Module -1: Introduction: - Basic features of turbulent flow – Irregularity, diffusivity, high Reynolds number, rotational, dissipative, continuum phenomenon. [4 hours]

Module-2: Characterization of turbulent flows: - Statistical averages, moments, probability density function, correlation, energy spectrum, Homogeneous and Isotropic turbulence. [10 hours]

Module-3: Scales in turbulent flows: - Richerdson’s energy cascade hypothesis, Scales – Integral, Kolmogorov and Taylor micro scales, Kolmogorov’s local isotropy hypothesis, I and II similarity hypothesis, universality in small scale fluctuations, -5/3 law, spectral dissipation. [6 hours]

Module-4: Equations governing turbulent flow: - Reynolds decompositions, Raynolds Averaged Navier-Stokes (RANS) equations, Equations for Reynolds stresses, mean and turbulent kinetic energy (TKE) governing equations, Energy transfer in turbulent flows, Closure problem, Reynolds averaged and mass-weighted equations for compressible flows. [10 hours]

Module-5: Simulation approaches and turbulence modeling: - Outline of approaches to prediction of turbulent flows – LES, DNS, and RANS Desirable futures of a model of turbulence Zero -, one - and two-equation models of turbulence Reynolds stress model Algebraic stress model Limitations of RANS approach. [6 hours]

To know the overview of turbulence in fluid flow, e.g., the nature, cause, origin, and sustainability of turbulence.

To understand the methods of characterizations of turbulent flows.

To understand the techniques of computations and modeling of turbulent flows.

After the completion of the course, the students will be able,
CO1: To understand the origin, basic features, and stainability of turbulent flow.
CO2: To know the tools and methods of turbulent flow characterizations.
CO3: To understand the inherent features of eddies, associated scales, and universality in turbulent flows.
CO4: To derive the basic governing equations in turbulent flows.
CO5: To know the different simulation approaches and modeling of turbulent flows.

P. A. Davidson, Turbulence: An Introduction for Scientists and Engineers, Oxford University Press , 2023.

P. A. Durbin, B. A. Pettersson Reif, Statistical Theory and Modeling for Turbulent Flows, John Wiley & Sons , 2021

A. S. Monin and A. M. Yaglom, Statistical fluid mechanics, volume II: mechanics of turbulence, Courier Corporation , 2024.

H. Tennekes, and J. L. Lumley, A first course in turbulence, MIT Press , 2021.