Qian Jian and His Contribution to Small-Scale Turbulence Studies

TL;DR

Qian Jian developed a statistical theory of small-scale turbulence based on Liouville's equation, providing new insights into turbulence closure, intermittency, and the effects of Reynolds number, significantly advancing theoretical understanding in fluid dynamics.

Contribution

Qian Jian's work introduces a novel statistical framework for small-scale turbulence, addressing key problems and proposing corrections to classical turbulence equations.

Findings

Inertial range exists only when Re > 2000.

Normal scaling is valid at infinite Re, anomalous scaling due to finite Re.

Derived a finite Re correction to Kolmogorov's equation.

Abstract

Qian Jian, a Chinese theoretical physicist and fluid dynamicist, devoted the second part of his scientific life to the physical understanding of small-scale turbulence to the exclusion of all else. Qian developed his own statistical theory of small-scale turbulence, based on the Liouville (1853) equation and a perturbation variational approach to non-equilibrium statistical mechanics, which is compatible with the Kolmogorov-Oboukhov energy spectrum. His statistical theory of small-scale turbulence, which appears mathematically and physically valid, successfully led to his contributions to (i) the closure problem of turbulence; (ii) one-dimensional turbulence; (iii) two-dimensional turbulence; (iv) the turbulent passive scalar field; (v) the cascade model of turbulence; (vi) the universal equilibrium range of turbulence; (vii) a simple model of the bump phenomenon; (viii) universal constants of turbulence; (ix) the intermittency of turbulence; and perhaps most importantly, (x) the effect of the Taylor microscale Reynolds number on both the width of the inertial range of finite Re turbulence and the scaling exponents of velocity structure functions. In particular, Qian found that the inertial range cannot exist when Re is smaller than 2000. In contrast to the prevailing intermittency models, he discovered that normal scaling is valid in the real Kolmogorov inertial range when Re approaches infinity while the anomalous scaling observed in experiments reflects the finite Re effect. He then made a correction to the famous Kolmogorov (1941c) equation and obtained the finite Re effect equation or the Kolmogorov-Novikov-Qian equation. He also independently derived the decay law of the finite Re effect. Qian steered us along the right path to an improved understanding of small-scale turbulence and solutions to its problems.