**Provider**Swayam

**Cost**Free Online Course

**Session**Finished

**Language**English

**Certificate**Paid Certificate Available

**Duration**12 weeks long

## Overview

Turbulence is everywhere—in the interiors and atmospheres of planets and stars, galaxies, biological systems including human body, engineering flows, etc. In this course, we will cover fundamental aspects of turbulence—Kolmogorov’s theory of turbulence in spectral and real space; two-dimensional turbulence; energy transfers; enstrophy and kinetic helicity cascades; more complex applications, such as passive scalar, turbulent thermal convection, and magnetohydrodynamic turbulence.

**INTENDED AUDIENCE:**Any Interested learners**PREREQUISITES:**Basic fluid dynamics, Calculus, Fourier transforms**INDUSTRY SUPPORT:**Companies working in CFD, turbulence## Syllabus

### COURSE LAYOUT

**Week 1:**Introduction; Basic equations of hydrodynamics in real space; Conservation laws

**Week 2:**Fourier Space Description of Hydrodynamics;

**Week 3:**Fourier description contd. Craya-Herring basis

**Week 4:**Instabilities

**Week 5:**Saturation of nonlinearity; Patterns

**Week 6:**Energy transfers in fluid flows

**Week 7:**Kolmogorov’s theory of turbulence (in Fourier space)

**Week 8:**Kolmogorov’s theory of turbulence (in real space)

**Week 9:**Enstrophy; Two-dimensional turbulence; Kinetic helicity

**Week 10:**Turbulence with a scalar; Passive scalar;

**Week 11:**Turbulent thermal convection

**Week 12:**Turbulence with a vector; Magnetohydrodynamic turbulence