Stretching and Alignment in General Flow Fields: Classical Trajectories from Reynolds Number Zero to Infinity

摘要: The aim of these lectures is to describe the general properties classical trajectories — be they associated with simple deterministic dynamical systems (Reynolds number very small) or paths followed by fluid particles in turbulent flow fields large). idea look for geometric characterizations an orbit which are applicable two, different, regimes and investigate way may change as transition made from flows what are, effectively, stochastic flows. reason that such approach possible case dynamics description terms particles, namely Lagrangian description, governed ordinary differential equations (as case, course, flows) complexity lies immensely complicated spatio-temporal behaviour velocity field. processes a consequence having given field, irrespective its origin, subject matter kinematics. govern field itself topic fluids this Navier-Stokes equation.