Mathematics of Turbulent Flows: A Million Dollar Problem! by Edriss S Titi
Δημοσιεύτηκε στις 28 Φεβ 2016
URL: https://www.icts.res.in/lecture/1/det...
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 engins, weather
and climate predictions. It is widely accepted by the scientific
community that turbulent flows are governed by the Navier-Stokes
equations, for large values Reynolds numbers, i.e. when the nonlinear
effects are dominating the viscous linear 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.
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 engins, weather
and climate predictions. It is widely accepted by the scientific
community that turbulent flows are governed by the Navier-Stokes
equations, for large values Reynolds numbers, i.e. when the nonlinear
effects are dominating the viscous linear 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.
Κατηγορία
Άδεια
- Τυπική άδεια YouTube
ANAΡΤΗΣΗ ΑΠΟ ΤΟ YOUTUBE 13/3/2016
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