Turbulent flow is a daily phenomenon: from the kitchen sink to flows on galactical scales. The course will explore turbulence from the point of view of dynamical systems and out-of-equilibrium statistical mechanics. We will study different ways for a system to become chaotic and turbulent, with an emphasis on non-linear instability. We will then focus on the statistical description of the turbulent state and learn why it is universal, why turbulence is out of equilibrium, and how to use conservation laws and symmetries to characterize it. At then of the course we will move from a field-theoretic description of turbulence to one of particles, and discuss the stochastic dynamics of particles in a turbulent flow. Throughout the course we will emphasize general principles and use example flows to demonstrate them. The final part of the course will focus on student presentations showcasing ongoing research in the field.
Learning Outcomes: At the end of the course the students will be able to:
· Understand the different transitions to chaos and possible resulting chaotic phases.
· Using conservation laws and symmetries to characterize the turbulent state/ an out of equilibrium system
· Analyze the stochastic motion of particles in a turbulent/chaotic flow.
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