they represented a congeries of varied languages, cultures and traditions. Moreover the status of Germany, in theory ruled by the Hapsburgs in their capacity of Holy Roman Emperors, had since the conclusion of the Thirty Years War been in some doubt. In practice the Hapsburgs could count on obedience always in their family dominions, not particularly extensive and mostly concentrated in the West (Vorderosterreich); sometimes in the South German Catholic states; and virtually not at all in the Protestant North. Then, too, in the second half of the seventeenth century Prussia had emerged as a power, which although still technically a part of the Empire, was increasingly capable and willing to pursue a thoroughly independent course. The position of Charles VI was thus not an entirely happy one. The long run alternatives which would seem to have confronted him were either to acquiesce in the continuing erosion of Hapsburg influence in Germany, which ultimately might well have resulted in his ruling over a Danubian Empire with a German-speaking minority; or to try to buttress his position in Germany, which would have required eventually a viable modus vivendi between his German and non-German subjects.

Comprehensive, unique coverage of turbulent flow including modern prediction and measurement

Turbulent Flow presents the essential physical and analytical background that enables readers to make informed decisions when choosing the best method for the study and prediction of turbulent flows. Critical focus is given to experimental and numerical methods as well as what these methods have revealed about turbulent motion.

Coverage includes an introduction to turbulence theory, the fundamental equations of turbulent flow and their meaning, the techniques used in physical experiments and computer simulations, a review of the progress made in understanding the properties of turbulence, turbulence closures and their applications, and large eddy simulation methods.

Cutting-edge material includes:

• State-of-the-art turbulence closure and simulation techniques
• Up-to-date presentations of major theoretical and experimental advances
• Vortex analysis of turbulence structure, transport, and modeling

Turbulent Flow is an essential book for students and an invaluable reference for mechanical and aerospace engineers, physicists and mathematicians in related disciplines, and engineers and scientists in such fields as chemical, biological, and ocean engineering.