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J. C. Wyngaard

Abstract

Recent large-eddy simulations of the vertical diffusion of a passive, conservative scalar through the convective boundary layer (CBL) show strikingly different eddy diffusivity profiles in the “top-down” and “bottom-up” cases. These results indicate that for a given turbulent velocity field and associated scalar flux, the mean change in scalar mixing ratio across the CBL is several times larger if the flux originates at the top of the boundary layer (i.e., in top-down diffusion) rather than at the bottom. The large-eddy simulation (LES) data show that this asymmetry is due to a breakdown of the eddy-diffusion concept.

A simple updraft-downdraft model of the CBL reveals a physical mechanism that could cause this unexpected behavior. The large, positive skewness of the convectively driven vertical velocity gives an appreciably higher probability of downdrafts than updrafts; this excess probability of downdrafts, interacting with the time changes of the mean mixing ratio caused by the nonstationarity of the bottom-up and top-down diffusion processes, decreases the equilibrium value of mean mixing-ratio jump across the mixed layer in the bottom-up case and increases it in the top-down case. The resulting diffusion asymmetry agrees qualitatively with that found through LES.

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J. C. Wyngaard

Abstract

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J. C. Wyngaard

Abstract

We present a theory for probe-induced flow distortion which is applicable in the atmosphere at heights greater than about 10 times the obstacle size. We use the theory to calculate the behavior of Reynolds shear stress and velocity variances ahead of a cylinder and a sphere. The stress is found to be most seriously distorted, the extent depending on the nature of the trailing wake. We show that the linear form of the theory should be adequate for most surface-layer applications, and we discuss how the theory can be applied to more complex geometries. We show that the “tilt correction” approach to the problem, which has been used by some workers, is incorrect in principle since it violates vorticity conservation, and is not even a good approximation in general.

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J. C. Wyngaard

Abstract

I prove that in a steady velocity field the frequency spectrum of a conservative scalar is unaffected by flow distortion. This is a good approximation in turbulent flow if (qa 1/3;/U 1 l 1/3;) ≪ 1, where q and l are velocity and length scales of the energy-containing turbulence, a is the crosstream dimension of the body, and U 1 is the mean flow speed. Rapid-distortion theory gives the same result under more restrictive conditions. Both sets of criteria seem easily met for scalar mixing ratio measurements in typical aircraft applications but are more difficult to satisfy on towers.

At aircraft speeds, crosstalk from air density fluctuations can seriously contaminate species density signals measured in regions of strong flow distortion. These errors can be very important in aircraft measurements of the vertical fluxes of CO2 and water vapor, whose sensors typically measure species density rather than mixing ratio. These errors can be minimized through boom design.

Temperature measurements from aircraft can also be seriously affected by flow distortion; an error in the fluctuating temperature signal is generated by the exchange of kinetic energy and enthalpy during the flow distortion process. Appearing in the temperature signal as crosstalk from velocity fluctuations, the error is proportional to the amount of flow distortion and the deviation of the sensor recovery factor from 1.0.

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J. C. Wyngaard and J. L. Lumley

Abstract

Design data and experimental results are presented for an eight-pole optimally flat filter which makes available the first seven derivatives of the filtered input signal.

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L. J. Peltier and J. C. Wyngaard

Abstract

The conventional theory of the scattering of transmitted acoustic, microwave, and optical radiation by turbulence uses the refractive index structure-function parameter C N2. The authors calculate the vertical profiles of the structure function parameters on which C N2 depends, those for temperature and humility, C T2 and C Q2, and their joint structure-function parameter, C TQ, from large-eddy simulation (LES) data for convective boundary layers. The results agree well with experimental measurements.

