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Page 1: What is turbulence?
Page 2: What is turbulence?

What is turbulence? Daniel P. Lathrop

University of Maryland

Goal: grant an intuitive sense of turbulence and its importance in nature, science, and engineering

Outline: 1. Definitions 2. Examples

1. Geophysics 2. Astrophysics 3. Engineering 4. Quantum turbulence 5. Optical turbulence

Page 3: What is turbulence?

Turbulence: an emergent phenomena Rivers!"Niagra Falls"

Page 4: What is turbulence?

Reynolds number R or Re = U L / ν

Re ~ Inertia / viscosity Large R Turbulence

Page 5: What is turbulence?

Turbulence definitions

Turbulence: A Spatially extended field with a large, continuous range of aperiodic spatial and temporal dynamics

Newtonian fluid turbulence: Turbulence in a classical, Newtonian viscous fluid

Kolmogorov turbulence: Turbulence exhibiting spatial power spectra with

Quantum turbulence: A turbulent complex field or interacting set of complex fields

Optical turbulence: A turbulent field of electromagnetic amplitudes

Page 6: What is turbulence?

Turbulence at small scale:

strain vorticity

Page 7: What is turbulence?

Watson: You have to admit Holmes that a supernatural explanation to this case is theoretically possible. Holmes: Agreed, but it is useless to theorize before one has data. Inevitably one begins to twist facts to suit theories instead of theories to suit facts.

Page 8: What is turbulence?
Page 9: What is turbulence?

So many natural flows are necessarily turbulent, but we cannot simulate them.

Turbulence: Fluctuating in time and space Aperiodic Large range of time and length scales Deterministic

Page 10: What is turbulence?

So many natural flows are necessarily turbulent, but we cannot simulate them.

Turbulence: Fluctuating in time and space Aperiodic Large range of time and length scales Deterministic

Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.

John von Neumann

Page 11: What is turbulence?

Eyjafjallajokull 2010"Volcanic eruptions

Page 12: What is turbulence?

Volcanic eruptions Cleveland volcano"

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Atmospheric flows Cumulous"

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Atmospheric flows Cumulonimbus"

Page 15: What is turbulence?

Atmospheric flows Cumulonimbus"

10000 m

2000 m

Page 16: What is turbulence?

Atmospheric flows Cumulonimbus"

2000 m

400 m

Page 17: What is turbulence?

Atmospheric flows Cumulonimbus"

400 m

40 m

Page 18: What is turbulence?

Geophysical turbulence Rivers!"

Page 19: What is turbulence?

Geophysical turbulence Rivers!"Missouri River" flood"

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Page 21: What is turbulence?

Simple Earth Nonrotating; Spherical

Isothermal T = 2.725 o K

Zero axial tilt

Quiet atmosphere Quiet crust

Quiet mantle Quiet core

Core magnetics B = 0

Page 22: What is turbulence?

Simple Earth Nonrotating; Spherical

Isothermal T = 2.725 o K

Zero axial tilt

Quiet atmosphere Quiet crust

Quiet mantle Quiet core

Core magnetics B = 0?

Habitable Home One Day Period; Oblate spheroid

Tcore / Tspace ~ 103

23.5o, precessing

Turbulent, zonal atmosphere Brittle quaking crust

Complex convecting mantle Turbulent convecting core

Active self-inducing geodynamo

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Astrophysical turbulence Galaxy: M51"

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Solar turbulence:

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Page 34: What is turbulence?

Aerospace Engin. turbulence Rocket Lauch"

Page 35: What is turbulence?

Aerospace Engin. turbulence

Turbofan engine design"

Boundary layer turbulence"

Subcritical instabilities""noise driven"

Turbulence control:""suction!"

Page 36: What is turbulence?

Turbulent jet"C. Fukushima and J. Westerweel"

What is meant by JET in fluid dynamics?

Page 37: What is turbulence?

Quantum Fluids

A state of matter with long range quantum order

Type of synchronization partial phase sync of the individual atomic wave functions

E.g. BEC atomic systems 4He 3He Cooper pair electrons in superconductors Vacuum

Quantum Turbulence –> turbulence in a quantum fluid Why does it matter?

Page 38: What is turbulence?

Background: Superfluid Helium

Page 39: What is turbulence?

Two-Fluid Model

•  Superfluid helium acts as if it’s a mixture of a normal and superfluid component

•  Normal and superfluid have separate velocity fields vn and vs, respectively

Page 40: What is turbulence?

Superfluid Order Parameter

•  Order parameter for superfluid helium is a complex field,

Ψ(x) = Aeiφ A is amplitude, and φ is the phase •  Superfluid velocity given by

h = Planck’s constant m = mass of helium atom

Page 41: What is turbulence?

Quantized Vortices •  Lowest energy state: n=1, so φ wraps 2π

around a defect •  Induces a superflow around the line:

Page 42: What is turbulence?
Page 43: What is turbulence?

What is quantum turbulence?

An evolving set of quantized vortices:

aperiodic large range of length scales

and curvatures rings vortices ending at walls knots

Simulations by Patricio Jeraldo and Nigel Goldenfeld

Page 44: What is turbulence?
Page 45: What is turbulence?

What is turbulence? Daniel P. Lathrop

University of Maryland

Goal: grant an intuitive sense of turbulence and its importance in nature, science, and engineering

Outline: 1. Definitions 2. Examples:

1. Geophysics 2. Astrophysics 3. Engineering 4. Quantum turbulence 5. Optical turbulence