Theory of Turbulence Notes

This page will contain links to other pages where notes taken from papers, books, and classes will reside.
==Books==
===A First Course in Turbulence - Tennekes and Lumley===
*Chapter 1
*Chapter 2
==Internet Sources==
===Videos from National Committee for Fluid Mechanics Films===
http://web.mit.edu/hml/ncfmf.html
====Turbulence Video Link====
==Class Notes==
NOTE: NOT FULLY SYNCED WITH HANDWRITTEN NOTES
===Class 1===
References
Turbulence Modeling for CFD by Wilcox
A First Course in Turbulence by Tennekes and Lumley
Viscous Fluid Flow by White
See hand out page 2 for first assignment
Part two "…on periodic flow" (optional)
-Keep notebook (mine will be online)
-Read Chapter 5 Viscous Fluid Flow
look at
form of inertial terms and form of viscous terms in Navier-Stokes equations
inertial terms
u \frac{\partial u}{\partial x}
looking at the dimensions
U \frac{U}{L}
viscous terms
\nu 
Now at large Re, viscous terms go to zero.
But near the walls, we might want to think of small length scales (l) for viscous terms such that in boundary layer, require that the viscous terms are proportional to the inertial terms.
\frac{U^2}{L} \backsim \frac{\nu U}{l^2} 
(see notes)
So l should be understood to be a transverse length scale (perpendicular to wall), represents boundary layer thickness.
===Class 2===
N-S Equations
\arrow V = {u, v, w}
RANS Equations
*u = \bar u + u'
*v = \bar v + v'
*w = \bar w + w'
Time fluctuating components average out to zero
\bar {u'} = \bar {v'} = \bar {w'} = 0
\frac{\text{D} \bar u}{\text{D} t} = 
(See hand notes on Notation)
Conservation of mass (incompressible fluids):
\frac{\partial \tilde u_i}{\partial x_i} = 0
Steady flow N-S Equations:
\tilde u_j \frac{\partial \tilde u_i}{\partial x_j} = \frac{1}{\rho} \tilde \sigma _{ij}