Turbulence in Non-Newtonian Fluids

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Abstract
The dissipation of turbulent energy is examined in incompressible isotropic fluids in which deformation depends only on current values of strain rate (Reiner-Rivlin fluids). For isotropic, homogeneous, decaying turbulence, two special cases are examined exactly—the Gaussian process and the inertial subrange. Generalizing from these and from known properties of turbulence in Newtonian media, it is concluded that anomalous properties of turbulence observed in non-Newtonian media (the Toms effect) cannot be expected for a Reiner-Rivlin model (nor for a simple power-law fluid, which is a subclass) and that the explanation for these observations must therefore be sought in visco-elasticity (i.e., dependence on history of strain). It is shown in addition that the form of the probability density of the strain tensor is almost surely quite sensitive to the form of the stress-deformation relation.

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