Transition & Turbulence

We have been studying the receptivity and instability of shear layer for some time now. The receptivity problem is formulated in the Laplace-Fourier transform framework. We have solved the complete space-time dependent receptivity problem of zero-pressure gradient boundary layer and discussed the issue of completeness of the basis function in Sengupta et al. (1994) .

We have been also studying the problem of free-stream excitation problem, with emphasis on convected vortices problem. It had been erroneously stated earlier that such excitation does not have the receptivity via the usual Orr-Sommerfeld route. This has been solved correctly in a couple of conference papers. However, the major work done in this area has clarified the idea of BY-PASS transition.

By-Pass Transition:

Here the main aim is to study By-Pass transition that takes a laminar flow directly to the turbulent stage without having to go through the stage of wavy disturbance growth. By-Pass mechanism refers to those routes that do not follow the onset of transition via Tollmien-Schlichting waves growing exponentially.

In this context, two classes of problems have been studied, where a wall-bounded shear layer is excited by free stream vortices:

A. By-Pass Transition by periodic vortex train: By-Pass transition triggered by periodic convected vortices. As explained in Sengupta et al. (2002) , the periodic vortex-train causes rapid transition when its speed of convection is

within a selected range . This interesting aspect was observed experimentally by Kendall (1987). The growth of disturbance is more than the exponential growth of a monochromatic TS wave, because the disturbance follows a constant- phase speed route, as shown in the figures below with respect to spatial analysis:

The passage of disturbance along constant -c route entails excitation of disturbance field that continuously changes its circular frequency- unlike the case of controlled transition triggered in the lab by constant frequency wall excitation. For details read, Sengupta et al. (2002).

B. By-Pass Transition by aperiodic vortex:

Unlike the scenario in A above, here TS waves are not created at all. The physical mechanism is introduced in Sengupta et al. (2003) . via experiments and theory. The experiments were conducted, in the water channel of NUS in collaboration with Prof. TT Lim, on a flat plate zero-pressure gradient shear layer. The experiment was designed to have absolute control over the strength and sign of the vortex that was created by spinning a cylinder and made to translate over the shear layer at a constant height. The experiment is described next:

The physical arrangement of the experiment is sketched below,

A typical experimental sequence is displayed next where By-Pass transition is seen to occur.

The Numerical Simulation: The above experiment was numerically simulated by solving 2D Navier- Stokes equation in a box.

A typical simulation is shown below:

Animation

Still-frames of the simulation is shown for stream function and vorticity below at representative times

For details of the physical mechanism and a new theory for receptivity based on energy consideration, see the paper by Sengupta et al. (2003) .

Upstream Propagating Waves in Shear Layers :

For the first time the existence of upstream propagating waves was established by us and reported in Sengupta & Nair (1997) and Sengupta et al. (1997)

The link of this to the by-pass transition mechanism is currently being explored.