Turbulence and turbulent momentum fluxes. Meteorology 505: Environmental Biophysics Dan Rajewski, Post-Doc. February 5, 2015

Transcription

1 Turbulence and turbulent momentum fluxes Meteorology 505: Environmental Biophysics Dan Rajewski, Post-Doc. February 5, 2015

2 Overview What is turbulence and how does it relate to wind speed? How do you measure fluxes and interpret the data What is the influence of wind farms on canopy fluxes of energy?

3 What can you tell from this data? LST [hours]

4 What can you tell from this data? NIGHT DAY sunrise LST [hours] DAY NIGHT sunrise

5 Wind speed profile (derived last lecture)

6 What do u w and v w mean? These terms are representing the vertical flux of momentum between the surface (e.g. crop canopy) and the layer of air above the canopy (boundary layer) Wind is 3-dimensional up (w>0) NORTH (v>0) Horizontal wind speed is a magnitude WEST (u<0) EAST (u>0) u v 2 2 SOUTH (v<0) and vector of components <u,v> down (w<0)

7 Wind responds to changes of forcing in time

8 How do we determine momentum fluxes? Mean Kinetic energy (MKE) = ½ mv 2 For a unit mass MKE~ 0.5 v 2 so then TKE = 0.5 v 2 is the Turbulence Kinetic Energy These terms explain the vertical exchange of momentum above the surface

9 Determining fluxes from mean wind (u,w) NIGHT DAY Take 1-hr subset of 10-minute averaged wind speed and vertical velocity to get u w sunrise LST [hours] NIGHT DAY sunrise

10 Calculation of u w Start with a time series of u and w: u wind speed vs. Time Instantaneous u wind speed (m/s) Instantaneous u vertical velocity (m/s) UP EAST DOWN WEST U i Time (20 Hz) vertical velocity vs. Time Time (20 Hz) u u u w w w i i Determine the mean and perturbation around the mean for both quantities This data shows sampling of wind speed at 20 times per second!

11 Calculating fluxes and variances For any variable X: determine the mean and perturbation components to find the variance n 2 2 X ( Xi X) n i 1 n X (x i) x n i 1 X 1 1 x 2 x 2 2 X 1 2 statistical variance standard deviation of mean = square root of variance 1 TKE u v w

12 Calculating fluxes and variances For any variables X and Y: determine the mean and perturbation components to find the covariance n 1 cov( xy, ) ( X ) i X Yi Y n i 1 n 1 cov( xy, ) (x ) i y i xy n i 1 uw, vw, uv statistical co-variance co-variance determines the common relationship between two variables

13 What does u w look like? Height 1 2 What happens if the air at (1) is displaced upward and displaced downward at (2)? Wind speed THINK of mixing a fluid: How does it respond?

14 What does u w look like? (1) is being carried up by a turbulent eddy (w > 0), but because it has lower wind speed, it is bringing upward a negative perturbation (u < 0) Height Net downward flux of momentum (2) is brought down by a turbulent eddy (w < 0), and has a higher wind than at (1) so it has a positive perturbation (u > 0) In BOTH cases the product of u w is (> 0) (< 0) negative (downward) 1 2 Physical interpretation: The turbulence feeds off of the gradient in wind speed Wind speed is non-zero The supply of turbulence comes from the wind speed above the surface Wind speed Energy of mean momentum = Energy of turbulence (fluctuations in momentum) MKE TKE

15 Visualizing fluxes and turbulence NIGHT DAY sunrise Why is turbulence low at night? NIGHT sunrise DAY At night turbulence is generated by the gradient in wind speed close to the surface

16 Visualizing fluxes and turbulence NIGHT DAY sunrise How is the turbulence different among the three directions? NIGHT sunrise DAY This case is for a windy day therefore there is more production of turbulence to the wind speed gradient (shear) than for buoyancy (heating)

17 Turbulence generated by wind speed Turbulence generated by heating (buoyancy) Stull, Introduction to Boundary Layer Meteorology, 1988

18 Visualizing fluxes and turbulence NIGHT DAY sunrise What do you notice about the vertical flux of momentum (cov uw) vs. cov (vw)? NIGHT sunrise DAY Southerly wind is feeding the turbulent flux to the surface (flux <0) LST [hours]

19 Turbulence detection on campus January 16 7:15 AM to 4:45 PM (LST) What did you notice about the snap shots of smoke? How did it change throughout the course of the day? What does that indicate about the turbulence?

