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Understanding Boundary Layer Meteorology: Non-Dimensional Numbers and Reynolds Stresses

Reviewing Reynolds averaging, non-dimensional numbers, Richardson numbers, and stress computations in meteorology. Learn about Reynolds number and their impacts on flow behavior for turbulence transition. Explore concepts with relevant links and detailed explanations.

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Understanding Boundary Layer Meteorology: Non-Dimensional Numbers and Reynolds Stresses

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  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 • 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: RiB = (g/v)z(v-)/(u2+v2)

  4. Reynolds averaging and Reynolds Stresses t1 should be enough larger than t2 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….

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