New Trends In Turbulence

i i i “yaglom” 2001/9/26 page 1 i COURSE 1 THE CENTURY OF TURBULENCE THEORY: THE MAIN ACHIEVEMENTS AND UNSOLVED PROBLEMS A. YAGLOM Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevsky 3, 109017 Moscow, Russia, and Department of Aeronautics & Astronautics, MIT 33-219, 77 Massachusetts Avenue, Cambridge, MA 02139-9307, U.S.A. i i i i i “yaglom” i 2001/9/26 page 2 i i Contents 1 Introduction 3 2 Flow instability and transition to turbulence 6 3 Development of the theory of turbulence in the 20th century: Exemplary achievements 3.1 Similarity laws of near-wall turbulent flows . . . . . . . . . . . . . 3.2 Kolmogorov’s theory of locally isotropic turbulence . . . . . . . . . 11 11 30 4 Concluding remarks; possible role of Navier–Stokes equations 39 i i i i i i i “yaglom” 2001/9/26 page 3 i THE CENTURY OF TURBULENCE THEORY: THE MAIN ACHIEVEMENTS AND UNSOLVED PROBLEMS A. Yaglom 1 Introduction The flows of fluids actually met both in nature and engineering practice are turbulent in the overwhelming majority of cases. Therefore, in fact the humanity began to observe the turbulence phenomena at the very beginning of their existence. However only much later some naturalists began to think about specific features of these phenomena. And not less than 500 years ago the first attempts of qualitative analysis of turbulence appeared – about 1500 Leonardo da Vinci again and again observed, described and sketched diverse vortical formations (“coherent structures” according to the terminology of the second half of the 20th century) in various natural water streams. In his descriptions this remarkable man apparently for