Mean and Turbulent Parts - The Spectral Gap

• As discussed previously and shown to the right, a spectral gap separates large-scale motions from turbulent scale motions.
• Again, the spectral gap refers to those spatial and temporal scales that show little variation in wind speed. 
• In the figure to the right, the spectral gap is centered on temporal scales ranging from about 30 minutes to a few hours.
• This encompasses many mesoscale phenomena.
• Hence, you would not observe this power spectrum if studying growing cumulus clouds, for example.
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• Q:  Where does the grid spacing for many of the operational NWP models fall within Fig. 2.2?  Answer
• Q:  Based on your answer above, can the operational NWP models make a deterministic forecast of turbulence?  Answer
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Separation of Variables into Mean and Turbulent Parts

• Given an atmospheric flow situation where the large-scale flow is distinctly separated by a spectral gap from the turbulent scales, it is quite easy to isolate the large-scale motions from turbulence and therefore, study the turbulent motions.

• OK, so you are given a time series of wind speed for a period of two days.
  • If you compute the mean wind speed, U, this represents the mean wind due to the large-scale flow.
  • u' represents the flow due to turbulence, then
  • U = U + u', where U is the actual instantaneous velocity.
  • therefore, u' = U - U 
• Q:  So, in laymans terms, what is u'? Answer 
• Given a portion of your wind speed time series, you can visualize u' and U as shown in Fig. 2.3
• Q:  How often must you take wind measurements to well sample turbulent eddies ranging in size from a few cm to a couple km in scale?
• Assume a mean wind speed of 5 m/s and that the turbulence is not changing with time:

• Such a sampling frequency requires special instrumentation:
• http://www.campbellsci.com/csat3

• Since turbulence is a three-dimensional problem that is also characterized by it's thermodynamic and chemical properties, we can generally partition the following variables into their mean and turbulent parts:
  • U = U + u'
  • V = V + v'
  • W = W + w'
  • q_v = q_v +q_v'
  • q = q + q'
  • c = c + c'