Energy spectra in polymer-doped turbulent soap films

We investigate the energy spectra of turbulent soap films doped with a dilute amount of a very large molecular weight polymer ($>$ 1M). We perform experiments in a soap-film channel that in the absence of polymers manifests decaying turbulence and a direct enstrophy cascade: the energy spectrum E(k) $\propto$ k$^{-3}$. For polymer-doped flow, where the polymer is added gently to the soapy solution, we observe that the energy spectrum switches to E(k) $\propto$ k$^{-5/3}$, which is consistent with the inverse energy cascade of forced 2D turbulence. This switching of the spectral exponent from 3 to 5/3 occurs for polymer concentrations as low as 2 wppm. For lower concentrations, the spectral exponent is unaffected. We also find that our results are sensitive to the method of polymer doping. If we stir our polymer-doped solution repeatedly, the effect of the polymer diminishes: the exponent of the energy spectrum switches back from 5/3 to 3.