Reginald J. Hill

Models of the scalar spectrum for turbulent advection

Several models are developed for the high-wavenumber portion of the spectral transfer function of scalar quantities advected by high-Reynolds-number, locally isotropic turbulent flow. These models are applicable for arbitrary Prandtl or Schmidt number, v/D , and the resultant scalar spectra are compared with several experiments having different v/D . The ‘bump’ in the temperature spectrum of air observed over land is shown to be due to a tendency toward a viscous-convective range and the presence of this bump is consistent with experiments for large v/D . The wavenumbers defining the transition between the inertial-convective range and viscous-convective range for asymptotically large v/D (denoted k * and k 1 * for the three- and one-dimensional spectra) are determined by comparison of the models with experiments. A measurement of the transitional wavenumber k 1 * [denoted ( k 1 *) s ] is found to depend on v/D and on any filter cut-off. On the basis of the k * values it is shown that measurements of β 1 from temperature spectra in moderate Reynolds number turbulence in air ( v/D = 0·72) maybe over-estimates and that the inertial-diffusive range of temperature fluctuations in mercury ( v/D ≃ 0·02) is of very limited extent.

Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation

Recent experiments reveal the high-wave-number form of the power spectrum of temperature fluctuations in turbulent flow. It is precisely this high-wave-number portion of the temperature spectrum that strongly affects optical propagation in the atmosphere. An accurate model of the spectra of advected quantities, such as temperature, has been developed and is applied here to optical propagation. An outstanding feature of the model and the observed temperature spectrum is a “bump” at high wave numbers. The accurate model of the temperature spectrum is used to compute the temperature structure function, the variance of log intensity as a function of Fresnel-zone size, the covariance function of log amplitude, the structure function of phase, as well as the phase coherence length. These results are compared with the predictions of Tatarskii’s spectrum. The bump in the temperature spectrum produces a corresponding bump in the temperature structure function, the variance of log intensity, and the structure function of phase. The accurate model is also used to determine the shape of the structure function of aerosol concentration fluctuations; it is found that this structure function varies as the logarithm of the separation distance for small separations.

Statistics of Surface-Layer Turbulence Over Terrain with Metre-Scale Heterogeneity

Refuge has patchy vegetation in sandy soil. During midday and at night, the surface sources and sinks for heat and moisture may thus be different. Although the Sevilleta is broad and level, its metre-scale heterogeneity could therefore violate an assumption on which Monin-Obukhov similarity theory (MOST) relies. To test the applicability of MOST in such a setting, we measured the standard deviations of vertical (σw) and longitudinal velocity (σu), temperature (σt), and humidity (σq), the temperature-humidity covariance (¯tq), and the temperature skewness (St). Dividing the former five quantities by the appropriate flux scales (u*, *, and q*) yielded the nondimensional statistics σw/u*, σu/u*, σt/|t*|, σq/|q*|, and ¯tq/t*q*. σw/u*, σt/|t*|, and St have magnitudes and variations with stability similar to those reported in the literature and, thus, seem to obey MOST. Though σu/u* is often presumed not to obey MOST, our σu/u* data also agree with MOST scaling arguments. While σq/|q*| has the same dependence on stability as σt/|t*|, its magnitude is 28% larger. When we ignore ¯tq/t*q* values measured during sunrise and sunset transitions – when MOST is not expected to apply – this statistic has essentially the same magnitude and stability dependence as (σt/t*)2. In a flow that truly obeys MOST, (σt/t*)2, (σq/q*)2, and ¯tq/t*q* should all have the same functional form. That (σq/q*)2 differs from the other two suggests that the Sevilleta has an interesting surface not compatible with MOST. The sources of humidity reflect the patchiness while, despite the patchiness, the sources of heat seem uniformly distributed.

Measuring surface-layer fluxes of heat and momentum using optical scintillation

An experiment is described showing that an optical scintillation instrument gives reliable values of heat and momentum fluxes in the surface layer, subject to the usual restrictions of homogeneity and steady state. This instrument measures the turbulence inner scale and refractive-index structure parameter, which are used to obtain the fluxes from Monin-Obukhov similarity relationships. The instrument gives space-averaged values over a propagation path that can range in length from tens to hundreds of meters. The history of the use of optical propagation to estimate fluxes is reviewed.

