Extending Kolmogorov theory to polymeric turbulence

We present a formalism that reconciles polymeric turbulence with the classical Kolmogorov phenomenology. By relying on an appropriate form of the Kármán-Howarth-Monin-Hill equation, we define extended velocity increments and structure functions that also incorporate the non-Newtonian, polymeric contribution. The <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi mathvariant="normal">p</a:mi><a:mi>th</a:mi></a:mrow></a:math>-order extended structure functions exhibit a power-law behavior in the elastoinertial range of scales, with exponents deviating from the analytically predicted value of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi mathvariant="normal">p</c:mi><c:mo>/</c:mo><c:mn>3</c:mn></c:mrow></c:math>. These deviations are readily accounted for by considering local averages of the total dissipation rather than global averages. We also demonstrate the scale invariance of multiplier statistics of the extended velocity increments, whose distributions collapse for a wide range of scales.