Forced and decaying 2D turbulence: Experimental study
We report experimental results obtained on freely decaying and forced two-dimensional turbulence. The flow is produced in a thin stratified layer of electrolyte, using an electromagnetic forcing. The velocity and vorticity fields are measured using a particle image velocimetry (PIV) technique. The study of the temporal evolution of the system confirms in detail the scaling theory of Carnevale et al. (1991). We further measure the merging time τ, the mean free path λ, and the mean square displacement σ v 2 of the vortices. We find the following laws: τ ∼ t 0.57, λ∼t 0.45, σ v 2 ∼t 1.3. The statistics of passive particles (albeit virtual) in the system is also studied. They move hyperdiffusively, with an exponent identical to that obtained for the vortex motion. We find the dispersion of the particles is controlled by Lévy flights, produced by the jets formed by the dipoles. We finally underline the close relationship between the decay of turbulence decay and the dispersion phenomena. We further turn to the forced case. We find the energy spectrum displays a clear k −5/3 law with a Kolmogorov constant lying in the range 5.5–7.5, which is consistent with the current numerical estimates. The dispersion of pairs of passive particles is found to be controlled by Richardson law, throughout the inertial range of scales revealed by the analysis of the flow field. No evidence for the existence of Levy flights has been found. At variance with the decaying case, it is not clear whether coherent structures may play any role in the control of the main characteristics of the inverse cascade, along with the pair dispersion in the corresponding inertial range of scales.
KeywordsParticle Image Velocimetry Coherent Structure Vortex Center Vorticity Field Inertial Range
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