Solve turbulence? Predict the fluctuations at small scales
11
Energy cascade
12
Kolmogorov's similarity hypotheses
13
The energy spectrum
14
Solve turbulence? Predict the dissipation experienced at large scales ..:
15
Friction factor in turbulent rough pipes
16
Fluctuations and Dissipation
17
Solve turbulence? Connect the scales ...
18
Transitional turbulence in pipe flow: puffs
19
How much turbulence is in the pipe?
20
Turbulence & Phase Transitions
21
Why is fully-developed
22
Why is turbulence unsolved?
23
How was critical phenomena solved?
24
Transition to turbulence
25
Stability of laminar flow
26
Precision measurement of turbulent transition
27
Pipe flow turbulence
28
Theory for the laminar-turbulent transition in pipe flow
29
Logic of modeling phase transitions
30
Identification of long-wavelength collective modes at the laminar- turbulent transition
31
Digression: how we should use computer simulation as a tool to make discoveries
32
Computer Simulation & Excessive Realism
33
DNS of 3D Navier-Stokes equations
34
Predator-prey oscillations in pipe flow
35
What drives the zonal flow?
36
Stochastic model of predator-prey dynamics
37
Derivation of predator-prey equations
38
Stochastic predator-prey recapitulates turbulence data
39
Pipe flow turbulence
40
"Puff splitting" in predator-prey systems
41
Roadmap: Universality class of laminar-turbulent transition
42
Directed percolation & the laminar- turbulent transition
43
Directed percolation transition
44
DP in 3 + 1 dimensions in pipe
45
Origin of superexponential scaling
46
Directed percolation vs. transitional turbulence
47
Universality class of predator-prey system near extinction
48
Q&A
Description:
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 - Lecture 1