Josette MarquardtThishan KarandanaYunpeng Shan

Outline

Introduction to Richardson Number

Evaluation to convection

Evaluation to wind shear

Conclusion

Introduction to Richardson Number1. Calculation

Bulk Richardson NumberGradient Richardson Number

Richardson Number = (-1)*(work by buoyancy)/(work by wind shear)

Flux Richardson Number

' '

' ' ' '

v

v

gw

Riu v

u w v wz z

Ri >0, Stable PBL condition TKE decreases

<0, Unstable PBL condition TKE increases

Introduction to Richarson Number2. Development of Boundary Layer

Introduction to Richardson Number3. Conversion of Richardson Number

There is no wind shear

Wind shear

Z

X

Z

X

Y

X

Y

X

2 2

v

v

gz

RiU Vz z

i

Vt x

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i

Vt x

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2

1( 1)

''1

v

v

gtV

RiVtV

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It seems that turbulence during daily time is dominated by dry convection, while turbulence at night is controlled by wind shear.

(Wyngaard J. C. 1990)

Introduction to Richardson Number4. Comparison between convection and wind shear

Observing data is used to check if this assumption is true.

Evaluation to convection1. Convections caused by the Long Wave Radiation(LWR)

Here we can see that 15% out-coming long wave radiation is absorbed by atmosphere. We assume that a constant portion of this energy has been converted into TKE.

Heated atmosphere will show an increasing potential temperature which also means a positive Ri’’ and increasing TKE.

2

1( 1)

''1

v

v

gtV

RiVtV

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After sun rising, surface temperature, potential temperature and long wave radiation increased obviously. As a result of it, more energy could be provided in order to maintain the turbulence.

Evaluation to convection2. Kinetic Energy Variation caused by Potential TemperatureAfter sun rising, TKE had an obvious increasing trend and stayed a fluctuate condition from 09:30. The same thing happened to flow kinetic energy(FKE). 2 2 2

2 2 2

1( )21[( ') ( ') ( ') ]2

FKE u v w

TKE u v w

Evaluation of wind shear1. Richardson Number variation caused by wind shear

Y

X

2

1( 1)

''1

v

v

gtV

RiVtV

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Wind shear =

2 2 2 1/ 22 2 2 1/ 2

1 ( 1) ( ) ( 1) ( ) ( 1) ( )[( ) ( ) ( ) ]

( ) _ _ _

u t u t v t v t w t w t

u v w diff t diff t diff t

Evaluation of wind shear2. Turbulence caused by wind shear in the morning

After sun rising, there was an increasing trend for both TKE and FKE. When it came to 09:30, this increasing trend converted into a fluctuating condition. Although direction of horizontal wind varied, the increasing trend from 07:00 to 9:30 was obvious.

There was an increasing trend of wind shear, but TKE portion did not show any rising. It seems that the wind shear do not make a significant contribution to TKE

Increasing absolute value of w means more and more dry convection happened during this time.

Evaluation of wind shear3. Comparison of two physical mechanism

Comparison of averaged 1min U,V and W data with calculated based on raw data

1. A modified Richardson Number was used in order to investigate contribution of long wave radiation and wind shear to TKE.

2. From sun rising to about 9:30, TKE and FKE increased obviously, while the ratio that TKE is divided by sum of TKE and FKE stayed constant.

3. Both TKE and FKE stayed in a fluctuation condition , rather than going on increasing, after 9:30 when surface received enough solar energy, although surface temperature kept rising.

4. By comparison, it seems that convection caused by long wave radiation make a larger contribution to developing turbulence after sun rising.

Conclusion