Characteristics of boundary layer flow


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Characteristics of boundary layer flow

  2. 2. WIND ENERGY METEOROLOGY CHARACTERISTICS OF BOUNDARY LAYER FLOW Influence of surface ‣ friction, shear, turbulence strong vertical gradients vertical fluxes of momentum, heat, .. Turbulence ‣ turbulent eddies are generated mechanically by strong shear as flow adjusts to condition at surface ‣ thermal generation of turbulence through buoyancy by destabilized stratification (--> thermal stability)Dienstag, 19. April 2011
  3. 3. WIND ENERGY METEOROLOGY CHARACTERISTICS OF BOUNDARY LAYER FLOW Governing quantities ‣ wind speed („driving“ large scale wind field) ‣ surface roughness ‣ thermal stability 3Dienstag, 19. April 2011
  4. 4. WIND ENERGY METEOROLOGY PLANETARY BOUNDARY LAYER: GENERAL CHARACTERISTICS Stability ‣ Structure of PBL is influenced by underlying surface and by stability of the PBL ‣ Surface roughness ‣ Unstably stratified PBL enhances turbulence production -> intensified exchange -> more uniform distribution of momentum, etc. ‣ Stably stratified PBL turbulence produced by shear is suppressed -> weak exchange -> weak coupling with surface . 4Dienstag, 19. April 2011
  5. 5. WIND ENERGY METEOROLOGY PLANETARY BOUNDARY LAYER: GENERAL CHARACTERISTICS Diurnal pattern ‣ Strong mixing during daytime with upward heat flux from surface ‣ Strong turbulent mixing -> nearly uniform vertical profiles (‘mixed layer‘) ‣ top of PBL is capped by inversion ‣ inversion height rises quickly early in the morning with max. height of few km during daytime ‣ turbulence dies out in night time when vertical heat flux turns -> shallow stable layer near surface ‣ nocturnal boundary layer height is typicaly 50 to 200 m only . 5Dienstag, 19. April 2011
  6. 6. WIND ENERGY METEOROLOGY PLANETARY BOUNDARY LAYER: GENERAL CHARACTERISTICS Turbulence ‣ Diffuse processes in the PBL are dominarted by turbulence (molecular diffusion can in general be neglected) ‣ Time scales of turbulent motion: few seconds to about half an hour ‣ Length scales: millemeters to few hundred meters (these scales have to be parameterized in large scale models) . 6Dienstag, 19. April 2011
  7. 7. WIND ENERGY METEOROLOGY TURBULENCE Karman vortex streets... the laboratory, for the atmosphere, for a water flowing past a cylinder cumulus-topped boundary layer flowing past an island Stull (2006) 7Dienstag, 19. April 2011
  8. 8. WIND ENERGY METEOROLOGY GENERATION OF TURBULENCE ‣ Generation can be mechanically, thermally, and inertially. ‣ Mechanical turbulence, a.k.a. forced convection, results from shear in the mean wind. It is caused by: ‣ frictional drag (slower winds near the ground than aloft) ‣ wake turbulence (swirling winds behind obstacles) ‣ free shear (regions away from any solid surface) ‣ Thermal or convective turbulence, a.k.a. free convection, consists of plumes or thermals of warm air that rises and cold air that sinks due to buoyancy forces. ‣ Inertial turbulence: Generation of small eddies along the edges of larger eddies (within the turbulent cascade). Special form of shear turbulence (shear is generated by larger eddies) Stull (2006) 8Dienstag, 19. April 2011
  9. 9. WIND ENERGY METEOROLOGY TURBULENCE Spectrum of turbulent kinetic energy (TKE) ‣ The energy spectrum indicates how much of the total TKE is associated with each eddy scale. ‣ The total TKE is given by the area under the curve. ‣ Permanent generation of TKE from shear or buoyancy at large scales. ‣ TKE cascades through medium-size eddies to be dissipated by molecular viscosity at the small- eddy scale (TKE is not conserved!). Stull (2006) 9Dienstag, 19. April 2011
  10. 10. WIND ENERGY METEOROLOGY SPECTRUM OF HORIZONTAL WIND VELOCITY Source: Burton, 2001 (based on van der Hoven (1957)) 10Dienstag, 19. April 2011
  11. 11. WIND ENERGY METEOROLOGY ORIGIN OF TURBULENCE ‣ Turbulence is a natural response to instabilities in the flow and tends to reduce the instability. ‣ Example 1: Thermal instability: Vertical turbulent motion of cold and warm air to reduce a large vertical temperature gradient. ‣ Example 2: Dynamic instability: Vertical shear in the horizontal wind: Turbulence mixes the faster and slower moving air. ‣ Persistent mechanical turbulence in the atmosphere needs a continual destabilization by external forcings. Stull (2006) 11Dienstag, 19. April 2011
