Dispersion due to meandering

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Dispersion due to meandering

• Dean Vickers, Larry Mahrt
• COAS, Oregon State University
• Danijel Belušic
• AMGI, Department of Geophysics, University of
  Zagreb
• dbelusic_at_irb.hr

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Overview

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

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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

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Turbulence vs. mesoscale
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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.

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Types of small mesoscale motions

1. Gravity flows (sometimes multiple flows
   superimposed)
2. Flow distortion by terrain/obstacles
3. Transient mesoscale motions (gravity waves,
   meandering)
4. Nonstationary low-level jets
5. Solitons

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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

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Effects on dispersion (1)

• To a first approximation, the variation of wind
  direction s? is inversely proportional to the
  mean wind speed

and is usually parameterized in models as
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Indeed
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Effects on dispersion (2)

• Therefore, s? (i.e. meandering) is significant
  only in weak winds
• The lateral dispersion is then

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Effects on dispersion (3)

• Now, the parameterizations actually state that
  the variability of cross-wind component sv is
  constant ? not completely true, but it is
  independent of V and stability

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Effects on dispersion (4)

• What does that actually mean?

• The dispersion due to meandering does NOT depend
  on wind speed and stability?!

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Effects on dispersion (5)

• Lets compare the two expressions

Space or time??

• In time, the dispersion due to meandering does
  NOT depend on wind speed nor stability.

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Particle model

• Lagrangian stochastic particle model
• Particle position updated as
  Xp(tdt) Xp(t) (Uu)dt
• Turbulence described by a Markov Chain Monte
  Carlo process with one step memory

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Wind field for particle models

• Observed from single mast (assume spatially
  homogeneous)
• Mesoscale model
• LES model
• Observed using a tower network (this study)

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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)

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CASES-99 network
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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!

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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

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Animations
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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

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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

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Measure of particle dispersion

• Travel time dependence of particle dispersion
  computed as
• sx2 (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
• sxy (sx2 sy2)½

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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

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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 sxy f(suvM ) 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