Boundary Layer Meteorology Lecture 3 Review summation Einstein

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

Summation (Einstein) notation

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 • 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)

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

Reynolds averaging and Reynolds Stresses

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….