20 Visualization of turbulent momentum flux: think rotational eddies up up up north north north west south east u w Net transfer is downward west south v w east Net transfer is downward west south east u v Net transfer is lateral down down down

21 Measuring turbulent fluxes: sonic anemometer Each axis of the sonic anemometer sends brief pulses of ultrasonic signals in opposite directions. The time of flight of the first signal (out) is given by: and the time of flight of the second signal (back) is given by: The wind speed, u a, along any axis can be found by inverting the above relationships, then subtracting the second equation from the first and solving for u a : The wind speed is measured on all three non-orthogonal axis to give u a, u b, and u c, where the subscripts a, b, and c refer to the nonorthogonal sonic axis. The non-orthogonal wind speed components are then transformed into orthogonal wind speed components, u, v, and w, with the following: u ua v A u b w u c A is a 3X3 transformation coordinate matrix

22 Data corrections to sonic anemometer sonic anemometer conversion of coordinates from instrument to meteorological coordinates Uz>0 w>0 Ux>0 Uy>0 v>0 (south) X u>0 (west) sonic tilt correction so that all measured fluxes are for true vertical, north, and west sensor sags due to the weight or may not point directly North

23 LiDAR (Laser radar) measurement Lidar (laser-beam radar) measures vertical profile of wind speed and turbulence Data output is every 2 min from composite scans every 2 sec from 40 to 220 m at 20 m intervals every 2 sec Measures standard deviations of 3-D wind field SoDAR measures wind in the same way as a LiDAR except that it uses sound waves LiDAR and SoDAR CANNOT measure covariances (turbulence fluxes) Picture by: Russell Doorenbos 23

24 How is turbulence data used? Sonic anemometers measure: uu, vv, ww, uw, vw, u' v Image taken from LiCOR Biosciences but also heat fluxes: ut, vt, wt, TT With an additional sensor to measure gas concentrations of H2O and CO2, moisture and carbon fluxes can be estimated 2 uh 2O, vh 2O, wh 2O, H2O 2 uco 2, vco 2, wco 2, CO 2 Gas analyzer

25 Heat, moisture and CO 2 fluxes H c wt p Sensible heat flux E wc v F C wc c x g Latent heat flux Carbon Dioxide flux

26 Spectral analysis Spectral analysis shows how to relate the size of the turbulence (xaxis) to the intensity of energy (y-axis) Normalized u-power spectrum (fp uu u * -2 ) Low frequency large eddies High frequency small eddies The area under the curve is equal to the variance or co-variance for that averaging period This represents the energy cascade

27 CWEX (Crop/Wind-energy Experiment): measurements of crop microclimate conditions within wind farms 27

28 CWEX Investigators Dan Rajewski 2, Gene Takle 1,2,, Tom Horst 3, Steve Oncley 3,, Julie Lundquist 4, Mike Rhodes 5, John Prueger 6, Richard Pfieffer 6, Jerry Hatfield 6, Samantha Irvin 2, Kris Spoth 2 Russell Doorenbos 2, 1 Geological & Atmospheric Sciences, 2 Agronomy Iowa State University, Ames, IA 3 National Center for Atmospheric Research 4 Atmospheric and Oceanic Sciences, 5 Aerospace Engineering Sciences University of Colorado, Boulder, CO 6 National Laboratory for Agriculture and the Environment, Ames, IA 28

29 Motivation Convergence of two unlike energy industries in the same geographical area presents an interaction (I): Wind turbine/wind farm influences on crop microclimate and overall yield (II): Crop and field management impacts on wind power Can strategies of optimization be developed by studying this interaction? 29

30 Potential Impact on Crops: Discussions with Agronomists Reduce daytime max temps: avoid summer moisture stress Increase nighttime temps: decrease grain fill (respiration), extend growing season (avoid late spring freeze, avoid early fall frost) Enhance evaporation: reduce dew duration (reduce favorable conditions for pests and pathogens; accelerate fall crop dry-down) Enhance evaporation: accelerate spring soil drying; accelerate moisture loss during drought Enhance atmospheric CO 2 exchange with the crop: enhance daytime photosynthesis; enhance nighttime respiration Enhance CO 2 pumping from soil: enhance photosynthesis Reduce mean wind speed at top of the canopy: reduce potential for lodging and green snap in corn Enhance plant movement through increased turbulence: increase light penetration into canopy and enhance photosynthesis Modify mesoscale-scale convergence/divergence patterns: altered/enhanced rainfall patterns (????????) Green = favorable, Red =unfavorable 30

