THE PHENOMENOLOGY OF SMALL-SCALE TURBULENCE

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

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.