This book addresses the idealised problem posed by homogeneous, isotropic turbulence. It is written from the perspective of a theoretical physicist, but is designed to be accessible to all researchers in turbulence, both theoretical and experimental, and from all disciplines.

• Part I: The fundamental problem, the basic statistical formulation, and the phenomenology of energy transfer


• 1: Overview of the statistical problem


• 2: Basic equations and definitions in x-space and k-space


• 3: Formulation of the statistical problem


• 4: Turbulence energy: its inertial transfer and dissipation


• Part II: Phenomenology: some current research and unresolved issues


• 5: Galilean invariance (GI)


• 6: Kolmogorov's (1941) theory revisited


• 7: Turbulence dissipation and decay


• 8: Theoretical constraints on mode reduction and the turbulence response


• Part III: Statistical theory and future directions


• 9: The Kraichnan-Wyld-Edwards (KWE) covariance equations


• 10: Two-point closures: some basic issues


• 11: Renormalization group (RG) applied to turbulence


• 12: Work in progress and future directions


• Part IV: Appendices


• A: Implications of isotropy and continuity for correlation tensors


• B: Properties of Gaussian distributions


• C: Evaluation of the L(k; j) coefficient

The author has had wide experience in both engineering and physics departments. After early career experience in research and development in the nuclear power industry, he returned to university to study theoretical physics. Following the completion of a PhD in turbulence theory, he took up the post of Senior Scientific Officer in the Theoretical Physics Division at AERE, Harwell. Thereafter he held successively lectureships in engineering science and physics, a readership in physics, and a personal chair in statistical physics at Edinburgh University. On his retirement in 2006, he was appointed Professor Emeritus, and now also holds a Senior Professorial Fellowship. He has been guest professor at the University of Delft, and visiting fellow at Wolfson College and the Isaac Newton Institute, Cambridge. During the period 2007-09 he held a Leverhulme Emeritus Fellowship.