This preview shows pages 1–2. Sign up to view the full content.
Turbulence
Lecture 22
Smaller scale motions cause the lack of large scale motion; nonlinearity counteracts this.
In the grid experiment far downstream where the nonlinearities are very weak – “final period of
decay.”
()
0
0
i
ii
i
ii
u
pu
pu
p
rx
x
Pr
∂
∂∂
′
==
′′
∂
=
±
=
Pressure forces have no effect on
ii
R
, but only on each component.
The pressure forces
redistribute the energy among the components.
The Inertial terms
ij
I
at zero spatial lag.
00
ij
j
i
k
i
k
j
i
j
k
kk
k
I
u
uu
u
uuu
xx
x
∂
=−
−
=
∂
±
by homogeneity.
0
ij
I
=
±
ii
0
, the inertial terms don’t affect overall content of the energy spectra (Fourier transform
of
R
)
The nonlinear terms conserve energy, change the scales of energy.
Pressure terms also conserve energy, they don’t change the scales, but they change directions.
The equation for
(
,
ij
)
R rt
±
or its Fourier Transform are the starting point for a number of theories.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 06/07/2011 for the course EGM 6341 taught by Professor Mei during the Spring '09 term at University of Florida.
 Spring '09
 MEI

Click to edit the document details