Mechanics of fluid deformations in rigid body rotations and plane channel F

Abstract

This book is wide ranging, in the area of viscous fluid mechanics in general, and in the areas of rotating viscous flow and plane channel flow in particular. At first, it appears that the theme is classical fluid dynamics, as plane channel flow is one of the great historical problems in fluid dynamics, but a closer examination shows a modern book that is distinctly original. It combines functional analysis, geometry, vector analysis, and most importantly presents a new approach to rotational viscous flows. The book builds up to Part 5 (Plane Channel Flow Stability), where a new viewpoint on vortical flows, as infinitedimensional rotations, is presented. The three chapters in Part 5 are a beautiful blend of insight and elementary analysis, leading into rigorous functional analysis. On the other hand, the functional analysis is presented in a way that is very accessible. Concepts such as non-commutative inertia, vortex phantoms, vortex catastrophe, adjoined spectral problem, and a range of rigorous concepts of stability are introduced and explained. The book ends with a major lemma which takes over two pages to state! However, it is a very accessible lemma (on the Rayleigh function), and takes only two more pages to complete the proof. The remainder of the book is a buildup to Part 5 via Parts 1–4. Part 1 (Velocity Strain) is a review of the basics of fluid motion from a perspective that the author will need later, with a distinctly geometric flavour. Part 2 (Rigid Body Rotations) reviews angular motion in classical mechanics and in particular angular friction with the dissipative spinning top as an example, giving new insight into this classical problem. Part 3 (Conservation Laws) discusses momentum conservation, role of viscosity and heat conductivity, with the highlight of this part a discussion of ‘centrifuge’, which is used to explain some of the anomalies of rotating viscous flows. Torsional rotations are discussed, including some deep analysis of the author, explaining some of the strange behaviour witnessed in experiments. This analysis is supported by direct numerical simulations. Part 4 (Turbulence) starts to get into more challenging aspects of fluid flow. The main theme is the concept of a ‘turbulence force’. The force is normal integration of the correlation matrix of the velocity pulsation. It is in principle measurable experimentally and can be extracted from numerical simulations. A range of results using the turbulence force and its generalisations are proved, going so far afield as to relate it to dark matter in astrophysics. This book is a welcome addition to the literature in fluid mechanics, and I have no hesitation in recommending it. The book is not a textbook as it is too advanced in most places. It is a book about insight along with a body of methodology, which takes the study of channel flow and rotating viscous flows in a new direction. Its most effective audience is postdoctoral scholars and academic researchers, as it presents an alternative view of how to study rotating viscous flows, thereby widening the research perspective. The book is of reasonable length, coming in at less than 300 pages, but it is a bit pricey at £85 for the hardback, although many university libraries willmake it available electronically for researchers.