Boundary Layer Meteorology Lecture 3

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Boundary Layer Meteorology Lecture 3

• Review summation (Einstein) notation
• Introduce some Non-Dimensional Numbers
• Reynolds averaging and Reynolds Stresses
• Review chapter 2 of Garratt

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Summation (Einstein) notation
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Some Non-Dimensional Numbers

• Reynolds number Re VL/?
• Reynolds number is ratio of acceleration (or
  inertial force) to friction force. It governs
  transition to turbulence (at high Reynolds
  numbers , e.g. about 2300 for pipes highly
  variable, depending on shape of the flow!).
• For more detail, see http//physics.mercer.edu/hp
  age/friction/ajp/reynolds.html
• Richardson numbers ratio of buoyant production
  (or destruction) to shear production of
  turbulence.
• Flux Rf (g/?v)w?/(uw du/dz vw dv/dz)
• Gradient Ri (g/???d??dz)/(du/dz)2
• Bulk RiB (g/?v)z(?v-??)/(u2v2)

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Reynolds averaging and Reynolds Stresses
t1 should be enough larger than t2 so that the
average is independent of time.
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Reynolds averaging and Reynolds Stresses
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Understanding Reynolds Stress
Random fluctuations will always tend to remove
local maxima or minima, since, for a maximum they
carry with them momentum from elsewhere, which
must be smaller than the momentum at the maximum.
Similarly, they will tend to remove curvature.
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