THE PHENOMENOLOGY OF SMALL-SCALE TURBULENCE

TLDR

Small‑scale turbulence has attracted intense research, drawing diverse interpretations and philosophical reflections on its multiplicity of meanings. Here, we selectively review this work, emphasizing scaling phenomenology and the kinematics of small‑scale structure. The review begins with classical Kolmogorov universality, then surveys intermittency, refined similarity, anomalous scaling, derivative statistics, models, and the structure and kinematics of small‑scale turbulence, largely based on direct numerical simulations of homogeneous turbulence in a periodic box.

Abstract

I have sometimes thought that what makes a man's work classic is often just this multiplicity [of interpretations], which invites and at the same time resists our craving for a clear understanding. Wright (1982, p. 34) , on Wittgenstein's philosophy ▪ Abstract 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 existing work on intermittency, refined similarity hypotheses, anomalous scaling exponents, derivative statistics, intermittency models, and the structure and kinematics of small-scale structure—the latter aspect coming largely from the direct numerical simulation of homogeneous turbulence in a periodic box.