faraday waves.

We report on the numerical and theoretical study of the subcritical bifurcation of parametrically amplified waves appearing at the interface between two immiscible incompressible fluids when the layer of the lower fluid is very shallow. As a critical control parameter is surpassed, small amplitude surface waves bifurcate subcritically toward highly nonlinear ones with twice their amplitude. We ...