The instanton method and its numerical implementation in fluid mechanics

摘要: A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one the last open problems classical physics. In this review we discuss recent developments related to application instanton methods turbulence. Instantons are saddle point configurations underlying path integrals. They equivalent minimizers Freidlin-Wentzell action and known be able characterize rare events such systems. While there an impressive body work concerning their analytical description, focuses on question how compute these numerically. a short introduction present relevant mathematical physical background before stochastic Burgers equation detail. We algorithms instantons numerically by efficient solution corresponding Euler-Lagrange equations. second focus discussion recently developed numerical filtering technique that allows extract from direct simulations. following modifications make them when applied two- or three-dimensional dynamical problems. illustrate ideas using two-dimensional Navier-Stokes