Some Remarks on Scaling and Universality in Turbulence

UNIVERSALITY in TURBULENCE: an EXACTLY SOLUBLE MODEL

The present note contains the text of lectures discussing the problem of universality in fully developed turbulence. After a brief description of Kolmogorov’s 1941 scaling theory of turbulence and a comparison between the statistical approach to turbulence and field theory, we discuss a simple model of turbulent advection which is exactly soluble but whose exact solution is still difficult to a...

Intermittency and universality in a Lagrangian model of velocity gradients in three-dimensional turbulence

The universality of intermittency in hydrodynamic turbulence is considered based on a recent model for the velocity gradient tensor evolution. Three possible versions of the model are investigated differing in the assumed correlation time-scale and forcing strength. Numerical tests show that the same (universal) anomalous relative scaling exponents are obtained for the three model variants. It ...

Critical Exponents and Universality in Fully Developed Turbulence

Multi-fractal model for hydrodynamic fully-developed turbulence (FDT) has been used to provide a detailed structure for the critical exponent σ describing the scaling form of energy (or enstrophy) dissipation rate ǫ (or τ) that appears to exhibit an interesting universality covering radically different hydrodynamic FDT systems. This result also appears to provide a consistent framework for clas...

Universality and scaling phenomenology of small-scale turbulence in wall-bounded flows

The Phenomenology of Small-scale Turbulence

Small-scale turbulence has been an area of especially active research in the recent past, and several useful research directions have been pursued. Here, we selectively review this work. The emphasis is on scaling phenomenology and kinematics of small-scale structure. After providing a brief introduction to the classical notions of universality due to Kolmogorov and others, we survey the existi...