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J. C. Wyngaard, L. J. Peltier, and S. Khanna

Abstract

The surface fluxes in the fine-mesh numerical codes used in small-scale meteorology are typically diagnosed from resolvable-scale variables through surface-exchange coefficients. This is appropriate if the aspect ratio (length/height) of the grid volume adjacent to the surface is very large, as in mesoscale models. The aspect ratio can approach unity in large-eddy simulation (LES) codes for the planetary boundary layer, however. In that limit the surface-exchange coefficients are random variables, and it is shown through analysis of surface-layer measurements and LES results that their fluctuation levels can be large.

As an alternative to surface-exchange coefficients, the authors derive conservation equations for the surface scalar and momentum fluxes in LES. Scaling relations for resolvable-scale variables in the surface layer are developed and used to simplify these equations. It is shown that, as the grid aspect ratio decreases toward unity, local time change, horizontal advection, production due to horizontal velocity convergence, and random noise terms cause the local surface-exchange coefficients to fluctuate. A simple closure of the equations is adopted, which has little effect on surface-layer structure calculated through LES with a Smagorinsky-based subgrid-scale (SGS) model. Through analysis of very high-resolution LES fields, the authors find the SGS model to be a poor representation of surface-layer physics and conclude that the surface-flux conservation equations need to be coupled with a greatly improved SGS model in the surface layer.

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J. C. Wyngaard, O. R. Cote, and Y. Izumi

Abstract

No abstract available.

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J. C. Wyngaard, S. P. S. Arya, and O. R. Coté

Abstract

It is shown that although Coriolis forces cause large production rates of stress in a convective planetary boundary layer, there is a control mechanism, involving mean wind shear which prevents stress levels from becoming large. Higher-order-closure model calculations are presented which show that the stress profiles are essentially linear, regardless of wind direction, providing the geostrophic wind shear vanishes and the wind speed jump across the capping inversion is negligible. It is shown that it will he very difficult to verify these predicted stress profiles experimentally because of averaging time problems. A simple two-layer model is developed which leads to geostrophic drag and heat transfer expressions in fairly good agreement with Wangara data.

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S. P. S. Arya and J. C. Wyngaard
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K. S. Rao, J. C. Wyngaard, and O. R. Coté

Abstract

The effects of an abrupt change of surface roughness on the mean flow and turbulence structure in the neutral surface layer are numerically investigated by a higher-order turbulence closure theory, which includes dynamical equations for Reynolds stresses and the viscous dissipation rate. The closed system of governing equations, together with the specified initial and boundary conditions, is solved by an explicit finite-difference method on a digital computer.

The numerical model predicts the distributions of mean wind, shear stress, turbulent energy and other quantities, with no a priori assumptions regarding the distributions of any of these variables in the transition region. The distributions of the nondimensional wind shear, the dissipation and mixing length scales, and the ratio of stress to turbulent kinetic energy are shown to differ significantly from their equilibrium flow variations.

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R. A. Brost, J. C. Wyngaard, and D. H. Lenschow

Abstract

This paper discusses the turbulence profiles and budgets for two days of radiation, dynamical and thermodynamical observations by the NCAR Electra in shallow marine stratocumulus off the California coast in June 1976.

The boundary layer is characterized by relatively high wind speeds (12–20 m s−1) and low liquid water contents (0.1 g kg−1); the clouds are not very convective and seem to have little influence on the turbulence budgets. In cloud, drizzle has a significant impact on the liquid water budget and occasionally even on the total water budget even though no drizzle is observed at the surface. The stresses, velocity variances, and their budgets behave as in a neutral boundary layer, sometimes with an additional peak in the cross-wind variance at the inversion due to shear production.

There is scant evidence of direct production of vertical velocity variance at cloud top due to radiative cooling or latent heat release; it is maintained principally by the pressure-scrambling terms through redistribution of the shear-produced energy. We find, however, that while the Rotta parameterization for pressure scrambling in the stress budgets works well near the surface and sometimes throughout the layer, it is unsatisfactory in the variance budgets.

Fluctuations of temperature and moisture on a scale of several hundred meters in cloud satisfy the Clausius-Clapeyron equation. When the boundary layer is well mixed in equivalent potential temperature and total water substance, the vertical turbulent fluxes of these quantities are usually almost linear. The efficiency of cloud-top radiative cooling in producing mixed-layer convection is also discussed.

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George H. Bryan, John C. Wyngaard, and J. Michael Fritsch

Abstract

The spatial resolution appropriate for the simulation of deep moist convection is addressed from a turbulence perspective. To provide a clear theoretical framework for the problem, techniques for simulating turbulent flows are reviewed, and the source of the subgrid terms in the Navier–Stokes equation is clarified.

For decades, cloud-resolving models have used large-eddy simulation (LES) techniques to parameterize the subgrid terms. A literature review suggests that the appropriateness of using traditional LES closures for this purpose has never been established. Furthermore, examination of the assumptions inherent in these closures suggests that grid spacing on the order of 100 m may be required for the performance of cloud models to be consistent with their design.

