Correlation dimension analysis and capillary wave turbulence in Dragon-Wash phenomena

This paper describes the evolution of surface capillary waves of deep water excited by gradually increasing the lateral external force at a single frequency. The vertical velocities of the water surface are measured by using a Polytec Laser Vibrometer with a thin layer of aluminium powder scattering on the surface to reflect the laser beam. Nonlinear interaction processes result in a stationary Fourier spectrum of the vertical surface velocities (the same as the surface elevation), i.e. I_\omega \sim \omega ^ - 3.5. The observed spectrum can be interpreted as a wave-turbulent Kolmogorov spectrum for the case of `narrowband pumping' for a direct cascade of energy. Correlation dimension analysis of the whole development process reveals four distinct stages during the wave structure development and identifies the wave turbulence stage.