Turbulence and Coherent Structures

In the last 25 years, one of the most striking advances in Fluid Mecha­ nics was certainly the discovery of coherent structures in turbulence: lab­ oratory experiments and numerical simulations have shown that most turbulent flows exhibit both spatially-organized large-scale structures and disorganized motions, generally at smaller scales. The develop­ ment of new measurement and visualization techniques have allowed a more precise characterization and investigation of these structures in the laboratory. Thanks to the unprecedented increase of computer power and to the development of efficient interactive three-dimensional colour graphics, computational fluid dynamicists can explore the still myste­ rious world of turbulence. However, many problems remain unsolved concerning the origin of these structures, their dynamics, and their in­ teraction with the disorganized motions. In this book will be found the latest results of experimentalists, theoreticians and numerical modellers interested in these topics. These coherent structures may appear on airplane wings or slender bodies, mixing layers, jets, wakes or boundary-layers. In free-shear flows and in boundary layers, the results presented here highlight the intense three-dimensional character of the vortices. The two-dimensional large­ scale eddies are very sensitive to three-dimensional perturbations, whose amplification leads to the formation of three-dimensional coherent vorti­ cal structures, such as streamwise, hairpin or horseshoe vortex filaments. This book focuses on modern aspects of turbulence study. Relations between turbulence theory and optimal control theory in mathematics are discussed. This may have important applications with regard to, e. g. , numerical weather forecasting.

Remarks on turbulence theory.- Hydrodynamic visualization of organized structures and turbulences in boundary layers, wakes, jets or propellor flows.- I. Free Shear Flows.- The emergence of characteristic (coherent?) motion in homogeneous turbulent shear flows.- Generation of coherent structures in free shear layers.- Use of the proper orthogonal decomposition in a plane turbulent mixing layer.- On the three-dimensional dynamics of coherent structures forming in free, shear flows.- Visualizations of helium jets in air.- Thermal striping: structures in interacting jets.- II. Boundary Layers.- Three-dimensional aspects of the organized motion in a turbulent boundary layer.- Large-eddy simulation of boundary layers with a step change in pressure gradient.- III. Fundamentals.- Intermittent structure of dissipation in isotropic turbulence viewed from a direct simulation.- The spatial structure of homogeneous turbulence at Reynolds numbers around 1000.- Wavelet analysis of fully developed turbulence data and measurements of scaling exponents.- How solenoidal can be the Lamb vector in turbulent flow? Consequences and implications.- IV. Chaos and Instablity.- Bifurcations and bursting of streaks in the turbulent wall layer.- The dynamics of organized structures in the axisymmetric jet mixing layer.- Instability of the rectangular duct flow and generation of the secondary flow.- V. Vortex Breakdown.- Vortex breakdown: a coherent transition trigger in concentrated vortices.- Numerical simulation of vortex breakdown via 3-D Euler equations.- VI. Two-dimensional Turbulence.- The coherent vortices of two-dimensional and geostrophic turbulence.- Experiments on forced, quasi-two-dimensional turbulence at upwelling fronts.- Merging of two-layer baroclinic vortices.- Transmission of acoustic waves through mixing layers and 2D isotropic turbulence.- VII. Geophysical Fluid Dynamics.- Spectra and correlation functions of surface layer atmospheric turbulence in unstable thermal stratification.- Organized structures in strongly stratified flows.- Fossile and active turbulence.- Coherent structures in stratified turbulent shear flows deduced from direct simulations.- Influence of a shear on a stably-stratified flow.- Gravity wave patterns in the wake of a sphere in a stratified fluid.- VIII. Compressible and Reacting Flows.- The compressible mixing layer.- Numerical simulations of supersonic plane Couette flow instability.- Reactive scalar as a tracer of organized structures in turbulent mixing layers.- IX. MHD Turbulence.- Large-eddy simulation of MHD turbulent channel flow under a uniform magnetic field.- Coherent structures in MHD turbulence and turbulent dynamo.- List of Participants.- Author Index.- Colour Plates.