1. Introduction: i) Deterministic study: Experimental and numerical approaches for receptivity / instability/ transitionii) Stochastic studies: Experimental and theoretical approaches to transition to turbulenceiii) Why linear and nonlinear approaches needed? iv) Obtaining equilibrium flow and its instability.v) Simulating transitional / turbulent flows by DNS and LES
2. DNS of Navier-Stokes Equation: i) Numerical methods for developing DNS/ LES codes with respect to numerical properties of model equations for: (a) convection equation; (b) convection-diffusion equation and (c) Taylor-Green vortex problem.ii) Error dynamics of various methods used in LES and DNS.iii) High accuracy compact schemes iv) Dispersion relation preservation (DRP) properties of numerical methodsv) Design of DRP schemes for DNS/LESvi) Numerical Filtering: Error control via stabilization, dealiasing etc. vii) Formulations of DNS: Various forms of governing equations and associated error metrics' behavior.viii) Details of (a) stream function-vorticity and (b) velocity-vorticity formulations for DNS/ LES of fluid flow and heat transfer. 3. Receptivity and Instability: i) Linear stability / receptivity theories: Classical approaches and Signal problem. ii) Solving stiff differential equations: compound matrix and implicit Runge-Kutta methodsiii) Ambiguities of spatial and temporal linear theories: Example of mixed convection problem. iv) Spatio-temporal approach: Bromwich contour integral method. v) Centrality of nonlinear and nonparallel effects: Solving receptivity problem by DNS. vi) Direct simulation of instability of mixed convection flows: New generic theorems of instability.
4. Analysis by different nonlinear theories for fluid flowsa. Theory based on total mechanical energy; Vortex -induced instabilityb. Enstrophy transport equation and its use in vorticity dynamicsc. Proper orthogonal decomposition (POD) based approach to study nonlinear/ linear instability.
5. 2D Turbulence: i) From linear theory to DNS of 2D turbulence via deterministic routes. ii) By-pass transition routes of transition to turbulence: Flow past NLF airfoil.iii) Excitation by periodic free-stream convecting vortices
6. 3D Routes to Turbulence: i) Experimental demonstration of 3D routes: K- and H-types of transition. ii) Computational evidences for (a) spanwise modulated excitation and (b) Gaussian circular patch excitationCharacterization of coherent vertical structures

About the Author:
Prof. Tapan K. Sengupta, Ph.D. (Georgia Tech.) has devoted all his time in research and teaching of transition and turbulence, apart from his interest in aerodynamics. To aid in these research areas, he has developed scientific computing for fluid flow and wave phenomenon for more than three decades. He has written four single-author books in these subjects, apart from editing two more volumes on transition and high performance computing. He has been a Senior Research Associate in Univ. of Cambridge, Senior Visiting Fellow in National Univ. of Singapore, Senior Associate of the International Centre of Theoretical Physics (ICTP) at Trieste, Italy, visiting IdeX Professor of Excellence at Univ. of Bordeaux, France, Fellow at Univ. of Cambridge, UK at Murray-Edwards College and Univ. Engg., Department. He has been the Regional Editor of Computers & Fluids (Elsevier), New York, USA.
Dr. Swagata Bhaumik, PhD (IIT Kanpur, 2013) is currently visiting Assistant Professor, Department of Aerospace Engineering, IIT Kanpur. His PhD topic was: "Direct Numerical Simulation of Transitional and Turbulent Flows", where he used his own developed high-accuracy 3D incompressible Navier-Stokes solver to investigate and characterize the dynamics of spatio-temporal wave-front and its role in causing flow transition. From 2014 to 2016 he was a Post-Doctoral researcher in the Ohio State University where he worked on the prediction and estimation of perfectly- and imperfectly-expanded jet noise. He has a Master's degree in Aerospace Engineering (Aerodynamics) from IIT Kharagpur (2007) and a Batchelor's degree in Mechanical Engineering from NIT Rourkela (2001).