  12. 12. WIND ENERGY METEOROLOGY STATISTICAL DESCRIPTION OF TURBULENCE (I) ‣ Aim: Describing net effect of many eddies, rather than the exact behavior of any individual eddy ‣ A certain point in the atmosphere (e.g., a measurement sensor) is affected by many eddies of all sizes -> randomness ‣ But: for a given time period, say 10 minutes, the measurement will fluctuate around a well-defined mean value --> turbulence is quasi-random ‣ Then, the fluctuating portion of the flow is given by subtracting the mean from the instantaneous component: Stull (2006) 12Dienstag, 19. April 2011
  13. 13. WIND ENERGY METEOROLOGY STATISTICAL DESCRIPTION OF TURBULENCE (II) ‣ The intensity of turbulence (in the u direction) is then defined by the variance: ‣ If σu2 is relatively constant with time, the flow is said to be stationary ‣ If σu2 is relatively uniform in space, the flow is said to be homogeneous Stull (2006) 13Dienstag, 19. April 2011
  14. 14. WIND ENERGY METEOROLOGY STATISTICAL DESCRIPTION OF TURBULENCE (III) ‣ Fluctuations in velocity are often accompanied by fluctuations in scalar values ‣ E.g.: rising warm air in a field of thermals (positive potential temperature θ, positive vertical velocity w), surrounded by regions with sinking cold air (negative θ, negative w) ‣ A measure of the amount that θ and w vary together is the covariance (cov): Stull (2006) 14Dienstag, 19. April 2011
  15. 15. WIND ENERGY METEOROLOGY STATISTICAL DESCRIPTION OF TURBULENCE (IV) ‣ If warm air parcels are rising and cold parcels are sinking, as in a thermally direct circulation, then ‣ The variance of velocity represents the kinetic energy associated with the motions on the scale of the turbulence. ‣ Similarly, the covariance is a measure of flux due to these motions, such as the vertical heat flux . ‣ This ‘kinematic‘ heat flux (Kms -1) is related to the usual heat flux QH (Wm-2) by Stull (2006) 15Dienstag, 19. April 2011
  16. 16. WIND ENERGY METEOROLOGY 16Dienstag, 19. April 2011
  17. 17. WIND ENERGY METEOROLOGY TURBULENT KINETIC ENERGY (I) ‣ When the kinetic energy of an air parcel is , the specific kinetic energy, i.e. per unit mass, associated with turbulent fluctuations is: ‣ TKE is the turbulent kinetic energy ‣ In a laminar flow TKE = 0. ‣ Larger values of TKE indicate a greater intensity of the microscale turbulence. Stull (2006) 17Dienstag, 19. April 2011
  18. 18. WIND ENERGY METEOROLOGY TURBULENT KINETIC ENERGY (II) from a simple balance we may write a simple forecast equation for turbulence kinetic energy: with advection by mean wind (Ad), mechanical generation (M), buoyant generation/consumption (B), transport by turbulence itself (Tr), and viscous dissipation (ε) approximated by and the dissipation length scale Lε. The dissipation rate ε will always cause TKE to decrease. --> Turbulence is a dissipative process. Stull (2006) 18Dienstag, 19. April 2011
  19. 19. WIND ENERGY METEOROLOGY TURBULENT KINETIC ENERGY (III) statically stable atmosphere: ‣ buoyancy reduces TKE by converting it to potential energy by moving cold air up and warm air down ‣ existence of turbulence depends on the relative strengths of mechanical generation (M) by wind shear versus buoyant consumption (B) by static stability ‣ ratio of these two terms defines the dimensionless Richardson number Ri:: approximated by the vertical gradients of wind and potential temperature Stull (2006) 19Dienstag, 19. April 2011
  20. 20. WIND ENERGY METEOROLOGY TURBULENT KINETIC ENERGY (IV) ‣ Laminar flow becomes turbulent when Ri drops below the critical value Ric = 0.25. ‣ Turbulent flow often stays turbulent, even for Richardson numbers as large as 1.0, but becomes laminar at larger values of Ri. ‣ The presence or absence of turbulence for 0.25 < Ri < 1.0 depends on the history of the flow. ‣ Flows for which Ric < 0.25 are said to be dynamically unstable. Stull (2006) 20Dienstag, 19. April 2011
  21. 21. WIND ENERGY METEOROLOGY TURBULENT TRANSPORT & FLUXES Covariances can be interpreted as fluxes Ex.: idealized eddy circulation in atmosphere with a constant gradient of potential temperature θ turbulent heat fluxes for small- eddy vertical mixing in adiabatic processes, air parcels preserve their potential temperature θ left: statically unstable ( ) covariance is positive right: statically stable ( ) covariance is negative Stull (2006) 21Dienstag, 19. April 2011
