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