Experimental Study of Parametric Autoresonance in Faraday Waves

The excitation of large amplitude nonlinear waves is achieved via parametric autoresonance of Faraday waves. We experimentally demonstrate that phase locking to low amplitude driving can generate persistent high-amplitude growth of nonlinear waves in a dissipative system. The experiments presented are in excellent agreement with theory.Comment: 4 pages, 4 eps figures, to appear in Phys. Rev. Let

Surface-tension-driven flow in a slender cone

After a droplet has broken away from a slender thread or jet of liquid, the tip of the thread or jet recoils rapidly. At the moment of break-off, the tip of the thread/jet is observed to have the shape of a cone close to the bifurcation point. In this paper, we study the evolution of an ideal fluid which is initially conical, where the only force acting on the fluid is due to surface tension. We find an asymptotic solution to the problem in terms of the aspect ratio of the cone which is assumed to be small. Using a similarity transformation, which is valid for small times after the bifurcation, we identify a rapidly oscillating nonlinear wave which propagates away from the tip, as observed in experiments

Sideband instability and modulations of Faraday waves

Three-mode interaction equations are derived for Faraday waves in a long rectangular container. Two water depths are studied, revealing very different behaviour. Our equations include conservative and non-conservative cubic nonlinear terms, and quintic conservative nonlinear terms. Instability of a single standing wave to neighbouring modes is examined. Resultant three-mode interactions display rich structure, with fast and slow timescales. For the smaller depth, but not the greater, recurrent nearly calm intervals are separated by strong wave activity. Our results agree quite well with experimental findings of Craik and Armitage [Faraday excitation, hysteresis and wave instability in a narrow rectangular wave tank, Fluid Dyn. Res. 15 (1995) 129-143] and with unpublished observations by Armitage, Craik and Sterratt, here briefly described. (C) 1999 Elsevier Science B.V. All rights reserved.</p