Based on these arguments, numerical simulations of squall lines were conducted with grid spacings between 1 km and 125 m. The results reveal that simulations with 1-km grid spacing do not produce equivalent squall-line structure and evolution as compared to the higher-resolution simulations. Details of the simulated squall lines that change as resolution is increased include precipitation amount, system phase speed, cloud depth, static stability values, the size of thunderstorm cells, and the organizational mode of convective overturning (e.g., upright towers versus sloped plumes). It is argued that the ability of the higher-resolution runs to become turbulent leads directly to the differences in evolution.

There appear to be no systematic trends in specific fields as resolution is increased. For example, mean vertical velocity and rainwater values increase in magnitude with increasing resolution in some environments, but decrease with increasing resolution in other environments. The statistical properties of the simulated squall lines are still not converged between the 250- and 125-m runs. Several possible explanations for the lack of convergence are offered. Nevertheless, it is clear that simulations with O(1 km) grid spacing should not be used as benchmark or control solutions for resolution sensitivity studies.

The simulations also support the contention that a minimum grid spacing of O(100 m) is required for traditional LES closures to perform appropriately for their design. Specifically, only simulations with 250- and 125-m grid spacing resolve an inertial subrange. In contrast, the 1-km simulations do not even reproduce the correct magnitude or scale of the spectral kinetic energy maximum. Furthermore, the 1-km simulations contain an unacceptably large amount of subgrid turbulence kinetic energy, and do not adequately resolve turbulent fluxes of total water.

A guide to resolution requirements for the operational and research communities is proposed. The proposal is based primarily on the intended use of the model output. Even though simulations with O(1 km) grid spacing display behavior that is unacceptable for the model design, it is argued that these simulations can still provide valuable information to operational forecasters. For the research community, O(100 m) grid spacing is recommended for most applications, because a modeling system that is well founded should be desired for most purposes.

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R. A. Brost, D. H. Lenschow, and J. C. Wyngaard

Abstract

The mean radiational, dynamical and thermodynamical structure of the marine stratocumulus-topped mixed layers of the California coast is described for two days in June 1976 using data from the NCAR Electra aircraft. We suggest that the synoptic conditions found may be typical of about half of the shallow stratocumulus-topped boundary layers that occur in this region during summer. The inversion was low near the coast and increased in height to the west, consistent with the average westward increase in sea-surface temperature. North–south inversion height change was largely due to entrainment and mean mesoscale vertical motions. Below the inversion, strong winds (12–20 m s−1 from the north) and horizontal inhomogeneities resulted in large advection terms in mean field equations. The sloping inversion often produced large vertical shears of the actual and geostrophic wind velocities across the inversion. Because of low liquid-water contents (0.1 g kg−1), temperature and water vapor could be measured in cloud with in situ instrumentation without significant errors due to wetting.

The longwave radiative extinction length was found to be relatively short; 63% of the cloud-top jump in radiation flux occurred within 40 m. Radiative heat loss was largely balanced by shear-driven entrainment. Compositing vertical gradients provided by individual aircraft ascents and descents is shown to overestimate vertical gradients at the inversion.

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D. H. Lenschow, J. C. Wyngaard, and W. T. Pennell

Abstract

Terms in the budgets of turbulence kinetic energy, temperature and humidity variances, and temperature and humidity fluxes have been evaluated for a baroclinic, convective boundary layer using data obtained from the NCAR Electra aircraft during the Air Mass Transformation Experiment (AMTEX). Although the mean temperature and momentum budgets, which were also evaluated, are strongly influenced by the horizontal temperature gradient, the second-moment budgets are little affected. The mean momentum budget is not well balanced, probably due to a combination of neglect of horizontal advection (aircraft advection measurements are shown to be statistically unreliable) and error in the surface geostrophic wind. For the most part, the measured terms in the second-moment budgets agree with previous estimates. Turbulence dissipation, however, was systematically less than that found in previous tower-based experiments. We find that over most of the mixed layer the temperature variance is maintained by turbulent transport and the temperature flux by buoyant production while, in contrast, the humidity variance and flux are maintained primarily by gradient production. Near the top of the mixed layer both temperature and humidity statistics are strongly affected by entrainment processes.

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J. C. Wyngaard, O. R. Coté, and Y. Izumi

Abstract

Equations for the conservation of Reynolds shear stress and the two components of heat flux (velocity-temperature covariance) in the homogeneous atmospheric surface layer are derived. The behavior of the production and turbulent transport (flux divergence) terms in each budget is determined directly from measurements obtained over a wide range of stability conditions during the 1968 Kansas field program of AFCRL.

The data are presented in the dimensionless form suggested by Monin-Obukhoy similarity theory, and follow universal functions quite well. The theory is extended to the “local free convection” regime which exists under very unstable conditions, and specific power law forms are predicted. Several of these are verified and values are given for the proportionality factors in the power laws.

The flux divergence terms are small, implying that in each budget the local production and destruction rates are in balance. The third moments which represent the vertical fluxes of stress and heat flux are small under stable conditions, but are large on the unstable side and indicate that turbulence transfers shear stress and heat flux upward at a velocity u *.

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