Decay of a vortex lattice formed by gravity waves on the water surface

Abstract

Abstract The generation and decay of a vortex lattice formed by standing gravity waves of 3 Hz frequency on the water surface have been studied experimentally using the particle image velocimetry technique. During the process of excitation the formation of large-scale vortices as a result of interaction of eddies from a vortex lattice is observed. Immediately after the pumping had been turned off in the initial time interval of about 30 s, the time dependence of vortex motion energy E vort close to an exponential decrease was observed with a characteristic time of τ w ≈ 7 s , which is mainly due to the viscous losses of the surface waves. A decrease in wave amplitude leads to reduction in the Stokes drift of floating particles. In the second time interval from 30 to 200 s there is no exponential dependence E vort ( t ) , that is related, apparently, to an energy relaxation of different vortex scales: from the bath size to the pumping wavelength. In this time interval the vortex interaction is also recorded leading to redistribution of energy from the pumping region to large scales. It should be emphasized that the vortex motion generated by the interaction of nonlinear waves is conserved after the complete decay of the wave motion on the water surface, and there is a transfer of energy from small scales to large ones as a result of the process of unification of several lattice vortices into a large-scaled vortex – reverse energy flow. In the time interval above 200 s there is an exponential energy relaxation of vortices of the maximum scale because of the viscous bath bottom and sides friction.