Scaling of turbulent velocity structure functions: Plausibility constraints

The th-order velocity structure function in homogeneous isotropic turbulence is usually represented by, where the spatial separation lies within the inertial range. The first prediction for (i.e.) was proposed by Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941) using a dimensional argument. Subsequently, starting with Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82-85), models for the intermittency of the turbulent energy dissipation have predicted values of that, except for, differ from. In order to assess differences between predictions of, we use the Hölder inequality to derive exact relations, denoted plausibility constraints. We first derive the constraint between the exponents, where are any three positive numbers. It is further shown that this relation leads to. It is also shown that the relation, which complies with, can be derived from constraints imposed on using the Cauchy-Schwarz inequality, a special case of the Hölder inequality. These results show that while the intermittency of, which is not ignored in the present analysis, is not incompatible with the plausible relation, the prediction is not plausible, unless.