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W. S. Lewellen and S. Yoh

Abstract

A new formulation of partial cloudiness parameterization has been introduced that agrees with that for a random model in one limit and approaches the simple updraft/downdraft model of larger-scale models in the limit of very highly skewed flow. Each of the conserved variables, liquid potential temperature and total humidity, along with the vertical velocity, are assumed to have probability distributions that may be parameterized as combinations of two multivariate normal distributions. This allows the skewness of the variables to be controlled by the bias between the means of the two normals and their relative fractions. It also provides a smooth transition between the normal distribution and the two limiting delta function distribution of the updraft/downdraft model. Comparisons with large-eddy-simulation data show this new model to be valid over a much wider range of conditions than the single normal distribution.

When a simple cloud-top entrainment instability (CTEI) analysis is made using the new binormal model, variations in the dynamic characteristics, here represented by the skewness in the extended liquid water function, s, are found to mask the variation with respect to the ratio in the thermodynamic jump conditions. This helps to explain the observed poor correlation of empirical cloud fraction with this jump condition. On the other hand, the analysis suggests that the ratio of the mean value of the extended liquid water variable, s, to the square root of its variance, may be expected to show a much better correlation with the empirical cloud fraction.

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D. C. Lewellen and W. S. Lewellen

Abstract

A series of large-eddy simulations have been performed to explore boundary layer entrainment under conditions of a strongly capped inversion layer with the boundary layer dynamics driven dominantly by buoyant forcing. Different conditions explored include cloud-top cooling versus surface heating, smoke clouds versus water clouds, variations in cooling height and optical depth of longwave radiation, degree of cloud-top evaporative instability, and modest wind shear. Boundary layer entrainment involves transport and mixing over a full range of length scales, as warm fluid from the region of the capping inversion is first transported into the boundary layer and then mixed throughout. While entrainment is often viewed as the small-scale process of capturing warm fluid from the inversion into the top of the boundary layer, this need not be the physics that ultimately determines the entrainment rate. In these simulations the authors find instead that the entrainment rate is often limited by the boundary layer–scale eddy transport and is therefore surprisingly insensitive to the smaller scales of mixing near the inversion. The fraction of buoyant energy production available to drive large eddies that is lost to entrainment rather than dissipation was found to be nearly constant over a wide range of simulation conditions, with no apparent fundamental difference between top- versus bottom-driven or cloudy versus clear boundary layers. In addition, it is found that for quasi-steady boundary layers with dynamics driven by cloud-top cooling there is an effective upper limit on the entrainment rate for which the boundary layer dynamics just remains coupled, which is often approached when the cloud top is evaporatively unstable.

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D. C. Lewellen and W. S. Lewellen

Abstract

An idealized model of the relationship between entrainment in cloud-topped boundary layers, circulation structure, and the degree of decoupling between the cloud and subcloud layers is developed based on simple turbulent flux distributions and the premise that the entrainment rate, both at cloud top and across cloud base when some stability exists there, is controlled by the large-eddy structure for quasi-steady buoyantly driven conditions. Layers are classified in three regimes depending on whether the cloud-top entrainment rate is ultimately limited by the transport of eddies spanning the full boundary layer (I), the cloud layer (II), or the subcloud layer (III). Algebraic relations are derived for the boundaries between, and entrainment fluxes in, each regime as a function of a convenient set of physical input parameters. The transition from regime II into III, representing the decoupling transition leading to a cumulus coupled layer, is emphasized. The model predicts that decoupling is promoted by a decrease in Bowen ratio or increase in cloud-top humidity to temperature jump ratio, and, depending on the point in parameter space, either promoted or inhibited by an increase in cloud-top radiative cooling or an increase in cloud depth. In spite of the complex cloud-layer dynamics involving cumulus plumes, a simple prediction is given for the quasi-steady cloud-top entrainment rate in regime III based on the subcloud dynamics. The model is compared with results from an extensive set of large-eddy simulations varying surface heat and moisture fluxes, cloud-top humidity and temperature jumps, and relative cloud depth. Good agreement is found with the predicted entrainment rates, the qualitative layer structure, and location of the decoupling boundary in the parameter space varied.

