Mean Motion and Fluctuations:

The concept of mean motion and fluctuations was first put forward by Leonardo da Vinci (1452-1519).

Later, in 1883 O. Reynolds conducted his famous experiment and conjectured about the Reynolds' decomposition. Turbulent flow consists of superimposed streaming and fluctuating (eddying) motion.

Figure 3.2

Reynolds' decomposition:

Hussain's decomposition:

	Coherent	incoherent

To start with we shall follow Reynolds' decomposition

Instantaneous quantity = average quantity + fluctuating component

Scales:

U at a point ( x ) at an instant ( t ) has dependence on U ( x , t - Δt ) or U( x ± Δx , t )

As eddy passes by a point P, one observes: at a point: U varies with time for a pair of points ( a,b ): U_a(t) U_b(t)<0 correlation

Figure 3.3

Typical distance over which correlation exists:

Length scale ( Δx )

Duration for which correlation exists:

Time scale ( ~ Δx / U )

Associated frequency: ( U / Δx ) Hz

Frequencies: (~ U / Δx Hz ) or wave numbers ( ~ 2π / Δx m^-1 )

Turbulence is composed of a collection of frequencies, time scales and length scales.

Consequences of turbulence:

Internal flow: increased pressure drop
                      increased heat transfer

External flow: vibrations
                       increased skin friction
                       increased heat transfer