Dispersion due to meandering

1. Dispersion due to meandering Dean Vickers, Larry Mahrt COAS, Oregon State University Danijel Belušić AMGI, Department of Geophysics, University of Zagreb dbelusic@irb.hr

2. Overview • Introduction (long) • Particle model • Dispersion due to meandering • Meandering vs. turbulence

3. Meandering intro • Meandering = mesoscale wind direction variation • Usually recognized by and studied in terms of its effects on dispersion in stable weak-wind ABL • Unknown dynamics

4. Turbulence vs. mesoscale

5. Modeling transient mesoscale motions Regional models, LES models, etc. do not include the common transient mesoscale motions: Not resolved Physics missing Eliminated by explicit or implicit numerical diffusion.

6. Types of small mesoscale motions Gravity flows (sometimes multiple flows superimposed) Flow distortion by terrain/obstacles Transient mesoscale motions (gravity waves, meandering) Nonstationary low-level jets Solitons

7. Based on 14 eddy-correlation datasets, the strength of mesoscale motions are: • Not related to u*, z/L, Ri or wind speed • Can be greater in complex terrain although less in thermally generated circulations. • Different types of mesoscale motions may have quite different dispersive behavior. • NOT PREDICTABLE

9. Effects on dispersion (1) • To a first approximation, the variation of wind direction σθ is inversely proportional to the mean wind speed: and is usually parameterized in models as:

10. Indeed…

11. Effects on dispersion (2) • Therefore, σθ (i.e. meandering) is significant only in weak winds • The lateral dispersion is then:

12. Effects on dispersion (3) • Now, the parameterizations actually state that the variability of cross-wind component σv is constant  not completely true, but it is independent of V and stability

14. Effects on dispersion (4) • What does that actually mean? • The dispersion due to meandering does NOT depend on wind speed and stability?!

15. Effects on dispersion (5) • Let’s compare the two expressions: Space or time?? • In time, the dispersion due to meandering does NOT depend on wind speed nor stability.

16. Particle model • Lagrangian stochastic particle model • Particle position updated as Xp(t+dt) = Xp(t) + (U+u’)dt • Turbulence described by a Markov Chain Monte Carlo process with one step memory:

17. Wind field for particle models • Observed from single mast (assume spatially homogeneous) • Mesoscale model • LES model • Observed using a tower network (this study)

18. Observations CASES-99 • Grassland in rural Kansas in October • Seven towers inside circle of radius 300 m • 13 sonic anemometers  20-hz (u,v,w,T) • Site has weak meandering (ranked 8th out of 9 sites studied)

19. CASES-99 network

20. Wind field • High temporal resolution (no interpolation required) • Meandering wind components and the turbulence velocity variances are spatially interpolated in 3-D every time step • Meandering resolved!

21. Decomposition • Velocity variances are partitioned into meandering and turbulence based on the time scale associated with the gap region in the heat flux multiresolution cospectra • Turbulence and meandering are generated by different physics and have different influences on the plume

22. Animations

27. Case studies show • Spatial streaks and bimodal patterns in the 1-h average distribution • Double maximum patterns with higher C on the plume edges and minimum C on plume centerline • Wind direction often jumps between preferred modes rather than oscillate back and forth • Time series are highly non-stationary even when 1-h average distribution is ~ Gaussian

28. Removing record-mean flow • Particles leave the tower network domain too quickly with any significant mean wind, so the record-mean wind is removed • Removing mean wind has a huge impact on the spatial distribution, however, it has little impact on the travel-time dependence of particle dispersion (verified using particle simulator) • This allows us to look at all the records including the stronger wind speeds

29. Measure of particle dispersion • Travel time dependence of particle dispersion computed as σx2 = [(Xp(t)-[Xp(t)])2], where t is travel time and brackets denote an average over all particles • E.g., for 1-h records there are 72,000 samples of Xp for all travel times • σxy = (σx2 + σy2)½

31. The entire dataset shows • The meandering motions, not the turbulence, are primarily responsible for the horizontal dispersion, and streaks, bimodal patterns and non-stationary time series are a consequence • Meandering dominates in weak winds, strong winds, stable and unstable conditions • Tracer experiments cannot measure the travel time dependence and therefore they suggest that meandering is only important in weak winds

32. Problems • Horizontal dispersion is parameterized in terms of turbulence, while meandering dominates horizontal dispersion (and has different properties than the turbulence) • Regional models under-represent meandering motions • While σxy = f(σuvM ) works well, such a velocity scale is not available in models, nor does it appear predictable, nor is it very useful since distributions are highly non-Gaussian