### Credits:

3-0-0-0 (9 Credits)

### Course Content:

The primary objective of the course is to teach fundamentals of turbulent flows, an important topic in fluid dynamics. The course coverage includes: Statistical representation of turbulent flows, energy cascade, Kolmogorov hypothesis, free shear and wall-bounded flows apart from introduction to turbulence modelling and experiments.

### Prerequisites:

Knowledge of heat transfer, fluid mechanics and viscous flow theory.

### Brief Syllabus

Introduction: Origin of turbulence, irregularity, diffusivity, three-dimensional motions, dissipation, wide spectrum, length scales; Statistical Description of Turbulence: Probability density, moments, correlations, integral micro scales, homogeneous and isotropic turbulence, Kolmogorov hypothesis, energy cascade, turbulence spectra; Turbulent Transport: Reynolds decomposition, turbulent stresses, Reynolds equations, mixing-length model, dynamics of turbulence; Free Shear Flows: Mixing layer, turbulent wakes and jets, grid turbulence; Wall-bounded Turbulent Flows: Channel and pipe flows, Reynolds stresses, turbulent boundary layer equations, logarithmic-law of wall; Introduction to turbulence modelling and experimental methods

### Lecturewise Breakup (considering the duration of each lecture is 50 minutes)

I. Introduction: (3 Lectures)

• Nature of turbulent flows, irregularity, diffusivity, threedimensional motions, dissipation, wide spectrum, origin of turbulence, eddy motions and length scales.

II. Statistical Description of Turbulence: (7 Lectures)

• Random nature of turbulence,distribution function, probability density, moments, correlations, Taylor's hypothesis, integral micro scales, homogeneous and isotropic turbulence,Kolmogorov hypothesis, scales of turbulence, energy cascade, turbulence spectra..

III. Turbulent Transport of Moment and Heat: (6 Lectures)

• Reynolds decomposition, turbulent stresses, vortex stretching, Reynolds equations, mixing-length model, Reynolds' analogy, dynamics of turbulence.

IV. Free Shear Flows: (6 Lectures)

• Mixing Layer, Turbulent Wakes and Jets, Grid Turbulence.

V. Wall-Bounded Turbulent Flows: (6 Lecture)

• Channel and pipe flows, Reynolds stresses, turbulent boundary layer equations, logarithmic-law of walls, turbulent structures.

VI. Turbulence Modelling: (6 Lectures)

• Introduction, eddy-viscosity hypothesis, algebraic model, k-ε and k-ω model, Reynolds-stress model, near-wall treatment,iIntroduction to LES and DNS.

VII. Experimental Methods: (5 Lectures)

• Introduction, hot wire anemometry, uncertainty analysis and laser doppler anemometry.

### References:

1. Turbulent Flows, Stephen B. Pope, Cambridge University Press

2. A First Course in Turbulence, H. Tennekes and J. L. Lumley, MIT Press