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Key Words homogeneous turbulence, passive scalar problem, Kolmogorov theory, turbulent diffusion
* Abstract This essay is based on the G.K. Batchelor Memorial Lecture that I delivered in May 2000 at the Institute for Theoretical Physics (ITP), Santa Barbara, where two parallel programs on Turbulence and Astrophysical Turbulence were in progress. It focuses on George Batchelor's major contributions to the theory of turbulence, particularly during the postwar years when the emphasis was on the statistical theory of homogeneous turbulence. In all, his contributions span the period 1946-1992 and are for the most part concerned with the Kolmogorov theory of the small scales of motion, the decay of homogeneous turbulence, turbulent diffusion of a passive scalar field, magnetohydrodynamic turbulence, rapid distortion theory, two-dimensional turbulence, and buoyancy-driven turbulence.
1. INTRODUCTION
George Batchelor (1920-2000) (see Figure 1) was undoubtedly one of the great figures of fluid dynamics of the twentieth century. His contributions to two major areas of the subject, turbulence and low-Reynolds-number microhydrodynamics, were of seminal quality and have had a lasting impact. At the same time, he exerted great influence in his multiple roles as founding Editor of the Journal of Fluid Mechanics, co-Founder and first Chairman of Euromech, and Head of the Department of Applied Mathematics and Theoretical Physics (DAMTP) in Cambridge from its foundation in 1959 until his retirement in 1983.
I focus in this article exclusively on his contributions to the theory of turbulence, in which he was intensively involved over the period 1945 to 1960. His research monograph, The Theory of Homogeneous Turbulence, published in 1953, appeared at a time when he was still optimistic that a complete solution to the problem of turbulence might be found. During the 1950s, he attracted an outstanding group of research students, many from his native Australia, to work with him in Cambridge on turbulence. By 1960, it had become apparent to him that insurmountable mathematical difficulties in dealing adequately with the closure problem lay ahead. As he was to say later (Batchelor 1992), "by 1960 ... I was running short of ideas; the difficulty of making any firm deductions about turbulence was beginning to be frustrating, and I could not see any real break-through in the current publications." Over the next few years,...