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Monumental Breakthrough in Turbulence Theory
Posted Friday, October 12, 2018

 

AFIT Provost and His NRC Postdoctoral Fellows Make a Monumental Breakthrough in Turbulence Theory


Photo from a NASA study on wingtip vortices qualitatively illustrates the wake turbulence

In a soon to appear article in the prestigious mathematics journal Mathematische Nachrichten,  the Provost and Vice Chancellor of Air Force Institute of Technology, Dr. Sivaguru S. Sritharan and his former National Research Council postdoctoral fellows Dr. Manil T. Mohan and Dr. Sakthivel Kumarasamy will publish a breakthrough advance in the theory of turbulence phenomena in aerodynamics.

Modern perspective on turbulence started with the 1893 paper by Osborn Reynolds and also the papers of A. Kolmogorov in the 1940s. These works assume that the turbulence phenomena can be characterized by a concept called ergodicity which in essence says that statistical time averages converge to averages in the state space and also that there is a well-defined statistically stationary state of the aerodynamic fields. It was conjectured by A. Kolmogorov that subject to suitable noise, the statistically stationary state would be unique and this situation is called ergodicity in mathematics.

In an extensive paper titled "Ergodicity of three dimensional stochastic Navier-Stokes equation subject to Levy noise", Dr. Sritharan and his postdoctoral fellows prove rigorously that the Kolmogorov conjecture for turbulence is indeed true for a general class of jump noise called Levy noise. Many of the turbulence closure models used today in the simulation of turbulent flow rely on this conjecture and the soon to appear paper by Sritharan and his colleagues will resolve this issue decisively, laying a pathway for future research in controlling aerodynamic flows, machine learning of statistically stationary states of turbulent fields, etc.