Ph.D. (Engg) : Characterization of time-frequency behavior of flow intermittency in transitional boundary layers

The importance of transitional flow studies can be realized from the fact that it acts as a bridge between the laminar and turbulent flows. The present work deals with the investigation of time-frequency characteristics of transitional flows and their modelling, which is presented in three parts.

First, we propose a wavelet-transform based smooth detector function which is used to detect the presence of turbulent spots in a signal. We also propose a novel wavelet transform based algorithm to calculate the intermittency for various transitional and turbulent boundary layers with the primary objective to remove the subjectivity of current methods. The method is also used to calculate the intermittencies for temporal and spatial distributions of velocities of a computational dataset. The algorithm involves calculation of a sensitive detector and then obtaining an indicator based on Monte-Carlo like iterations. A cut-off on the number of iterations ​is obtained based on RMS of the laminar part of the signal. The method is also able detect the turbulent/non-turbulent interface in wall-normal and wall-parallel planes. This wide spectrum of results prove the generality of the scheme, which to our knowledge has been demonstrated for the first time.

Secondly, the substructures of stream-wise velocity fluctuations within a turbulent spot are investigated using time-spectral and probability density function(PDF) based analyses. The pre-multiplied Fourier spectrum shows that the turbulent spots appear rather  “suddenly” at the onset of transition. The high frequency structures inside a near-wall turbulent spot at the onset of transition are found to be highly time localized. The presence of large amplitude events near the onset location hints towards a near “singular” structure within a nascent spot that has high frequencies, amplitudes and time localization. It is also seen that the transition process only modifies the structures at higher frequencies and the lower frequencies remain almost unchanged. For lower frequencies, the structure throughout the transition zone, for all the transition as well as the turbulent boundary layer cases show a universal nature.

In the third part, Cellular Automaton (CA) is used to model the growth, propagation and merging of turbulent spots. CA simulations are shown to handle a variety of different practical/theoretical spot generation scenarios. These simulations are computationally inexpensive and easily parallelizable. They represent a promising avenue for modelling the kinematics of turbulent spots.