Formation of an energy cascade in a system of vortices on the surface of water

Abstract

The formation of an energy cascade in a system of vortices generated by perpendicular standing waves with a frequency of 6 Hz on the water surface has been experimentally studied. It has been found that peaks appear on the energy distribution over wave vectors E(k) after switching on pum**. These peaks are transformed with time because of the energy redistribution over scales. The stationary distribution E(k) established 300 s after switching on pum** can be described by a power-law function of the wave vector E(k) ∼ k^1.75. It has been shown that waves with frequencies of about 18, 15, 12, 9, and 3 Hz appear on the surface of water owing to the nonlinear interaction at the excitation of a 6-Hz wave. It is assumed that the energy cascade of the turbulent motion in the wave vector range of 0.3–5 cm⁻¹ is formed by the nonlinear interaction between vortices generated by all waves propagating on the surface and direct energy fluxes toward high wave vectors dominate.