Vortex Motion on the Surface of Shallow and Deep Water

Abstract

The attenuation of vortex motion on the surface of shallow and deep water is investigated. The vortex flow is formed by two mutually perpendicular waves excited by plungers at a frequency of 6 Hz (wavelength λ = 5.6 cm) on the surface of water measuring 70 × 70 cm and depth h. After reaching a stationary state in the vortex system, the wave pumping is switched off and the attenuation of the surface flow is recorded. On the surface of shallow water, λ/2π ≈ h, when the characteristic size of vortices L exceeds the depth of the liquid, L \( \gg \) h, the time dependence of the energy of the vortex flow Е(t) is described by an exponential function at all pumping levels while the dependence of enstrophy Ф(t) = Ω²(t) is exponential only in the range of wave vectors 0–0.3 cm^–1. On the surface of deep water, λ/2π < h, L ≈ h the dependences Е(t) and Ф(t) are far from exponential in all wavenumber ranges. At high pumping wave amplitudes, the dependences Е(t) and Ф(t) are nonmonotonic, which can be attributed to the influence of volumetric flows.