## Atmospheric turbulence: models and methods for engineering applications |

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Page 76

Tz( / / *„(A,(iP,ic)K2cos<p</<f)rfXrfic It) y0 y0 /-ff/2 = i*„(0) = kuf(x) (54) In the next

subsection we shall see that certain assumptions about the properties of

turbulence allow us to determine the form of these spectra over part of their wave

number ranges. 3.7.5 Consequences of

are invariant to rotation of the coordinate axes is referred to as

physical implications of

a theoretical ...

Tz( / / *„(A,(iP,ic)K2cos<p</<f)rfXrfic It) y0 y0 /-ff/2 = i*„(0) = kuf(x) (54) In the next

subsection we shall see that certain assumptions about the properties of

turbulence allow us to determine the form of these spectra over part of their wave

number ranges. 3.7.5 Consequences of

**Isotropy**A motion field in which statisticsare invariant to rotation of the coordinate axes is referred to as

**isotropic**. Thephysical implications of

**isotropy**will be discussed in Chapter 4; here we use it asa theoretical ...

Page 96

If

equal, since the variance of one component changes into that of another as the

coordinate system rotates by 90°. But in fact, the variances of the velocity

components in the atmospheric boundary layer are not equal, as we will see later

. For this reason alone, it is clear that small-scale motions in the lower

atmosphere are not

components are not ...

If

**isotropy**prevails, then the variance of the three velocity components must beequal, since the variance of one component changes into that of another as the

coordinate system rotates by 90°. But in fact, the variances of the velocity

components in the atmospheric boundary layer are not equal, as we will see later

. For this reason alone, it is clear that small-scale motions in the lower

atmosphere are not

**isotropic**. Another consequence of**isotropy**is that the velocitycomponents are not ...

Page 97

In the case of

two functions — the longitudinal and lateral correlations, or equivalently,

longitudinal and lateral spectral densities. A longitudinal correlation or spectral

density is computed from wind components in the same direction as the line

separating the two measurement points. Hence the correlation of u components

computed from observation points along the x axis is longitudinal and so is the

correlation of v ...

In the case of

**isotropy**or local**isotropy**, this set of nine functions reduces to justtwo functions — the longitudinal and lateral correlations, or equivalently,

longitudinal and lateral spectral densities. A longitudinal correlation or spectral

density is computed from wind components in the same direction as the line

separating the two measurement points. Hence the correlation of u components

computed from observation points along the x axis is longitudinal and so is the

correlation of v ...

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### Contents

PART ONE FOUNDATIONS OF TURBULENCE THEORY | 1 |

Fundamentals of Fluid Flow | 10 |

Statistical Descriptions | 33 |

Copyright | |

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### Common terms and phrases

American Meteorological Society applications approximation assume assumption atmospheric turbulence average boundary layer calculate Chapter characteristic function coefficients coherence constant convection correlation function cospectra decreases defined density function depends diffusion distribution eddy ensemble equation estimate exceedance statistics Figure fluctuations forcing frequency friction velocity Gaussian Gaussian process gradients gust heat flux height Hence horizontal increases inertial range integral isotropic Kaimal Lagrangian large-scale linear mean wind measurements mechanical turbulence Monin-Obukhov scaling motion neutral air nonlinear normal observations obtain Panofsky parameters peak planetary boundary layer probability density function properties Published with permission ratio response Richardson number roughness length Royal Meteorological Society scalars spectra spectral density spectrum stable air standard deviation strong winds structure surface layer temperature theory turbulent flow uniform terrain unstable air values variables variance velocity components vertical velocity wave number wind components wind direction wind profile wind shear wind speed