A Cascade Theory of Drag Reduction

and

Published under licence by IOP Publishing Ltd
, , Citation M. Tabor and P. G. de Gennes 1986 EPL 2 519 DOI 10.1209/0295-5075/2/7/005

0295-5075/2/7/519

Abstract

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 U(r*)/r* (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 rk. This defines a critical concentration, which depends on both polymer and flow parameters.

Export citation and abstract BibTeX RIS

10.1209/0295-5075/2/7/005