Lagrangian evolution and modeling of the velocity gradient tensor in hydrodynamic turbulence
Johns Hopkins University
It is well recognized now through experiments and large-scale simulations that the small scale structure of fluid turbulence is highly intermittent and non-Gaussian. Moreover, there is a host of well-known trends in the phenomenology of turbulence, such as differences in levels of intermittency between transverse and longitudinal velocity, with passive scalar increments, and turbulence in 2D, 3D and even 4D turbulence. Also, there are non-trivial and very interesting geometric aspects of the velocity gradient tensor, such as alignment trends between the vorticity vector and the eigenvector of the strain-rate tensor. This knowledge, reviewed in this talk, is gleaned mostly from experiments or numerical simulations of turbulence, typically using on the order of 10^9 degrees of freedom. We also describe our efforts at reproducing these observations based on low-dimensional dynamical models that typically take the form of stochastic differential equations for a few degrees of freedom, evolving in time in a Lagrangian frame of reference (moving with the fluid).