Scaling Laws for Partially Developed Turbulence

We formulate multifractal models for velocity differences and gradients which describe the full range of length scales in turbulent flow, namely: laminar, dissipation, inertial, stirring ranges. The subsume existing inertial turbulence. In localized ranges turbulence is only partially developed, we propose scaling laws with exponents modified from their values. local regions, even within a fully developed not isotropic nor scale invariant due to influence larger structures (or absence). For this reason, that an important issue study can address. turbulence, flow be far universal, so standard become inapplicable. model proposed here serves as replacement. Details fitting parameters τ p ζ dissipation are discussed. Some behavior unexplained. theories verified by comparing high resolution simulation data.