Turbulence - Arrow of Time and Equilibrium-Nonequilibrium Behaviour

Explore the fascinating world of turbulence and its relationship to the arrow of time and equilibrium-nonequilibrium behavior in this 42-minute lecture by Mahendra Verma. Delve into the controversy surrounding time reversal symmetry in fundamental forces and how it relates to real-world phenomena. Examine the second law of thermodynamics as a solution and use turbulence as a prime example. Investigate the Navier-Stokes equation, multiscale phenomena, and driven-dissipative nonequilibrium systems. Learn about Kolmogorov's theory of turbulence, energy transfer, and the properties of equilibrium thermodynamics. Analyze two-dimensional and rotating turbulence, and explore connections to cosmology and causality. Discover the equilibrium behavior of turbulent systems, including initial conditions, spectrally truncated Euler flows, and connections to kinetic theory. Gain insights from molecular-level simulations of turbulence and its decay, and understand the importance of initial conditions in these complex systems.

Turbulence: Arrow of time equilibrium-Equilibrium behaviour
What is the controversy?
Fundamental forces respect time reversal symmetry
Newton's laws of motion
In real life?
A solution: Second law of thermodynamics
Take turbulence as an example
NS equation
Multiscale phenomena Driven-dissipative nonequilibrium phenomena
Books
Hydrodynamic turbulence
Kolmogorov's theory of turbulence
Properties of ET
Energy transfer
Interpretations
Nice! Problem solved!
Viscous dissipation?
Coherent energy -Incoherent energy
Two-dimensional turbulence
Two-dimensional & rotating turbulence
Past works
Cosmological arrow of time
Causality
Conclusions-I
Equilibrium behaviour
Initial condition: Random velocity
Effective Dissipation and Turbulence in Spectrally Truncated Euler Flows
Connection with kinetic theory
Kinetic theory
Homogeneous isotropic gas under a equilibrium state
Molecular-Level Simulations of Turbulence and its Decay
Initial condition dependence
Moral of the story!
Q&A