  22. 22. WIND ENERGY METEOROLOGY VERTICAL STRUCTURE OF THE PLANETARY BOUNDARY LAYER geostrophic wind, ~1-2 km decreasing turbulent effects, change in wind direction, small change in wind speed ~100 m strong vertical wind shear, almost constant wind direction Ekman layer and Surface layer are each characterized by different physical constraints.Dienstag, 19. April 2011
  23. 23. WIND ENERGY METEOROLOGY EKMAN LAYER Source: 23Dienstag, 19. April 2011
  24. 24. WIND ENERGY METEOROLOGY EKMAN SPIRAL The theoretical Ekman spiral describing the height dependence of the departure of the wind field in the boundary layer from geostrophic balance. α is the angular departure from the geostrophic wind vg. 24Dienstag, 19. April 2011
  25. 25. WIND ENERGY METEOROLOGY LOGARITHMIC WIND PROFILE logarithmic wind profile in logarithmic (left) and linear (right) height scale u(z) = u*/k ln (z/ z0) k ≅ 0.4: von Karman constant u*= √τ/ρ: friction velocity z0: roughness length here: z0 = 0.05 m u* = 0.4 m/s 25Dienstag, 19. April 2011
  26. 26. WIND ENERGY METEOROLOGY LOGARITHMIC WIND PROFILE Validity: ‣ mean values ‣ horizontally homogeneous ‣ neutral stability 26Dienstag, 19. April 2011
  27. 27. WIND ENERGY METEOROLOGY ROUGHNESS CLASSES AND ROUGHNESS LENGTH TABLE Roughnes Roughness Energy Index Landscape Type s Class Length m (per cent) 0 0.0002 100 Water surface 0.5 0.0024 73 Completely open terrain with a smooth surface, e.g.concrete runways in airports, mowed grass, etc. 1 0.03 52 Open agricultural area without fences and hedgerows and very scattered buildings. Only softly rounded hills 1.5 0.055 45 Agricultural land with some houses and 8 metre tall sheltering hedgerows with a distance of approx. 1250 metres 2 0.1 39 Agricultural land with some houses and 8 metre tall sheltering hedgerows with a distance of approx. 500 metres 2.5 0.2 31 Agricultural land with many houses, shrubs and plants, or 8 metre tall sheltering hedgerows with a distance of approx. 250 metres 3 0.4 24 Villages, small towns, agricultural land with many or tall sheltering hedgerows, forests and very rough and uneven terrain 3.5 0.8 18 Larger cities with tall buildings 4 1.6 13 Very large cities with tall buildings and skycrapers 27Dienstag, 19. April 2011
  28. 28. WIND ENERGY METEOROLOGY INFLUENCE OF ROUGHNESS ON VERTICAL PROFILE © EWEA 2002 The vertical wind gradient for different values of surface roughness (built up area; scrub vegetation; open flat land or sea surface). Note that the wind power content of the wind at the same height (30 m) varies considerably. 28Dienstag, 19. April 2011
  29. 29. WIND ENERGY METEOROLOGY INFLUENCE OF THERMAL STABILITY ON VERTICAL WIND PROFILE wind speed variation with height in the surface layer for different static stabilities, plotted on linear (left) and semi-log graph (right) Stull (2006) 29Dienstag, 19. April 2011
  30. 30. WIND ENERGY METEOROLOGY ATMOSPHERIC STABILITY AND ADIABATIC MOTION Stability regimes in dry air Dry adiabatic lapse rate: 30Dienstag, 19. April 2011
  31. 31. WIND ENERGY METEOROLOGY DRY ADIABATIC LAPSE RATE Rate of temperature decrease with For an adiabatic process, the first law of height for a parcel of dry or thermodynamics can be written as unsaturated air rising under cp dT − αdp = 0 adiabatic conditions For an atmosphere in hydrostatic equilibrium „adiabatic“: no heat transfer into or out of the parcel dp = −ρgdz When air rises (e.g., by convection) it Combining both equations (eliminate pressure): expands due to the lower pressure. As the air parcel expands, it does dT g Γd = − = = −0.98 K/100m work at the environment, but gains dz cp no heat. -> It loses internal energy and its with g: standard gravity temperature decreases. ρ: density cp: specific heat at constant pressure The rate of temperature decrease α: specific volume with height is 0.98 °C per 100 m. 31Dienstag, 19. April 2011
  32. 32. WIND ENERGY METEOROLOGY GEOSTROPHIC DRAG LAW with G: geostrophic wind speed, u*: friction velocity, k: von Karman constant, f: Coriolis parameter, z0: roughness length, and A and B: dimensionless functions of stability (for neutral conditions: A=1.8, B=4.5). Large-scale pressure differences determine the fictitious geostrophic wind, which is representative for the wind speed driving the boundary layer (under certain simplifying circumstances). The geostrophic drag law relates this wind field to the boundary layer wind. Using information about surface roughness and stability, it is then possible to calculate the wind speed near the surface. 32Dienstag, 19. April 2011