Several Events Of Transition -

Transitional flow consists of several events as shown in Fig. 31.8. Let us consider the events one after another.

1. Region of instability of small wavy disturbances- 

Consider a laminar flow over a flat plate aligned with the flow direction (Fig. 31.8).

• In the presence of an adverse pressure gradient, at a high Reynolds number (water velocity approximately 9-cm/sec), two-dimensional waves appear.
• These waves are called Tollmien-Schlichting wave( In 1929, Tollmien and Schlichting predicted that the waves would form and grow in the boundary layer).
•  These waves can be made visible by a method known as tellurium method. 

2. Three-dimensional waves and vortex formation-

• Disturbances in the free stream or oscillations in the upstream boundary layer can generate wave growth, which has a variation in the span wise direction.
• This leads an initially two-dimensional wave to a three-dimensional form.
• In many such transitional flows, periodicity is observed in the span wise direction. 
• This is accompanied by the appearance of vortices whose axes lie in the direction of flow.

3. Peak-Valley development with streamwise vortices-

• As the three-dimensional wave propagates downstream, the boundary layer flow develops into a complex stream wise vortex system.
• Within this vortex system, at some spanwise location, the velocities fluctuate violently . 
• These locations are called peaks and the neighbouring locations of the peaks are valleys (Fig. 31.9).

4. Vorticity concentration and shear layer development-
    
At the spanwise locations corresponding to the peak, the instantaneous streamwise velocity profiles demonstrate the following

•  Often, an inflexion is observed on the velocity profile.
•  The inflectional profile appears and disappears once after each cycle of the basic wave.

5. Breakdown-
    
The instantaneous velocity profiles produce high shear in the outer region of the boundary layer.

• The velocity fluctuations develop from the shear layer at a higher frequency than that of the basic wave.
• These velocity fluctuations have a strong ability to amplify any slight three-dimensionality, which is already present in the flow field.
• As a result, a staggered vortex pattern evolves with the streamwise wavelength twice the wavelength of Tollmien-Schlichting wavelength .
• The span wise wavelength of these structures is about one-half of the stream wise value. 
• The high frequency fluctuations are referred as hairpin eddies.

This is known as breakdown. 

6. Turbulent-spot development-

• The hairpin-eddies travel at a speed grater than that of the basic (primary) waves. 
• As they travel downstream, eddies spread in the spanwise direction and towards the wall.
• The vortices begin a cascading breakdown into smaller vortices.
• In such a fluctuating state, intense local changes occur at random locations in the shear layer near the wall in the form of turbulent spots.
• Each spot grows almost linearly with the downstream distance.

  The creation of spots is considered as the main event of transition .


Fig. 31.8 Sequence of event involved in transition

Fig. 31.9 Cross-stream view of the streamwise vortex system