Description
Springer Wave Propagation And Time Reversal In Randomly Layered Media by Jean-Pierre Fouque
The content of this book is multidisciplinary by nature. It uses mathematical tools from the theories of probability and stochastic processes, partial differential equations, and asymptotic analysis, combined with the physics of wave propagation and modeling of time reversal experiments. It is addressed to a wide audience of graduate students and researchers interested in the intriguing phenomena related to waves propagating in random media. At the end of each chapter there is a section of notes where the authors give references and additional comments on the various results presented in the chapter. I Overview.- 1 Main Objective.- 2 Mysteries and Secrets.- 3 Turbulent Flow and History of Aviation.- 4 The Euler Equations.- 5 The Incompressible Euler and Navier-Stokes Equations.- 6 Triumph and Failure of Mathematics.- 7 Laminar and Turbulent Flow.- 8 Computational Turbulence.- 9 A First Study of Stability.- 10 d'Alembert's Mystery and Bernoulli's Law.- 11 Prandtl's Resolution of d'Alemberts's Mystery.- 12 New Resolution of d'Almenbert's Mystery.- II Mathematics of Turbulence.- 13 Turbulence and Chaos.- 14 A $1 Million Prize Problem.- 15 Work Uniqueness by Computation.- 16 Existence of e-Weak Solutions by G2.- 17 Stability Aspects of Turbulence in Model Problems.- 18 A Convection-Diffusion Model Problem.- 19 G2 for Euler.- 20 Summary of Mathematical Aspects.- III Secrets.- 21 Secrets of Ball Sports.- 22 Secrets of Flight.- 23 Secrets of Sailing.- 35 Secrets of Racing.- IV Computational Method.- 25 Reynolds Stresses In and Out.- 26 Smagorinsky Viscosity In and Out.- 27 Friction Boundary Condition as Wall Model.- 28 G2 for Navier-Stokes Equations.- 29 A Discrete Solver.- 30 G2 as Adaptive DNS/LES.- 31 Implementation of G2 with FEniCS.- 32 Moving Meshes adn ALE Methods.- V Flow Fundamentals.- 33 Bluff Body Flow.- 34 Boundary Layers.- 35 Separation.- 36 Transition to Turbulence.- VI Loschmidt's Mystery.- 37 Thermodynamics.- 38 Joule's 1845 Experiment.- 39 Compressible Euler in 1d.- 40 Burgers' Equation.- 41 Compressible Euler in 3d.- 42 EG2 for Compressible Flow.- 43 Philosophy of EG2.- 44 Does God Really Play Dice?- References.- Index