Elastic Energy Flux by Flexible Polymers in Fluid Turbulence

We present a study of the energy transfer in the bulk of a turbulent flow with dilute long-chain polymer additives. Based on prior work by Tabor and de Gennes [Europhys. Lett. 2, 519 (1986); Physica (Amsterdam) 140A, 9 (1986)], we propose a theory on the energy flux into the elastic degrees of freedom of the polymer chains. This elastic energy flux, which increases as the length scale decreases, gradually reduces the energy transferred to smaller scales through turbulence cascade and hence suppresses small scale fluctuations. The balance of the elastic energy flux and the turbulence energy cascade gives an elastic length scale, which describes the effect of polymer elasticity on turbulence in the inertial range. Predictions of this new energy flux balance theory agree excellently with our experimental results.