  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.
