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.

4

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.

5

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

11

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

13

1.3 Origin of turbulence

Laminar flow

Turbulent flow

Instability

τ, δ

small

Energy

14

1.3 Origin of turbulence

τ, δ

E Energy spectrum

15

1.3 Origin of turbulence

Laminar flow

Turbulent flow

Instability Transition to turbulence

Poorly understood