31 Turbine-Crop Interactions: Overview Do turbines create a measureable influence on the microclimate over crops? If so, does this influence create measureable biophysical changes? And if this is so, does this influence affect yield? Agricultural shelterbelts have a positive effect on crop growth and yield. Will wind turbines also have a positive effect? 31

32 Conceptual model of Turbine-crop Interaction via mean wind and turbulence fields, adapted from Wang and Takle (1995) over-speeding zone turbine wake H wind-ward reduction zone L Speed recovery H L leeward bleed through and speed up-zone Heat day night H 2 O CO 2 night day 32

33 Diffuse patches of wakes reaching the surface Heterogeneities of wind turbine wakes offshore of Denmark wake sheet from several lines of merging wakes double wake far wake near wake wake overhead but not reaching the surface Wake structure differences appear in 2 nd line of turbines Source: UniFly A/S Horns Rev 1 owned by Vattenfall. Photographer Christian Steiness 2008.

34 CWEX layout Central Iowa wind farm (~ MW turbines with 80-m hub height and 77 m and 82.5-m rotor diameter (D) ) Measurements taken on southern edge of a wind farm according to prevailing winds at nearby airports, 2013 measurements at northwest edge of the farm surface flux and LiDAR measurements above corn: 2010,2011; above soybean: CWEX-13 January July CWEX-10/11/12

35 Preliminary measurements in 2009 Cloudy, north wind measuring over corn Hot, high humidity with southerly flow cup anemometer 2 m above the canopy thermocouples at 1.5, 1.0, 0.5 m above the soybeans wind speed and temperature measured every 0.5 s at upwind and downwind masts

36 N CWEX-10: Flux tower measurements Cup anemometer at 9.1 m T & RH at 9.1 m and 5.3 m Sonic anemometer at 6.45 m Tipping bucket at 3.75 m Two towers (reference and near-wake location) additionally contained Net radiometer (net long wave and short wave radiation) at 5.3 m Open path CO 2 /H 2 0 IRGA LI-7500 gas analyzer Sonic anemometer and gas analyzer sampled at 20 Hz w/ 5 min averages T, RH, cup anemometer, rain gage output archived at 5 min All sensors are connected to a data-logger Systems are powered with solar panels and deep cycle batteries Picture by: Russell Doorenbos 36

37 CWEX-11: Instrumentation of towers NCAR ISU 10 m wind speed, direction Temp/RH 4.5 m Temp/H2O, wind, turbulence (NCAR 1-4) CO 2 (NCAR 1,3 only) 2 m Temp/RH 2 m Air Pressure S 8 m Temp/RH wind speed NOT SHOWN IN PHOTO: net radiation probe 2 m above canopy rain gauge at canopy leaf wetness probe at 2/3 canopy height 1 m Temp/RH Soil temp, moisture, soil heat flux (ISU1) 4.5 m Temp, wind, turbulence CO 2 and H 2 O (ISU1) E 3 m Temp/RH Picture by: Russell Doorenbos wind speed Picture by: Russell Doorenbos 37

38 Comparison on 10 m and 80 m wind speed from CWEX-11 Directional shear (change in wind direction with height) can be a complicating factor in wake impacts within the rotor depth vs. near the crop surface Rajewski et al., Bull Am Meteorol Soc,

39 Downwind-upwind station differences in friction velocity and TKE u * 200 m downwind of 1 st turbine line 1.3 km downwind of 1 st turbine line 2.6 km downwind of 1 st turbine line Turbines enhance canopy mixing mostly at night TKE 200 m downwind of 1 st turbine line South to North 1.3 km downwind of 1 st turbine line Higher nighttime turbulence farther into the wind farm South to North 2.6 km downwind of 1 st turbine line

40 Canopy turbulence during shutdown: August 27, LST Station north of two turbine lines has 2-3X ambient TKE and Heat flux before/after the OFF period 80-m wind direction vector Return to reference flow conditions during the shut down (lightning nearby)

