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