What is turbulence? Daniel P. Lathrop University of Maryland
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2 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
3 Turbulence: an emergent phenomena Rivers!" Niagra Falls"
4 Reynolds number R or Re = U L / ν Re ~ Inertia / viscosity Large R Turbulence
5 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
6 Turbulence at small scale: strain vorticity
7 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.
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9 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
10 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
11 Volcanic eruptions Eyjafjallajokull 2010"
12 Volcanic eruptions Cleveland volcano"
13 Atmospheric flows Cumulous"
14 Atmospheric flows Cumulonimbus"
15 Atmospheric flows Cumulonimbus" 2000 m m
16 Atmospheric flows Cumulonimbus" 400 m 2000 m
17 Atmospheric flows Cumulonimbus" 400 m 40 m
18 Geophysical turbulence Rivers!"
19 Geophysical turbulence Rivers!" Missouri River" flood"
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21 Simple Earth Nonrotating; Spherical Isothermal T = o K Zero axial tilt Quiet atmosphere Quiet crust Quiet mantle Quiet core Core magnetics B = 0
22 Simple Earth Nonrotating; Spherical Isothermal T = o K Zero axial tilt Quiet atmosphere Quiet crust Quiet mantle Quiet core Core magnetics B = 0? Habitable Home One Day Period; Oblate spheroid T core / T space ~ o, precessing Turbulent, zonal atmosphere Brittle quaking crust Complex convecting mantle Turbulent convecting core Active self-inducing geodynamo
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29 Astrophysical turbulence Galaxy: M51"
30 Solar turbulence:
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34 Aerospace Engin. turbulence Rocket Lauch"
35 Aerospace Engin. turbulence Turbofan engine design" Boundary layer turbulence" Subcritical instabilities" "noise driven" Turbulence control:" "suction!"
36 What is meant by JET in fluid dynamics? Turbulent jet" C. Fukushima and J. Westerweel"
37 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 4 He 3 He Cooper pair electrons in superconductors Vacuum Quantum Turbulence > turbulence in a quantum fluid Why does it matter?
38 Background: Superfluid Helium
39 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 v n and v s, respectively
40 Superfluid Order Parameter Order parameter for superfluid helium is a complex field, Ψ(x) = Ae iφ A is amplitude, and φ is the phase Superfluid velocity given by h = Planck s constant m = mass of helium atom
41 Quantized Vortices Lowest energy state: n=1, so φ wraps 2π around a defect Induces a superflow around the line:
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43 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
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45 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
Theoretical physics. Deterministic chaos in classical physics. Martin Scholtz
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