M. RAST - Turbulence: Are transport models possible or necessary? What might they look like?

• Coloquios

Mark Rast.

University of Colorado Boulder.

Jueves 22/5/2014, 14 hs.
 Aula Seminario, 2do piso, Pabellón I. 

Resumen:

It has been said that turbulence is the last important unsolved problem of classical physics. But what is the problem? Why is it so difficult to solve? And why work so hard to solve it? Is it possible that with ever increasing computational capabilities the problem will be bypassed before being solved? I will suggest that while advances in computational capabilities over the next decades may allow fundamental advances, understanding, not raw computer power, will remain the essential solution ingredient. Given this motivation, I will discuss recent efforts to employ mixed Eulerian/Lagrangian statistics to model scalar transport in a simple analog flow, that of a collection of point vortices. As expected, the mean squared Eulerian displacement along Lagrangian trajectories in such a flow scales ballistically for times shorter than the integral time and diffusively for longer times. However, the displacement distribution at any given time only approximates that of a random walk. Over inertial time scales, the probability of long distance transport is reduced from a random walk, and over times shorter than the Kolmogorov or longer than the integral times, the probability of long distance transport is enhanced. These deviations are due to the spatial and temporal intermittency of the flow, and can be statistically modeled as a collection of trapping events with durations uniformly distributed between the Kolmogorov and integral time scales. The findings have implications for turbulent transport beyond the simplified flow studied.