Reflections on atmospheric boundary layers and turbulence Part I

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Reflections on atmospheric boundary layers and
turbulencePart I

• L. Mahrt
• Les Houches
• June 2008

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• Understanding turbulence in homogeneous
  stationary conditions is necessary before
  attempting to understand more common situations
  where such conditions are not met.
• Parallel investigations of more complex realistic
  conditions are necessary with the recognition
  that scientific rigor will be less. This area has
  been neglected.

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Classical definitions of turbulence

• 1. Three-dimensional vortex stretching
  (two-dimensional turbulence is not turbulence).
• 2. Random, at least on scales smaller than the
  main coherent structures.
• 3. Diffusive (in contrast to waves for example).
  
• 4. Local, not periodic

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In the previous diagram, the basis set was not
specified.

• Fourier spectra is the traditional approach,
  originally motivated by solutions to linear
  equations. However eddies are highly nonlinear
  and local and not well represented in Fourier
  space (Heisenberg, Tennekes, Leseur).
  Interpreting Fourier spectra is tenuous.
  Generally requires additional procedures to look
  nice.
• Wavelet basis sets are local, but numerous
  options
• Multiresolution satisfies Reynolds averaging, but
  basis set is discontinuous.
• Since no basis can look like all of the eddies,
  there is always scale leakage.

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The vertical flux

• The vertical flux consists of a molecular part, a
  turbulent part and a part due to larger scales
  (e.g., mesoscale).
• For turbulence studies and evaluation of
  similarity theory, include only turbulence part.
• For budget studies, require total flux.
• Limiting factors at larger scales
• Random flux error may be much larger than
  systematic part
• The weak vertical motions on the mesoscale are
  difficult to measure even though it may lead to
  large flux (large scalar fluctuations).

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Distinction between mesoscale motions and
transitional hybrid motions

• Nonlinear gravity waves transport momentum
• w decaying -gt gravity waves, vortex modes
• Regeneration/instability stage
• Roll vortices
• Inactive eddies

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Similarity theory

• Describe the flow with a limited number of
  length, time and velocity scales.
• Surface layer scaling based on the heat flux, u
  and z.

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Additional similarity arguments

• Thin boundary-layer depth
• Local advection
• Low-level wind maximum/ Downward transport of
  TKE
• Roughness sublayer variables
• Strength of the submeso scale motions/nonstationar
  ity

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The real world

• Heterogeneity simultaneously on multiple scales
• Nonstationary simultaneously on multiple time
  scales

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From warm to cold
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From warm to cold
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From warm to cold
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The impact of surface heterogeneity, footprint
theory, blending height, internal boundary layers

• Blending height, if exists, is a scaling depth
• Footprint theory most valid for near neutral
  conditions with horizontally homogeneous
  turbulence and heterogenous scalar source
• Change to smaller roughness and change to
  downward heat flux lead to poorly defined
  internal boundary layers

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Conclusions

• 1. Distinction between turbulence and larger
  scales is sometimes ambiguous particularly with
  weak turbulence Fourier space requires extra
  caution.
• 2. Even with homogenous stationary conditions,
  the near-surface roughness sublayer is not fully
  understood.
• 3. Existing framework for representing surface
  heterogeneity is useful but not applicable to
  most surfaces.