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Understanding Filtered Equations and Turbulence: Why Filter Equations Matter

Explore the challenges of modeling turbulence across different scales with filtered equations. Learn about the complexities of turbulence and how filtering equations helps in analysis.

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Understanding Filtered Equations and Turbulence: Why Filter Equations Matter

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  1. Chp 3 Filtered eqs And Turbulence

  2. Why filter eqs? • The governing eqs permit motions on all scales: • Planetary scales: 1000’s of km • Cb’s: 10km • Turbulent eddies:100’s of m • Viscous eddies: 1mm A numerical model cannot cover the entire range of scales

  3. What is turbulence? • Difficult to define but you know it when you see it or feel it. • Turbulent flows have large Reynold’s numbers

  4. Fig. 3.1. Photograph of a cumulonimbus cloud showing turbulent eddies of many scales.

  5. First-order Turbulence Closure

  6. The TKE eq

  7. The Reynold’s Stress eq

  8. Scalar turbulent covariance eqs

  9. LES

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