1.  INTRODUCTION.  

 Examples of turbulent flows,  Nature and characteristics of turbulence,  Origin, maintenance and  decay of  turbulence,  Methods of analysis :  Introduction to Mathematical models,  Numerical  models,  Experimental work.

 2.  OVERVIEW OF RELEVANT MATHEMATICS - TOOLS. 

 Partial differential equations. Tensors, vectors, scalars.  Transformations of coordinates.  Statistical tools and their relevance: Averaging, Fluctuations, PDFs, Space  and  time correlations, Random processes, Wave number and frequency spectra, Coherence function, Structure function, Definition  and method of computation of turbulence scales.

3.  FLUID MECHANICAL BACKGROUND. 

Fluid dynamics, - velocity field, Conservation of mass,  Rate of relative displacement - deformation - vorticity, The stress tensor,  Equations of motion,       Conservation of energy,  Transport processes , Boundary conditions

4.  ANALYTICAL TREATMENT OF TURBULENCE, DERIVATION OF RELEVANT EQUATIONS.  Reynolds decomposition, The equations of motion, incompressible flow, Continuity equation, Momentum equation, Kinetic energy equation for the mean flow, Turbulent kinetic energy, Reynolds stress transport equations, Vorticity equation, Pressure fluctuations, Scalar transport equations :  Mean enthalpy,      Mean square scalar or temperature fluctuations,  Scalar or temperature flux equations

5. HOMOGENEOUS TURBULENCE, ISOTROPIC TURBULENCE.  

Kinematics and dynamics of homogeneous turbulence, Isotropic turbulence, Kinematics of isotropic turbulence,  spectral functions, further functions, triple velocity products, Dynamics of isotropic turbulence, Isotropic spectral relations, Expressions for velocity spectra, Decay of turbulence, Grid turbulence.

6.  SIMPLE TURBULENT FLOWS AND TURBULENT SHEAR FLOWS.

Boundary-free shear flows.  Analysis and applications. Turbulent wakes, Turbulent jets, Free shear layers, Mixing layers. Wall bounded shear flows ,  Mixing length analysis in the inertial sublayer,  Intermittency.

7.  SPECIAL PROBLEMS - APPLICATIONS 

Turbulent Diffusion, Lagrangian methods for analysis of concentration fluctuations - Industrial and Environmental  case studies.   Effects of rotation on turbulence,  Effects of buoyancy on turbulence,  Drag reduction in turbulent flows, Forces on Airfoils and Bluff bodies due to Turbulent Flows. Experience and hands on usage of home made and commercial software (CFD and Εngineering Codes).