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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 learnersPREREQUISITES: Basic fluid dynamics, Calculus, Fourier transformsINDUSTRY SUPPORT: Companies working in CFD, turbulence



Week 1: Introduction; Basic equations of hydrodynamics in real space; Conservation lawsWeek 2: Fourier Space Description of Hydrodynamics;Week 3: Fourier description contd. Craya-Herring basisWeek 4: InstabilitiesWeek 5: Saturation of nonlinearity; PatternsWeek 6: Energy transfers in fluid flowsWeek 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 helicityWeek 10:Turbulence with a scalar; Passive scalar;Week 11:Turbulent thermal convectionWeek 12:Turbulence with a vector; Magnetohydrodynamic turbulence