9316798 Kraichnan Under this award, the principal investigator will pursue three related topics directed at fundamental understanding of turbulent cascade processes: (1) a search for bounds on scaling exponents of the inertial range of three-dimensional incompressible Navier- Stokes turbulence; (2) development of analytical methods for predicting statistics of velocity differences across distances that fall within the inertial range of scales; (3) theoretical and numerical study of the probability of extreme values of velocity, vorticity, and other quantities of turbulent flow. The first project will make systematic use of exact multi-time dynamical constraints and multi-time realizability inequalities on statistics. The second project will exploit nonlinear mapping techniques in order to approximate probability distribution functions and other high-order statistics of velocity differences across inertial-range distances. The third project will use nonlinear mapping techniques to estimate the magnitude and sensitivity of extreme-value tails of probability distribution functions for turbulence and other nonlinear processes. This research will provide important insights for a variety of problems in atmospheric sciences including improvement of the modeling of subgrid-scale processes. ***
