## Turbulence, shmurbulence: how fat is it?

Series:
PDE Seminar
Wednesday, March 16, 2016 - 2:05pm
1 hour (actually 50 minutes)
Location:
Skiles 270
,
School of Physics, Georgia Tech
Organizer:
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)