Filtered eqs And Turbulence Chp 3 Filtered eqs And Turbulence

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

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

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

First-order Turbulence Closure

The TKE eq

The Reynold’s Stress eq

Scalar turbulent covariance eqs

LES

Subgrid partial cloudiness

Fig. 3.2. Estimated probability density functions for  (left) and rv (right), superimposed on a dashed curve of the standard normal density. Data are from 28 July for a flight leg over South Park, Colorado, at a height of 50 m off the surface, starting at 1152 MDT. Averaging interval was 1000 m. [From Banta (1979).]

Fig. 3.3. Estimated probability density function for rt – rs superimposed on standard normal curve (dashed line). Data are from the same flight leg as in Fig. 3.2. [From Banta (1979).]

Fig. 3.6. Histograms of t from 3-D data at three levels inside the cloud layer. The three theoretical models have also been plotted: (a) 550 m, (b) 1000 m, and (c) 1250 m. [From Bougeault (1981a).]

Fig. 3.7. One- and two-dimensional PDFs from a flight through a stratocumulus cloud. Shown in the lower-right corner are the flight-level data. The dotted line in the qt - l panel corresponds to saturation (i.e., points above are saturated, points below are sub-saturated). [From Larson et al. (2002).]

Fig. 3.8. As in Fig.3.7 but from a flight through a field of cumulus clouds. [From Larson et al. (2002).]

Fig. 3. 9. A double-Gaussian analytic fit to the data shown in Fig. 3 Fig. 3.9. A double-Gaussian analytic fit to the data shown in Fig. 3.8. The arrow in the top-right panel denotes a delta function. [From Larson et al. (2002).]