1. Scalar mixing2. Turbulence Spectrum3. Correlations4. Energy and Vorticity5. Transport Equations 6. More Length Scales
circular bars
square bars
0 4 8 12 16 20
r~
0
2
4
6
8
g
gm eas
Antonia, Smalley, Zhou, Anselmet & Danaila (2003)
0 4 8 12 16 20
r~
0
2
4
6
8
g
2Lq
gcal gm eas
Antonia, Smalley, Zhou, Anselmet & Danaila (2003)
22
1 2
20 rg r 5 10r 2f
3 m
0 4 8 12 16 20
r~
0
2
4
6
8
g
2Lq
gcal gm eas
• Batchelor (1959) argued that for Sc»1
• the rate of strain 1/ 2/
should be approximately uniform over regions of space which are small compared to
• the highest scalar wavenumber vectors would align with the compression axes of the local rate of strain tensor and be convected rapidly to higher until the wavelength decreases to aboutk
1/ 2/
1/ 2
1/ 2B Sc
• Viscous-convective subrange
1 1Bk
1 1E k q k
q Batchelor "constant"
1† † †E (k ) qk
1 2† † † †E (k ) qk exp( qk )
• Viscous-convective and viscous-diffusive subranges
Kraichnan (1968,1974)
1 1 1† † † † †2 2E (k ) qk [1 (69) k ]exp[ (69) k ]
Batchelor (1959)
Brethouwer, Hunt & Niewstadt (2003)
Sc=0.7
Brethouwer, Hunt & Niewstadt (2003)
Sc=25
(1997)
Sc=3, 5, 7
forced
Brethouwer & Niewstadt (1999)
R=22, Sc=144
forced vs decaying
Gravity currents, Waves, Froude number