Lansdowne Lecture - Mathematics of Turbulent Flows: A Million Dollar Problem

Title: Lansdowne Lecture - Mathematics of Turbulent Flows: A Million Dollar Problem
Speaker: Professor Edriss S. Titi, Texas A&M University and The Weizmann Institute of Science
Date and time: 18 Mar 2016, 7:00pm - 8:00pm
Location: David Turpin Building, A120

Presented by the Department of Mathematics and Statistics.

Turbulence is a classical physical phenomenon that has been a great challenge to mathematicians, physicists, engineers and computational scientists.  Chaos theory has been developed in the end of the last century to address similar phenomena that occur in a wide range of applied sciences, but the eyes have always been on the big ball – Turbulence.  Controlling the identifying the onset of turbulence has a great economic and industrial impact ranging from reducing the drag on cars and commercial airplanes to better design of fuel engines, weather and climate predictions.

It is widely accepted by the scientific community that turbulent flows are governed by the Navier-Stokes equations, for large Reynolds numbers, i.e. when the nonlinear advective effects dominate the linear viscous effects (internal friction within the fluids) in the Navier-Stokes equations.  As such, the Navier-Stokes equations form the main building block in any fluid model, in particular in global climate models.  Whether the solutions to the three-dimensional Navier-Stokes equations remain smooth, indefinitely in time, is one of the most challenging mathematical problems.  Therefore, it was identified by the Clay Institute of Mathematics as one of the seven most outstanding Millennium Problems in mathematics, and it has set one million US dollars prize for solving it.  Notably, reliable computer simulations of turbulent flows, is way out of reach even for the most powerful state-of-the-art supercomputers.  In this talk I will describe, using layman language, the main challenges that the different scientific communities facing while attempting to attack this problem. In particular, I will emphasize the mathematical point of view of turbulence.

Professor Edriss Titi is an expert in theoretical and computational fluid mechanics and geophysical flows. His contributions include the analysis of turbulent flows and more importantly the primitive equations, used in weather and climate predictions. The profound impact and originality of Titi's work has earned him multiple awards, including the Senior Alexander von Humboldt Research Award, and the best SIAM paper in PDEs. He is a fellow of SIAM, the Institute of Physics, and the AMS. His publications are in the top tier journals and he sits on the editorial boards of many renowned journals.

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