Intermittency

• Consider a turbulent flow confined to a limited region. To be specific we shall consider the example of a wake (Figure 33.1a), but our discussion also applies to a jet (Figure 33.1b), a shear layer (Figure 33.1c), or the outer part of a boundary layer on a wall.
  
  
• The fluid outside the turbulent region is either in irrotational motion (as in the case of a wake or a boundary layer), or nearly static (as in the case of a jet). Observations show that the instantaneous interface between the turbulent and nonturbulent fluid is very sharp.
  
  
• The thickness of the interface must equal the size of the smallest scales in the flow, namely the Kolmogorov microscale.
  
  
  


Figure 33.1  Three types of free turbulent flows; (a) wake  (b) jet and (c) shear layer [after P.K. Kundu and I.M. Cohen, Fluid Mechanics, Academic Press, 2002]



• Measurement at a point in the outer part of the turbulent region (say at point P in Figure 33.1a) shows periods of high-frequency fluctuations as the point P moves into the turbulent flow and low-frequency periods as the point moves out of the turbulent region. Intermittency I is defined as the fraction of time the flow at a point is turbulent.
  
  
• The variation of I across a wake is sketched in Figure 33.1a, showing that I =1 near the center where the flow is always turbulent, and I = 0 at the outer edge of the flow domain.