A cascade theory of drag reduction

We describe homogeneous, isotropic, three-dimensional turbulence in a dilute solution of neutral,flexible chains. Energy flows by the usual cascade down to a scale r such that the shear rates Ur U being the velocity become equal to the relaxation rate of one coil. At small scales r, the molecules follow affinely the deformation of a local volume element. At a certain smaller scale r the elastic stresses in the coils become comparable to the Reynolds stresses. The polymer truncates the cascade when r becomes larger than the usual Kolmogorov limit r. This defines a critical concentration, which depends on both polymer and flow parameters.