The Burgers Program for Fluid Dynamics

The presentation will briefly review a Lagrangian model for deforming droplets in turbulence, in which the cumulative deformation of fluid elements at small scales is crucial. In particular, we show how knowledge about the statistical distribution of finite-time Lyapunov exponents (FTLEs) can be used to find a critical Capillary number above which droplets will break up. Probability distribution functions of droplet sizes show power-law tails and diverging moments. Inspired by these connections between turbulent phenomena and Lyapunov exponents, we embark on a more systematic study of finite-time Lyapunov exponents in isotropic turbulence. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramer function. To obtain the Cramer function from data, we use both the method based on measuring moments and measuring histograms, and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two independent FTLEs in 3D flows. The joint Cramer function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. The results serve to characterize the fundamental statistical and geometric structure of turbulence at small scales including cumulative, time integrated effects. These are important for deformable particles such as droplets and polymers advected by turbulence (work done in collaboration with PhD student Perry Johnson, and Profs. L. Biferale and R. Verzicco). www.enme.umd.edu/events/fluid-dynamics-review-seminars bio: Charles Meneveau is the Louis M. Sardella Professor in Mechanical Engineering at Johns Hopkins University. His research interests are in the areas of theoretical, experimental, and numerical studies in turbulence; large-eddy-simulation and turbulence modeling; fractals and scaling in complex systems; applications of LES to environmental flows, wind energy and turbomachinery flows; and the development of database techniques for turbulence research.