1.1 Scope of the Book

Turbulence is well known to be one of the most complex and exciting fields of research that raises many theoretical issues and that is a key feature in a large number of application fields, ranging from engineering to geophysics and astrophysics. It is still a dominant research topic in fluid mechanics, and several conceptual tools developed within the framework of turbulence analysis have been applied in other fields dealing with nonlinear, chaotic phenomena (e.g., nonlinear optics, nonlinear acoustics, econophysics, etc.).

Despite more than a century of work and a number of important insights, a complete understanding of turbulence remains elusive, as witnessed by the lack of fully satisfactory theories of such basic aspects as transition and the Kolmogorov k ^{?5 / 3} spectrum. Nevertheless, quantitative predictions of turbulence have been developed. They are often based on theories and models that combine true dynamical equations and closure assumptions and are supported by physical and more and more numerical experiments.

Homogeneous turbulence remains a timely subject, even half a century after the publication of Batchelor s book in 1953, and this framework is pivotal in the present book. Homogeneous isotropic turbulence (HIT) is the best known canonical case; it is very well documented even if not completely understood from experiments and simple models to recent 4096 ³ full direct numerical simulation (DNS). Of course, this case is addressed (in Chapter 3), but more generally emphasis is put on homogeneous anisotropic turbulence (HAT)...