Kinematic and Eddy Fluxes

• Recall from our introductory discussion that the boundary layer plays a key role in transporting quantities such as:
  • mass
  • heat
  • moisture
  • momentum
  • and pollution
• The transfer of a quantity per unit area per unit time is called a flux.
• So, we need to define and calculate:
  • mass flux
  • heat flux
  • moisture flux
  • momentum flux
  • and pollution fluxes
• To begin this process, let's first determine the units of these quantities.  So, what are the units of:
  • mass flux
  • heat flux
  • moisture flux
  • momentum flux
  • pollution flux?  
• There is another type of flux that is important in boundary layer meteorology, that is the latent heat flux
  • It is easily calculated by multiplying the heat flux by the latent heat of vaporization (L_v)
• For the momentum flux, we often work with each of the three components, i.e.,
  • flux of U momentum
  • flux of V momentum
  • flux of W momentum
• The kinematic form of these fluxes can be found be dividing them by density, r (except of the heat flux, there you divide by rC_p , where C_p is the specific heat capacitiy at constant pressure.
• Note that density is approximately constant in the boundary layer and can be approximated by the sea-level value of 1.22 kg m^-3 in many cases.

MEAN KINEMATIC FLUXES

• Again, since we are partitioning the flow into mean and turbulent parts, we can also partition fluxes into mean and turbulent parts as well.
• The mean advective fluxes fluxes are essentially the advective terms in the large-scale equations of motion you learn about in Dynamics.
• Let's practice interpreting these types of fluxes.  Physically, what is:
  1. Wq = ?  Answer
  2. Wq = ?  Answer
  3. Uq = ?   Answer
  4. WU = ? Answer
  5. OK, let's test your knowledge..., how would you write the mean horizontal advective flux for ozone?
• from a statistics point of view, these fluxes are really just covariances between the two variables.
• Q:  do you think Wq is large or small?  Explain.

EDDY FLUXES

• Similar to the above mean advective fluxes, eddies also transport heat, moisture, momentum, etc, so we can write similar terms as above for eddy fluxes:
  1. w'q' = ? Answer 
  2. w'q' = ? Answer
  3. u'q' = ?  Answer
  4. u'w'=?   Answer
• Q:  Consider only one thermal in the boundary layer.  Over a period of time what is w' for this thermal? Answer 

• Q:  So, then is w'q'  = 0? Answer
• Let's take a look at Fig. 2.12
• We noted above that Wq is close to zero, however, as seen in this diagram, w'q' is not zero, but is significantly nonzero.  
• Hence, the importance of turbulence...., it's not the mean flow that transports heat, moisture, etc. from near the surface up through the boundary layer to the free troposphere (Wq @ 0)  , this is the role of turbulence!! (w'q' is nonzero)

• Now, let's look at the vertical profile of the more important eddy fluxes:  

• Any questions about fluxes, both mean or turbulent?
• Let's now do the flux lab.