Intermittency in the two-dimensional inverse cascade of energy: Experimental observations

Abstract

An extensive experimental study of the two-dimensional inverse energy cascade is presented. The experiments are performed in electromagnetically driven flows, using thin, stably-stratified layers. Complete instantaneous velocity fields are measured using particle imaging velocimetry techniques. Depending on the bottom-wall friction, two different regimes are observed: when the friction is low, the energy transferred from the forcing scale towards large scales accumulates in the lowest accessible mode, leading to a mean rotation of the flow and to an energy spectrum displaying a sharp peak at the minimum wave-number. This condensation is accompanied by the emergence of a very strong vortex around which the rotation is organized. At higher frictions, the inverse energy cascade conjectured by Kraichnan [Phys. Fluids 10, 1417 (1967)] is observed and is found to be stationary, homogeneous and isotropic, with a Kolmogorov constant consistent with numerical estimates. This inverse cascade does not appear to be characterized by the presence of strong coherent vortices. The characteristic size of the latter is of the order of the injection scale. Their statistical properties tend to show that the cascade is rather driven by a clustering mechanism involving same sign vortices rather than a sequence of merging events producing larger and larger vortices. Intermittency effects are also investigated for the inverse cascade range. It is found that, within experimental errors, there is no intermittency in the inverse cascade range of two-dimensional turbulence and that the statistics of velocity increments, either longitudinal or transverse, are close to Gaussian. These results constitute the first experimental study of intermittency in two-dimensional turbulence as well as the first observation of normal scaling in a field of research which has been increasingly concerned with anomalous exponents.