41 Spectral evidence before and during the shutdown period South North Turbines ON W-power spectra NLAE 1 NLAE 2 NLAE 3 NLAE 4 NLAE 1 NLAE 2 NLAE 3 NLAE 4 South North Turbines OFF ON: Increase in vertical velocity variance of: 2.0X downwind of first line of turbines 5.0X downwind of two lines of turbines OFF: Similar intensity of variance for all flux stations south and north of two turbine lines (Modified from Rajewski et al. Agric and For Meteorol., 2014)

42 Spectral evidence before and during the shutdown period South North Turbines ON VW-power spectra NLAE 1 NLAE 2 NLAE 3 NLAE 4 NLAE 1 NLAE 2 NLAE 3 NLAE 4 South North Turbines OFF ON: Increase in stream-wise co-variance of 2.0X downwind of first line of turbines 4.0X downwind of two lines of turbines OFF: Similar intensity of covariance for all flux stations south and north of two turbine lines (Modified from Rajewski et al. Agric and For Meteorol., 2014)

43 Detection of wind turbine impacts on H, E, and CO 2 fluxes: wind direction Case direction Turbine wake category Indicator OFF (combination turbines offline) ON (combination turbines operating) W (Westerly no-wake, turbines on and off ) WSW [B1] B1 (5.3 D to turbine) SW [B12G] gap between B1 and B2 (3.8 D to line) SSW [B2] B2 (2.7 D to turbine) S-SSE [B23G] gap between B2 and B3 (2.6 D to line) Sample size (N) DAY Sample size (N) NIGHT (Modified from Rajewski et al. Agric and For Meteorol., 2014) Most of these categories have a relevant sample size for testing the statistical significance of the differences 43

44 u * (NLAE 2-NLAE 1) Means and accumulated differences Mean difference, u * (m s -1 ) Daytime differences are negligible, similar justification as sensible heat flux for a 30-minute average Nighttime: 50-75% higher mixing at NLAE 2 at 2-5 D downstream of a turbine (Modified from Rajewski et al. Agric and For Meteorol., 2014) 44

45 DAY: Projection of wake influence on surface B2 B1 Site 1 H 2 O Site 3 CO 2 H 2 O CO Site 2 2 Daytime H 2 O and CO 2 flux increased by turbine mixing (response lag in time) Site A Site B Downward (counter-gradient) heat flux is reported on edge of turbine wake (indicating wake rotation 45

46 NIGHT: Projection of wake influence on surface B2 B1 Site 1 Heat CO 2 Site 3 Heat CO 2 Site 2 Nighttime Heat and CO 2 fluxes increased by turbine mixing (via u * and TKE) 2X of ambient downward heat flux at wake edges Stable stratification suppresses upward motion of turbine wake Site A Site B 46

47 NIGHT: ALIGNED DOUBLE WAKE Projection A1 B2 L H Heat Site 4 Heat Heat Site 3 Site 2B Site 2A L H Site 1 <25% higher Heat <0.25 C warmer <25% increase U,TKE 2X ambient heat flux C warmer 1.5X increase U,TKE 50-75% higher heat flux C warmer 25-50% increase U,TKE Wake structure from 1 st turbine dependent on ambient wind speed, direction thermal stability, and thrust specification of turbine 25-50% higher Heat <0.5 C warmer 50-75% increase U,TKE 47

48 NIGHT: MERGED WAKE Projection A5 B6 C12 C4 C1 D5 D1 ite 5 Site 4 Site 3 Site 2 Site 1 A1 B2 Turbine eddies become smaller and smaller after passing through additional turbine lines Merged wakes dissipate energy therein and are unable to change surface fluxes Negligible downwind-upwind differences in fluxes Surface wake interaction resumes several turbine lines downstream when a wake-boundary layer sheet has developed? 48

49 Key References Rajewski, D. A., Takle E.S., Lundquist J.K., et al., Crop Wind Energy Experiment (CWEX): Observations of Surface-Layer, Boundary Layer, and Mesoscale Interactions with a Wind Farm. Bull. Am. Meteorol. Soc. 94, (2013). doi: /BAMS-D Rajewski D.A., Takle E.S., Lundquist J.K., et al., Changes in fluxes of heat, H2O, and CO2 caused by a large wind farm. Agric For Meteorol. 194, (2014). doi: /j.agrformet Stull, R., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, 666 pp. Wang, H., E. S. Takle, and J. Shen, 2001: Shelterbelts and windbreaks: Mathematical modeling and computer simulation of turbulent flows. Ann. Rev. Fluid Mech., 33,

50 Thank you frozen turbulence after a blizzard 50