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D. C. Lewellen and W. S. Lewellen

Abstract

Results of large-eddy simulations of the development of young persistent ice contrails are presented, concentrating on the interactions between the aircraft wake dynamics and the ice cloud evolution over ages from a few seconds to ∼30 min. The 3D unsteady evolution of the dispersing engine exhausts, trailing vortex pair interaction and breakup, and subsequent Brunt–Väisälä oscillations of the older wake plume are modeled in detail in high-resolution simulations, coupled with a bulk microphysics model for the contrail ice development. The simulations confirm that the early wake dynamics can have a strong influence on the properties of persistent contrails even at late times. The vortex dynamics are the primary determinant of the vertical extent of the contrail (until precipitation becomes significant); and this together with the local wind shear largely determines the horizontal extent. The ice density, ice crystal number density, and a conserved exhaust tracer all develop and disperse in different fashions from each other. The total ice crystal number can be significantly reduced due to adiabatic compression resulting from the downward motion of the vortex system, even for ambient conditions that are substantially supersaturated with respect to ice. The fraction of the initial ice crystals surviving, their spatial distribution, and the ice mass distribution are all sensitive to the aircraft type, ambient humidity, assumed initial ice crystal number, and ambient turbulence conditions. There is a significant range of conditions for which a smaller transport such as a B737 produces as significant a persistent contrail as a larger transport such as a B747, even though the latter consumes almost five times as much fuel. The difficulties involved in trying to minimize persistent contrail production are discussed.

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D. C. Lewellen and W. S. Lewellen

Abstract

The modeling of the buoyancy flux in a partly cloudy atmospheric boundary layer is complicated by its dependence on the correlation between clouds and vertical velocity elements, which can vary significantly with the underlying layer dynamics (e.g., stratocumulus versus shallow cumulus). The buoyancy flux is sometimes modeled in terms of higher-order statistics, such as vertical velocity skewness or saturation variance, to try to capture some of these dynamical effects. In this work an approximate expression for the buoyancy flux is formulated solely in terms of the liquid potential temperature and total water profiles and their respective flux profiles. The predictions compare favorably with the results of an extensive set of large-eddy simulations (LES), including simulations of stratocumulus, shallow cumulus, and transitional behavior in between. This formulation is combined with previous results on the relation between cloud-top entrainment rate and circulation structure to predict the behavior of quasi-steady cumulus-coupled boundary layers as a function of a basic set of physical input parameters. These predictions also compare favorably with LES results.

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D. C. Lewellen and W. S. Lewellen

Abstract

An idealized analytical model and numerical large-eddy simulations are used to explore fluid-dynamic mechanisms by which tornadoes may be intensified near the surface relative to conditions aloft. The analytical model generalizes a simple model of Barcilon and Fiedler and Rotunno for a steady supercritical end-wall vortex to more general vortex corner flows, angular momentum distributions, and time dependence. The model illustrates the role played by the corner flow swirl ratio in determining corner flow structure and intensification; predicts an intensification of near-surface swirl velocities relative to conditions aloft of Iυ ∼ 2 for supercritical end-wall vortices in agreement with earlier analytical, numerical, and laboratory results; and suggests how larger intensification factors might be achieved in some more general corner flows. Examples of the latter are presented using large-eddy simulations. By tuning the lateral inflow boundary conditions near the surface, quasi-steady vortices exhibiting nested inner and outer corner flows and Iυ ∼ 4 are produced. More significantly, these features can be produced without fine tuning, along with an additional doubling (or more) of the intensification, in a broad class of unsteady evolutions producing a dynamic corner flow collapse. These scenarios, triggered purely by changes in the far-field near-surface flow, provide an attractive mechanism for naturally achieving an intense near-surface vortex from a much larger-scale less-intense swirling flow. It is argued that, applied on different scales, this may sometimes play a role in tornadogenesis and/or tornado variability. This phenomenon of corner flow collapse is considered further in a companion paper.

