Energy spectrum of non-Newtonian turbulence

Homogeneous and isotropic turbulence in a viscoelastic fluid is examined theoretically with the role of small parameter played by either the fluid relaxation time or the Weissenberg number. A Martin-Siggia-Rose framework is used to obtain a formal expression for the velocity correlation function of the non-Newtonian flow, and expanded to linear order in the relaxation time. The expansion coefficients are correlation functions of the base Newtonian flow. These correlations are not derived, but replaced by their values according to K41 theory. While substantial work will be necessary to validate the model against numerical and experimental data, preliminary results are encouraging.