Forced 2D Turbulence: Experimental Evidence of Simultaneous Inverse Energy and Forward Enstrophy Cascades

Abstract

We have performed measurements on forced and decaying 2D turbulence in flowing soap films. Unlike previous experiments, turbulence was excited by grids (arrays of cylinders) lining the walls of the flow channel. The resulting turbulent steady state agrees with the ideas of an inverse energy cascade accompanied by a forward enstrophy cascade. Energy spectra agree, respectively, with $k^{-5\mathrm{}/3}$ and $k^{-3\mathrm{}}$ power laws. Downstream from the forcing section of the channel, the turbulence decays freely, and the energy spectrum scales only as $k^{-3\mathrm{}}$. Our observations unite the results of several theories, and a number of simulations and experiments, into a single self-consistent set of measurements.