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J. W. Deardorff

Abstract

A review is presented on laboratory modeling of diffusion downwind of a continuous point source within a boundary layer of well defined height with turbulence driven by buoyant convection. Results of using mixed-layer scaling are summarized and comparisons with atmospheric field measurements discussed. Concentration probability distributions from the laboratory as a function of dimensionless downwind distance are presented in a manner which discloses the differences from a lognormal distribution.

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J. W. Deardorff

Abstract

A rate equation for soil-surface moisture fraction is developed which makes use of the more customary bulk soil moisture content, as well as the soil-surface evaporation rate minus precipitation rate. The two empirical constants involved are estimated from soil measurements of Jackson (1973). The evaporation rate relative to potential evaporation is taken as the ratio of soil-surface moisture fraction to its saturated threshold value. It is shown how the parameterization simulates the drying of the soil surface on a diurnal and longer time scale following irrigation or precipitation, and eliminates large errors of up to a factor of 5 which can be incurred by atmospheric prediction models that treat only the bulk soil moisture in the absence of foliage.

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J. W. Deardorff

Abstract

The advantages of using Betts' (1973) liquid-water potential temperature (θl ) and also a total moisture variable (qw ) within a shallow-cloud numerical model are enumerated. The saturation condition is parameterized as a function of these two variables and pressure, and the subgrid-scale buoyancy flux is expressed in terms of the subgrid-scale vertical fluxes of θl and qw .

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J. W. Deardorff

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Abstract not available.

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J. W. Deardorff

Abstract

The criterion for instability of dry air mixing into a cloud top is determined both graphically and mathematically. It is found to be identical to the buoyancy-flux instability criterion of Randall (1976) based on stratocumulus mixed-layer jump-model equations which yield a cloud top jump in θ e , for marginal stability of order Δθ e =−1 to −3 K (θ e ), is equivalent potential temperature).

Numerical calculations from a three-dimensional boundary-layer turbulence model with stratocumulus are examined from the viewpoint of cloud top entrainment instability. The entrainment rate is found to increase decisively when Δθ e , drops below the critical value. The resulting rapid entrainment is found to dry out the cloud from the bottom up, leaving the cloud-base height intact; in conjunction with the negative Δθ e value, this causes ∂θ e /∂z in the cloud layer to become negative. This in turn sets the stage for the final phase of stratocumulus breakup, whereby conditional instability of the first kind begins to operate and the cloud fraction becomes small.

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J. W. Deardorff

Abstract

No abstract available.

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J. W. Deardorff

Abstract

Anomalously large values of the Reynolds stress (downstream component) obtained from measurements analysed by Angell are explained as being associated with changes in velocity at the top of a deepening planetary boundary layer. The proposed explanation is tested both by a simple interfacial velocity-jump model, and by a detailed three-dimensional numerical model. A method of parameterizing the complicated vertical profiles of momentum flux is proposed for use within large scale, multi-level circulation models.

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J. W. Deardorff

Abstract

A numerical model for the study of three-dimensional, small-scale, horizontally homogeneous turbulence is presented for use with a two-dimensional grid in a vertical plane. The model is called pseudo three-dimensional because all quantities involving one of the horizontal dimensions are obtained by assumption during the calculations. It is applied to the problem of turbulent thermal convection between horizontal plates, with a Rayleigh number of 6.75×105, and Prandtl numbers of 0.71 and 10.

It is shown that this model allows turbulent motions to develop, whereas a two-dimensional model yields nearly steady convective rolls. The calculated heat flux is only about 5 per cent larger than experimental values, and the horizontal variances of temperature, vertical velocity and horizontal velocity are in rough agreement with observations at all levels. Terms in the vorticity and temperature variance equations are also evaluated, although experimental values are lacking for comparison.

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J. W. Deardorff

Abstract

Observations in the lower atmosphere and of laboratory convection which demonstrate the existence of upward heat flux, w′θ′¯ > 0, with vanishing or counter potential temperature gradient, ∂θ¯/∂z ≥ 0, are reviewed. Data of Telford and Warner (1964) are utilized to explain the magnitude of the counter gradient within the framework of the thermal variance equation. The diffusion or triple-correlation term, which can allow a counter-gradient flux to exist, is interpreted qualitatively.

For theoretical studies of the planetary boundary layer which employ an eddy coefficient for sensible heat, the modified definitionis suggested, with γ c ≈ 6.5 x 10-6C cm-1 in clear air.

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J. W. Deardorff

Abstract

Convection between horizontal plates maintained at two different temperatures is studied numerically for a Rayleigh number of 6.75×105 and a Prandtl number of 0.71. The two-dimensional and Boussinesq approximations are applied. The computed motion eventually takes the form of large-scale and nearly steady-state vortices which induce plumes of warm (cool) air to impinge strongly upon the cool (warm) plate. When the width is restricted by lateral, insulated walls and is equal to the height, eddies which appear in corners suppress the single large-scale vortex which forms and cause the heat transport to be about 20 per cent smaller than is observed experimentally for a region of width much greater than height. With a width twice the height, a large-scale vortex pair develops. The effect of corner eddies is then diminished, and the heat flux becomes 18 per cent larger than the experimental value. When the lateral walls at this width are replaced by cyclic boundaries, no small-scale eddies appear, and the heat flux is 34 per cent too large. The tendency for air leaving the vicinity of either plate to be concentrated into narrow plumes, with temperature anomaly diminishing with distance from the plate, allows the convective heat flux to occur in the central region in the absence of an unstable lapse rate.

The absence of aperiodic, turbulent motions in the two-dimensional model of limited width is corroborated by measurements within a “two-dimensional” convection chamber of width equal to height.

A quasi-linear model of thermal convection is found to yield a heat transport at least 55 per cent too large, and a kinetic energy 270 per cent too large, in comparison with the non-linear model. The effect of replacing the rigid-surface boundary conditions by free-surface conditions is to increase the heat transport by 190 per cent.

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