Modern views of wave propagation through turbulence with substantial intermittency, such as that found in the high Reynolds number flows in geophysics, suggest that the structure–function parameter be interpreted as a local flow variable rather than the traditional ensemble average. Through the refined Kolmogorov–Obukhov similarity hypotheses, a set of local structure–function parameters is defined that depends on locally averaged values of the molecular destruction rates of velocity and scalar variances. Through analysis of the locally averaged variance budgets, the coupling between the resolvable-scale fields in LFS and these local destruction rates are outlined, with the focus on scalars. Using data from direct numerical simulation, we test two models of the locally averaged destruction rate of scalar variance. Each emulates its approximately lognormal statistics and can be used with LES codes, enabling predictions of local structure–function parameter fields.

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S. J. Caughey, J. C. Wyngaard, and J. C. Kaimal

Abstract

The turbulence structure observed in seven early evening runs of the 1973 Minnesota experiments is presented and discussed. Wind and temperature sensors mounted on a 32 m tower and on the tethering cable of a large balloon spanned the entire depth of the rapidly evolving nocturnal boundary layer. Spectral shapes and the vertical profiles of turbulence variances and covariances, dissipation rates for turbulent kinetic energy and temperature variance, and energy-containing range length scales show remarkable order when plotted in dimensionless coordinates, even though properties varied widely among the runs. Observed dissipation rates and boundary layer depth agree well with predictions of the Brost-Wyngaard (1978) model. It is shown that the slight (0.0014) terrain slope and possibly baroclinity affected the boundary-layer evolution, and that although the turbulence structure was probably in equilibrium with the wind and temperature fields, these were strongly evolving during the runs.

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J. C. Wyngaard and S. F. Clifford

Abstract

A theory is developed for obtaining the vertical fluxes of momentum, heat and moisture in a quasi-steady, locally-homogeneous surface layer from measurements of the structure parameters of velocity, temperature and humidity. The momentum flux is shown to be generally more sensitive to measurement errors in the structure parameters and to uncertainties in certain turbulence parameters than are the heat and moisture fluxes. The structure parameters can, in principle, be obtained from path-averaged wave propagation measurements; for example, the temperature structure parameter C T 2, is readily obtained from optical scintillations. It is estimated that in the case of C T 2 a path-averaged optical measurement requires about 1% of the averaging time of a conventional measurement of C T 2 under typical conditions.

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Martin J. Otte and John C. Wyngaard

Abstract

The structure of the interfacial layer capping the atmospheric boundary layer is not well understood. The dominant influence on turbulence within the interfacial layer is the stable stratification induced by the capping inversion. A series of 26 high-resolution large eddy simulation runs ranging from neutral, inversion-capped to free-convection cases are used to study interfacial layer turbulence. The interfacial layer is found to be similar in many aspects to a classic stable boundary layer. For example, the shapes of interfacial layer spectra and cospectra, including the locations of the spectral peaks, agree with previous observations from nocturnal PBLs. The eddy diffusivities, variances, structure-function parameters, and dissipation rates within the interfacial layer, suitably nondimensionalized using local scaling, also agree with observations from nocturnal PBLs. These results may lead to improved models of the interfacial layer and entrainment, and may also have implications for remote sensing of the interfacial layer.

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S. P. S. Arya and J. C. Wyngaard

Abstract

By using a simple physical model of the baroclinic convective planetary boundary layer, the similarity functions of the geostrophic drag law are expressed as sums of a barotropic part, dependent only on the stability and boundary layer height parameters, and a baroclinicity dependent part. The latter are predicted to he sinusoidal functions of the angle between surface wind and geostrophic shear, their amplitudes being proportional to the normalized magnitude of geostrophic shear. These drag laws are confirmed by the results of a more sophisticated higher-order closure model, which also predict the magnitude of actual wind shears in the bulk of the mixed layer remaining much smaller than the magnitude of imposed geostrophic shear. The results are shown to be supported by some observations from the recent Wangara and ATFX experiments. The surface cross-isobar angle is predicted to increase toward the equator, a trend well confirmed by observations, but in obvious conflict with the drag laws proposed by others who have ignored the height of the lowest inversion base from their similarity considerations.

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