Universality of Kolmogorov law in spectrally condensed turbulence in thin layers

Abstract

The four-fifth Kolmogorov law relates the third-order structure function and the energy dissipation rate ε in three-dimensional turbulence (see, e.g. [1]. This law for 2D turbulence reads: $$S_{L3} = (3/2) \in r$$ , where $$S_{L3} = < \delta v_L^3 > $$ is the third moment of the longitudinal velocity increments at the scale r. Angular brackets denote averaging over the box size and time. This relationship allows the energy dissipation rate, or the energy flux within the inertial range to be determined by analyzing the third-order velocity moments in laboratory experiments or in observational data. The Kolmogorov law has been confirmed in direct numerical simulations of 2D turbulence [2], however previous experimental attempts to derive ε from the third-order longitudinal structure functions were not successful [3], probably due the insufficient statistics in the calculations of $$< \delta v_L^3 >$$ . In this paper we present the results of the S3(r) measurements in quasi-2D turbulence in laboratory experiments. We are particularly interested in estimating the energy flux in the energy inertial interval and in comparison of its value with independently obtained energy dissipation rate.