Quasilinear ridge structures in water surface waves

Abstract

Nodal patterns of stationary capillary waves formed on the surface of water enclosed in an agitated ripple tank with circular and stadium-shaped cylindrical walls are examined in the low-frequency (ν700 Hz) regimes. In the low-frequency regime, in agreement with predictions of quantum-chaos theory, the shape of the tank’s boundaries (integrable or nonintegrable) dictates the type of nodal patterns obtained. In the high-frequency regime we obtain nodal patterns characterized by short-range order (called ‘‘scarlets’’ because they are believed to be the precursors of quantum scars), as recently predicted in the quantum-chaos context by P. O’Connor, J. Gehlen, and E. J. Heller [Phys. Rev. Lett. 58, 1296 (1987)].