Statistical Mechanics of Developed Turbulence - Lecture 1

Explore the statistical mechanics of developed turbulence in this comprehensive lecture from the Bangalore School on Statistical Physics. Delve into topics like Kolmogorov's similarity hypotheses, energy cascades, and the energy spectrum. Examine the challenges of solving turbulence, including predicting small-scale fluctuations and large-scale dissipation. Investigate the connection between turbulence and phase transitions, focusing on the laminar-turbulent transition in pipe flow. Learn about innovative approaches using computer simulations and predator-prey dynamics to model turbulent behavior. Discover the universality class of the laminar-turbulent transition and its relation to directed percolation. Gain insights into Feynman's vision of renormalization group theory applied to turbulence and the current state of turbulence research. The lecture concludes with a Q&A session, providing an opportunity to deepen understanding of this complex subject.

Statistical mechanics of developed turbulence
Syllabus
Extra things you will learn!
Propaganda
Feynman's vision: RG & Turbulence
Goal
What is turbulence?
Take-home: 2 types of universality in turbulence
What does it mean: "solve turbulence?
Solve turbulence? Predict the fluctuations at small scales
Energy cascade
Kolmogorov's similarity hypotheses
The energy spectrum
Solve turbulence? Predict the dissipation experienced at large scales ..:
Friction factor in turbulent rough pipes
Fluctuations and Dissipation
Solve turbulence? Connect the scales ...
Transitional turbulence in pipe flow: puffs
How much turbulence is in the pipe?
Turbulence & Phase Transitions
Why is fully-developed
Why is turbulence unsolved?
How was critical phenomena solved?
Transition to turbulence
Stability of laminar flow
Precision measurement of turbulent transition
Pipe flow turbulence
Theory for the laminar-turbulent transition in pipe flow
Logic of modeling phase transitions
Identification of long-wavelength collective modes at the laminar- turbulent transition
Digression: how we should use computer simulation as a tool to make discoveries
Computer Simulation & Excessive Realism
DNS of 3D Navier-Stokes equations
Predator-prey oscillations in pipe flow
What drives the zonal flow?
Stochastic model of predator-prey dynamics
Derivation of predator-prey equations
Stochastic predator-prey recapitulates turbulence data
Pipe flow turbulence
"Puff splitting" in predator-prey systems
Roadmap: Universality class of laminar-turbulent transition
Directed percolation & the laminar- turbulent transition
Directed percolation transition
DP in 3 + 1 dimensions in pipe
Origin of superexponential scaling
Directed percolation vs. transitional turbulence
Universality class of predator-prey system near extinction
Q&A