Vortex Motion on the Surface of Shallow and Deep Water

The attenuation of vortex motion on the surface of shallow and deep water is investigated. The vortex flow was 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 was switched off, and the attenuation of the surface flow was recorded. On the surface of shallow water, λ/2π ≈ h, when the characteristic size of the vortices L exceeds the depth of the liquid, L >> h, the time dependence of the energy of the vortex flow Е(t) is described by an exponential function at all pumping levels, and the dependence of the enstrophy Ф(t) = Ω²(t) has an exponential dependence only in the range of wave vectors 0–0.3 см^–1. On the surface of deep water λ/2π < h, L ≈ h dependence Е(t) and Ф(t) are far from exponential in all ranges of wave numbers. At high pumping levels, the dependencies Е(t) and Ф(t) are nonmonotonic, which can be attributed to the influence of volumetric flows.