### Turbulence, shmurbulence: how fat is it?

- Series
- PDE Seminar
- Time
- Wednesday, March 16, 2016 - 14:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 270
- Speaker
- Predrag Cvitanovic – School of Physics, Georgia Tech

PDEs (such as Navier-Stokes) are in principle infinite-dimensional
dynamical systems. However, recent studies support conjecture that
the turbulent solutions of spatially extended dissipative systems
evolve within an `inertial' manifold spanned by a finite number of
'entangled' modes, dynamically isolated from the residual set of
isolated, transient degrees of freedom. We provide numerical
evidence that this finite-dimensional manifold on which the
long-time dynamics of a chaotic dissipative dynamical system lives
can be constructed solely from the knowledge of a set of unstable
periodic orbits. In particular, we determine the dimension of the
inertial manifold for Kuramoto-Sivashinsky system, and find it to
be equal to the `'physical dimension' computed previously via the
hyperbolicity properties of covariant Lyapunov vectors.
(with Xiong Ding, H. Chate, E. Siminos and K. A. Takeuchi)