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D. C. Lewellen and W. S. Lewellen

Abstract

Results are presented from a large set of large-eddy simulations of a class of unsteady vortex evolution that may sometimes play a role in tornadogenesis or tornado variability. Beginning with a high-swirl parent vortex with an excess of low-swirl flow through the surface/corner/core region, perturbation of the low-swirl near-surface inflow at a large radius can trigger a subsequent dynamic “corner flow collapse” producing dramatic near-surface intensification relative to conditions aloft of an order of magnitude or more in velocity scale. This paper presents a more detailed treatment of the physics and simulation of corner flow collapse, expanding upon the presentation given in a companion paper treating near-surface vortex intensification more generally for both steady and unsteady conditions. The basic scaling of the onset, intensification, structure, and duration of the phenomenon is explored as a function of some of the dominant physical parameters involved. A dimensionless rate of change of the low-swirl flux through the surface/corner flow during the process is identified as a critical governing parameter. Given the mode of triggering near the surface at large radii, the large intensification that can result, and the sensitivity to some of the parameters involved, corner flow collapse may provide a mechanism by which the rear-flank downdraft can promote tornadogenesis and help explain why seemingly similar conditions sometimes produce intense tornadoes and other times do not.

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W. S. Lewellen and M. Teske

Abstract

The second-order, invariant modeling technique for turbulent flows as developed by Donaldson is applied to the atmospheric surface layer. The steady, high-Reynolds number equations reduce to a universal set when the variables are scaled by the shear stress and vertical heat flux as suggested by Monin and Obukhov. Numerical integration of these equations yields results for the mean velocity gradient, mean temperature gradient, Richardson number, rms vertical velocity and temperature fluctuations, and horizontal heat flux which agree favorably with experimental observations over the complete range of stability conditions.

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D. C. Lewellen, W. S. Lewellen, and S. Yoh

Abstract

An investigation of the influence of the ratio of surface sensible heat flux to latent heat flux, the Bowen ratio. on the structure of boundary-layer clouds is carried out utilizing numerical large eddy simulations (LES). The role of cloud-top radiational cooling, cloud-top temperature and moisture jump conditions, and wind shear are included in a secondary way. Although no detailed comparisons have been made, the LES results appear to be qualitatively consistent with the Atlantic Stratocumulus Transition Experiment, the recent field study on marine boundary-layer cloud structure. Some conclusions that follow from an examination of these LES results are the following: First, there is a highly bimodal character to the cloud ceiling frequency within a very low Bowen ratio boundary layer. The updrafts tend to produce a lower cloud ceiling than the surrounding environment with its weak downdrafts. Second, a very low Bowen ratio with the aid of some boundary-layer shear makes the development of persistent microcell cloud circulations possible within the boundary layer. Third, when the surface latent heat flux is the dominant factor in the dynamics of the boundary layer, the approach to a conditionally stable lapse rate results in the potential for subsequent decoupling. Last, the maximum partial cloud fraction is very well represented by the relation suggested by Sommeria and Deardorff for a Gaussian probability distribution for the range of conditions studied.

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J. Xia, W. S. Lewellen, and D. C. Lewellen

Abstract

Since maximum Mach numbers in an F5 tornado are expected to, at least, reach ∼0.4, a study was undertaken to determine the major potential compressibility effects in such flows. Results from compressible large-eddy simulations of tornado corner flow dynamics are summarized. Comparison with previous incompressible simulations indicates that Mach number effects tend to be modest and may be estimated by an isentropic approximation. As the average maximum Mach number M within the tornado increases above one-half, the largest changes occur for “low-swirl” corner flows, those exhibiting a central vertical jet off the surface capped by a vortex breakdown, with the vortex breakdown found to occur at significantly greater heights as M increases. It also appears that the highest Mach numbers are most likely to occur during rapid transients in near-surface intensification that can sometimes occur during a tornado's evolution.

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