1. Boundary Layer Meteorology Lecture 3 Review summation (Einstein) notation Introduce some Non-Dimensional Numbers Reynolds averaging and Reynolds Stresses Review chapter 2 of Garratt

2. Summation (Einstein) notation

3. 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/hpage/friction/ajp/reynolds.html http://physics.mercer.edu/hpage/friction/ajp/reynolds.html Richardson numbers: ratio of buoyant production (or destruction) to shear production of turbulence. –Flux: Rf = (g/  v )w’  ’/(u’w’ du/dz + v’w’ dv/dz) –Gradient: Ri = (g/  d  dz)/(du/dz) 2 –Bulk: Ri B = (g/  v )z(  v -   )/(u 2 +v 2 )

4. Reynolds averaging and Reynolds Stresses t 1 should be enough larger than t 2 so that the average is independent of time.

5. Reynolds averaging and Reynolds Stresses

6. 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….