1 1.1 The nature of turbulence No definition of turbulence. Some characteristics Irregularity Diffusivity Large Reynolds number 3D voriticity fluctuations Dissipation Continuum
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1
1.1 The nature of turbulence
No definition of turbulence.
Some characteristics
IrregularityDiffusivityLarge Reynolds number3D voriticity fluctuationsDissipationContinuum
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1.1 The nature of turbulence
IrregularityDiffusivityLarge Reynolds number3D voriticity fluctuationsDissipationContinuum
randomness Statistical methodof heat, massmomentum etc.
Nonlinear inertiaViscous force
Rotational & 3DVorticity dynamicsVortex streching
Kinetic energy flows to internal energy
No quantum effect
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1.1 The nature of turbulence
Turbulent flows are flows.
Not a fluid properties
Turbulent characteristics are not determined by fluids
It is a nonlinear phenomenon so that a flow pattern strongly depends on initial and boundary conditions.
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1.2 Methods of analysis
Problem of closure
The number of unknowns > the number of equations
To supplement
Empirical dataCrucial assumptionsModels
Equations do not give the entire story.
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1.2 Methods of analysis
Models & assumptions
Turbulent flows → turbulent fluids
Eddy viscosityMixing length
Molecular motion ↔ turbulent fluctuation
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1.2 Methods of analysis
Dimensional analysisExtremely high degree of freedom
Turbulent structure depends on only a few parameters
Dimensional relationship between dependent and independent variables
Turbulent energy spectrum : ( ) 35−∝Ε ek
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1.2 Methods of analysis
Asymptotic invariance
Re → ∞
Very small molecular viscosity effect
Away from boundary
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1.2 Methods of analysis
Local invarianceTurbulence is controlled by a neighbor environment
δ
Time scale τLength scale δ
small
Turbulence is uniform
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1.2 Methods of analysis
Limit cycle
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1.3 Origin of turbulence
Increasing Re : Laminar flow
Turbulent flow
Instability
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Experimental Fluid DynamicsGoverning Equation and Flow Regime
Laminar and Turbulent flow
Transition to turbulence ：乱流遷移
Turbulence
Transition
Laminar
Stable solution of NS equation
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1.3 Origin of turbulence
Laminar flow
Turbulent flow
Instability
τ, δ
small
Energy
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1.3 Origin of turbulence
Laminar flow
Turbulent flow
Instability
τ, δ
small
Energy
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1.3 Origin of turbulence
τ, δ
E Energy spectrum
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1.3 Origin of turbulence
Laminar flow
Turbulent flow
Instability Transition to turbulence
Poorly understood
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