Qian [Tsien] 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. To place Qian's contribution in an appropriate position in the field of small-scale turbulence, a historical overview and a state-of-the art review are attempted. 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. Qian's 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) onedimensional 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 (π
π ) on both the width of the inertial range of finite π
π turbulence and the scaling exponents of velocity structure functions. In particular, Qian found that the inertial range cannot exist when π
π βͺ 2000. In contrast to the prevailing intermittency models, he discovered that normal scaling is valid in the real Kolmogorov inertial range when π
π approaches infinity while the anomalous scaling observed in experiments reflects the finite π
π effect (π π ). He then made a correction to the famous Kolmogorov (1941c) equation and obtained the finite π
π effect equation or the Kolmogorov-Novikov-Qian equation. He also independently derived the decay law of the finite π
π effect. Following up Kraichnan, Qian steered all of us along the right path to an improved understanding of small-scale turbulence and solutions to its problems. Qian is credited with his contribution to enhanced knowledge about the finite π
π effect of turbulence, which has profoundly shaped and stimulated thinking about the K41 turbulence, the K62 turbulence and the finite π
π turbulence.
