5R51. Navier-Stokes Equations and Turbulence. Encyclopedia of Math and its Applications, Vol 83. - C Foias (Dept of Math, Indiana Univ, Bloomington IA), O Manley (Consultant), R Rosa (Univ Fed do Rio de Janeiro, Rio de Janeiro, Brazil), and R Temam (Univ Paris-Sud, Orsay, France). Cambridge UP, New York. 2001. 347 pp. ISBN 0-521-36032-3. $90.00.

Reviewed by J Meng (NAVESEA, Keyport WA 98345).

This is an excellent book for interdisciplinary graduate level education and as a reference book for the turbulence research community. This book is the first to build a comprehensive common ground between themathematics and turbulence communities in terms of demonstrating that NSE constitutes a comprehensive model of incompressible flows. The major contributions are in showing how: The Kolmogorov spectrum for three dimensional turbulence; and Kraichnan spectrum for two-dimensional turbulence follow naturally from the NSE; the intermittency of turbulent flows is related to the fractal nature of energy dissipation in three dimensions; and on providing a bound on the sufficient number of degrees of freedom for this fluid flow.

This book provides a well-founded conviction that further understanding of turbulence is determinable from the NSE without invoking additional ad hoc assumptions so that more insights into the nature of turbulence can be gained from studying the intrinsic properties of the NSE which historically could not be arrived at by intuitive considerations. Navier-Stokes Equations and Turbulence serves as an excellent starting point to inspire scholars to take the next step of tying together the theoretical aspects with the known experimental phenomenology, such as the repeatable patterns of wall turbulence and free shear flows. Once accomplished, it would give tremendously more insights to the physical relevance and will no doubt provide even more impetus of progress in solving one of the greatest challenges in science.