Mixing and nonlinear stability
April 11 to April 15, 2016
American Institute of Mathematics,
San Jose, California
Jacob Bedrossian and Nader Masmoudi
This workshop will be devoted to expanding the mathematical analysis of
mixing phenomena arising in fluid mechanics and kinetic theory as well
as increasing communication between the different communities working in
the field. The specific focus will be on the relationship between mixing
and nonlinear stability problems, that is, how the fluid mixing itself
changes the dynamics. In fluid mechanics, mixing-related stability
mechanisms are connected to coherent structures at high Reynolds number
and thought to be important for understanding the stability of
hurricanes and other weather phenomena as well as potentially playing a
role in organizing 2D turbulence. Recent work also shows that these
effects are important for understanding the stability and subcritical
instability of 3D laminar flows. In plasma physics and galaxy dynamics,
the mixing effect known as Landau damping has long been recognized as a
fundamental stability mechanism in nearly collisionless kinetic models.
Despite its fundamental physical relevance and importance in practical
settings, the mathematical analysis of these mixing phenomena is very
under-developed due to subtle regularity issues connected with unusual
nonlinear resonances and even often a lack of clear understanding of
linear mixing phenomena.
The main topics of interest will likely cover:
- Understanding general pseudospectral aspects of associated linear
operators, with both zero and vanishingly small viscosity (or
collisions). Especially we will focus on aspects important for nonlinear
- Relevance to understanding the meta-stability of coherent structures in
2D fluids, understanding subcritical transition phenomena in 3D laminar
flows, and to understanding similar phenomena in plasma physics.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.