Review of optical scintillation methods of measuring the refractive-index spectrum, inner scale and surface fluxes

Abstract The background, recent progress and future trends of remote sensing of three environmental parameters using optical scintillation are reviewed. The parameters are the refractive-index spectrum of turbulence, the inner scale of turbulence, and the surface fluxes of heat, humidity and momentum.

Refractive index of air. 2. Group index

In a previous paper [Appl. Opt. 35, 1566 (1996)] one of us presented new equations for evaluation of the phase refractive index of air over a range of wavelengths and atmospheric parameters. That paper also gave an incorrect, although sufficiently accurate, procedure for calculating the group refractive index. Here we describe the results of a more rigorous derivation of the group index that takes proper account of the Lorentz-Lorenz formula, and we demonstrate that deviations from the Lorentz-Lorenz formula are insignificant to within a foreseeable precision of dispersion measurements for atmospheric conditions. We also derive and evaluate a simplification of the resultant equation that is useful for exploratory calculations. We clarify the limits of validity of the standard equation for the group refractive index and correct some minor errors in the previous paper.

Probability distribution of irradiance for the onset of strong scintillation

We calculated the probability distribution function (PDF) from simulations for an initially spherical wave propagated through homogeneous atmospheric turbulence. The onset of strong scintillation was calculated. By onset of strong scintillation, we mean conditions of weak scintillation changing to the condition of strong focusing. In addition, one case in the saturation regime was calculated. The simulations’ PDF’s are compared with several heuristic models of the PDF and are seen to progress from close to log normal for the cases of weakest scintillation to close to the log normally modulated exponential PDF (LNME PDF) for the cases of strong scintillation. The simulations’ PDF’s are not in agreement with the K PDF for any of the calculated cases. The best agreement was obtained in comparison with Beckmann’s PDF [P. Beckmann, Probability in Communication Engineering (Harcourt, Brace, & World, 1967)]. Beckmann’s PDF varies from being the log-normal PDF for weak scintillation to being the LNME PDF for strong scintillation and progresses further to the theoretically expected exponential PDF in the limit of saturated scintillation. We recommend that simulation be used to predict the irradiance PDF for plane and diverged waves in homogeneous turbulence in preference to using heuristic models. More complicated propagation cases remain in the domain of heuristic argumentation.

Turbulence-induced millimeter-wave scintillation compared with micrometeorological measurements

Scintillations of intensity and phase difference were measured at millimeter wavelengths in a horizontally homogeneous atmospheric surface layer. Simultaneous micrometeorological and optical propagation measurements characterized the clear-air turbulence. Predicted and measured propagation statistics are in good agreement. It is shown that the phase structure function showed a rolloff at large spacings as was expected because the outer scale of the turbulence and log-intensity and phase difference are Gaussian random variables. The mutual coherence function is exp(-D/2) to great accuracy, where D is the sum of phase and log-amplitude structure functions. Estimating heat and humidity fluxes from intensity variances is shown to be valid. >

Algorithms for Obtaining Atmospheric Surface-Layer Fluxes from Scintillation Measurements

Abstract Algorithms are derived for obtaining atmospheric surface-layer fluxes of heat, humidity, and momentum from scintillation measurements. Both the three-wavelength and two-wavelength methods are examined, as is combining the two-wavelength method with other micrometeorological measurements. Corrections for the effects of strong scintillation are discussed. Deriving turbulence inner-scale and refractive structure parameters from scintillation variances is discussed, as is using these quantities to obtain the energy dissipation rate and structure parameters of temperature and humidity. Given these latter quantities, Monin–Obukhov similarity theory is applied to specific humidity and temperature (equivalently, potential temperature) to obtain the fluxes.

Inner-scale effect on irradiance variance measured for weak-to-strong atmospheric scintillation

Experimental results are described of measurements of irradiance fluctuations of laser radiation through atmospheric turbulence. Simultaneous measurements of irradiance fluctuations, inner scale, and structure parameter were made in conditions of homogeneous turbulence during a number of summer days, from very early in the morning, before sunrise, until approximately noon. During the measurements the turbulence strength varied continuously, spanning very low as well as intermediate and very high levels. We used the data collected in selected intervals, during which turbulence was stationary, to obtain plots of irradiance variance versus the structure parameter for fixed ranges of values of the inner scale. The results clearly show the effect of the inner scale. For a given value of the structure parameter larger inner scales result in larger values of irradiance variance in the regime of strong scintillation.