H. A. Panofsky

The characteristics of turbulent velocity components in the surface layer under convective conditions

It is proposed that the ratios of the standard deviations of the horizontal velocity components to the friction velocity in the surface layer under convective conditions depend only onzi/L wherezi is the height of the lowest inversion andL is the Monin-Obukhov length. This hypothesis is tested by using observations from several data sets over uniform surfaces and appears to fit the data well. Empirical curves are fitted to the observations which have the property that at largezi/-L, the standard deviations become proportional tow*, the convective scaling velocity.Fluctuations of vertical velocity obtained from the same experiments scale withz/L, wherez is the height above the surface, in good agreement with Monin-Obukhov theory.

Atmospheric Scales and Spectral Gaps

Abstract The kinetic energy of the atmosphere is not spread uniformly over all wavelengths but has certain preferred scales, with gaps in between. Typically atmospheric structures are either fully three dimensional with horizontal wavelengths of the order of 100 m to several kilometers, such as convection cells (including thunderstorms) and mechanically driven eddies; or they are quasi-two-dimensional with horizontal dimensions of order of thousands of km. The first group of systems derives its energy from Kelvin-Helmholtz and hydrostatic instability, which depends on vertical gradients of wind and temperature; the second group is associated with barotropic or baroclinic instability, which depends on horizontal gradients of temperature and wind. Aloft, the small-scale systems are relatively less frequent than near the ground; on the other hand, intermediate-scale systems seem to be more common.

Turbulence characteristics along several towers

Observations from several towers are used to show how measurements of wind and temperature near the surface can be used to estimate the variances of the horizontal velocity and the dissipation rate up to the top of the towers, provided the roughness length is known. The roughness length usually varies with wind direction, and the traditional methods of estimating it tend to lead to over-estimates.Analysis of cross spectra between velocity components at different levels shows that Davenports Geometrical Similarity is satisfied. Coherence falls off exponentially with the ratio of height interval to wavelength, and the ‘decay parameter’ depends on Richardson number near the surface. Coherences at different sites show no significant differences in neutral air. The lateral velocity components have larger coherence and more time delay between levels than the horizontal components at all sites.Time delay and coherence are also discussed in other Cartesian directions, and it is suggested that these quantities, having relatively simple properties, can be used as building blocks for an empirical three-dimensional model of turbulence.

Horizontal coherence of wind fluctuations

The coherence for streamwise and cross-stream wind components is studied at four meteorological sites and compared with a representative wind-tunnel experiment. The coherence is approximated by a negative exponential in terms of a non-dimensional frequency, Δf and a decay parameter, a. Theoretical guidelines are developing to aid in identifying the pertinent variables affecting the decay parameters. These theoretical discussions indicate that for longitudinal separations, both the streamwise and cross-stream decay parameters are functions of roughness; the cross-stream decay parameter is a strong function of stability while the streamwise component is not. For lateral separations, it is found that both the streamwise and cross-stream decay parameters are functions of stability.Isopleths of the decay parameter are drawn on graphs with coordinates of angle and Richardson number for both the streamwise and cross-stream decay parameters of coherence. These empirical curves give an indication of the behavior of the decay parameters of coherence for a range of stabilities given by -0.9

Lateral coherence of longitudinal wind components in strong winds

A combination of lateral coherence measurements of wind speed at five locations suggests that the ‘decay constant’ is a monotonically increasing function of the ratio of separation to height, under neutral conditions.

On characteristics of wind direction fluctuations in the surface layer

It is shown that the ratio of standard deviation of lateral velocity to the friction velocity, ΣΝ/u*, and therefore wind direction fluctuations, are sensitive to mesoscale terrain properties. Under neutral conditions, ΣΝ/u* is almost 40% larger in rolling terrain than over a horizontal surface. In the lee of a low mountain, the fluctuations may be 2.5 times as strong as over horizontal terrain. In contrast, vertical velocity fluctuations are little influenced by mesoscale terrain features.

The validity of Taylor's hypothesis in the atmospheric surface layer

Taylors hypothesis is tested over Lake Ontario and Nebraska. In both places large eddies travel more rapidly than the local wind. A simple model is proposed for this effect.A condition is suggested for Taylors hypothesis to be satisfied based on consideration of coherence.

POWER-SPECTRUM ANALYSIS OVER LARGE RANGES OF FREQUENCY

Abstract It is shown that a spectrum covering a large range of frequencies can be found by superposing estimates of spectra of means over periods of different lengths. The method is illustrated by the power spectrum of temperature at University Park, Pennsylvania, covering periods from 2 to 7300 days. The spectrum is characterized by a major peak at four days and several minor ones, the reality of which is uncertain.

A model for dispersion from area sources in convective turbulence

Abstract Vertical mixing coefficients have been computed by integrating vertically changes of concentrations of nonreactive pollutants along horizontal trajectories, during convective conditions. Mixing coefficients are obtained for three separate periods, and analyzed according to the hypothesis of convective similarity. It was found that normalized mixing coefficients could be represented as “universal” functions of the ratio of the height to the mixing depth. These functions were small at small z and large z and reach a maximum at about half the mixing depth. In fact, the K -coefficients are so large in the middle of the boundary layer, that the concentrations there are effectively independent of height. In the surface layer, the mixing coefficients agree with the hypothesis that mixing coefficients for contaminants equal mixing coefficients for momentum (eddy viscosity). The observed universal functions also agreed fairly well with predictions made by Lumley and Zeman from second-order closure theory. However, laboratory measurements indicate larger mixing coefficients. It is suggested that K -values estimated both from second-order closure theory and from Los Angeles measurements are systematically underestimated. Nevertheless, it seems likely that K -theory is useful for determining pollutant concentrations from large, continuous area sources at the ground, under convective conditions.

Two-point velocity statistics over Lake Ontario

Cross-spectra between wind speeds on several masts in Lake Ontario have been analyzed. As previously predicted, coherence over water (small intensity of turbulence) between wind speeds measured on masts lined up with the wind appears to be larger than over land, and increases with decreasing Richardson numbers. As a result, in cold air over warm water, wind speed fluctuations are well predictable from upstream measurements. For large angles between the anemometer line and wind, the difference between coherence over land and water disappears. Furthermore, there is no significant difference in vertical coherence between water and land. When the wind is parallel to the anemometer line, small ‘eddies’ travel, in agreement with Taylors hypothesis, with the local mean wind speed. Large eddies travel significantly faster. Vertical phase delay increases with increasing Richardson number.