  In fully developed three dimensional fluid turbulence the fluctuating energy
is supplied at large scales, cascades through intermediate scales, and
dissipates at small scales. It is the hallmark of turbulence that for
intermediate scales, in the so called inertial range, the average energy flux
is constant and independent of viscosity [1-3]. One very important question is
how this range is altered, when an additional agent that can also transport
energy is added to the fluid. Long-chain polymers dissolved at very small
concentrations in the fluid are such an agent [4,5]. Based on prior work by de
Gennes and Tabor [6,7] we introduce a theory that balances the energy flux
through the turbulent cascade with that of the energy flux into the elastic
degrees of freedom of the dilute long-chain polymer solution. We propose a
refined elastic length scale, $r_\varepsilon$, which describes the effect of
polymer elasticity on the turbulence energy cascade. Our experimental results
agree excellently with this new energy flux balance theory.
