Introduction to Turbulence

• Turbulence is an intrinsic part of the boundary layer - must be quantified somehow in order to study it.  How???
• The randomness of turbulence makes deterministic description impossible, for example, using the equations of motion to predict the three-dimensional winds
• Therefore, one must use statistics, to study turbulence, we are therefore, necessarily limited to average or expected values of turbulence.
• Q:  What does turbulence look like in the boundary layer with commonly used observing systems like the weather station in front of Vail Hall???
• A:  See the wind speed time series to the right-->
  • At first glance, the time series looks like an irregular, noisy mess! 
  • However, one can visually pick out a mean wind speed, which appears to be ????
  • So what creates the apparent random variations about the mean??? - turbulence.
  • Q:  When is the turbulence intensity relatively large? Answer
  • Q:  When is the turbulence intensity relatively small? Answer
  • Although the turbulence looks random, one can pick out periodic peaks in wind speed.
    • See if you can find a periodicity of 5 and 10 minutes.  Others?
  • What you are really seeing is a spectrum of turbulence, or eddy sizes (according to Taylors Hypothesis) passing by the sensor
• Q:  If there exists a dominant periodicity in the wind speed of 10 minutes, what is the spatial scale of this turbulence? Answer 
  • You can also do this for the other turbulence scales and then create a turbulence spectrum. 
  • A turbulence spectrum is given to the right --> 
• Q:  How does one physically interpret the turbulence spectrum? Answer 
• Based on the figure to the right, notice:
  • the spectral peak on the synoptic scale - this represents the "mean" flow one might observe at a weather station
  • a smaller peak with a period of about 24 hours - the diurnal cycle
  • a minimum in energy (the spectral gap) in the mesoscale!!!!!!
  • another peak on smaller, turbulence scales
  • Q:  based on the figure, which eddy sizes are more energetic and therefore, contribute more to the total turbulent kinetic energy??? Answer 
  • Q:  Do you think that the spectrum to the right is representative of all flows in the atmosphere?  Why or why not?
• Turbulence, as discussed above, is critically important for the "energy cascade" that occurs in the atmosphere
  • What does this mean????
  • Q:  How is the kinetic energy associated with synoptic-scale disturbances eventually dissipated????
  • A:  Through a cascade of energy from large to small scales. 
    • Another words, energy associated with large-scale motion eventually is transferred to the larger turbulence scales (i.e., the large eddies)
    • The large eddies then transport this energy to small-scale eddies.
    • These smaller scale eddies then transfer the energy to even small-scale eddies..., and so on
    • eventually, the energy is dissipated into heat via molecular viscosity.
  • The following poem was written by Lewis Richardson in 1922 that captures the essence of this process:
    • Big whorls have little whorls,
    • Which feed on their velocity;
    • And little whorls have lesser whorls,
    • And so on to viscosity

And who said meteorologists can't be creative!!!