Showing papers on "Boundary layer published in 1981"

Convective instability of a thickened boundary layer and its relevance for the thermal evolution of continental convergent belts

Abstract: When crust thickens during crustal shortening, the underlying mantle lithosphere must shorten and thicken also, causing the submersion of cold, dense material into the surrounding asthenosphere. For a range of physical parameters the thickened boundary layer that forms the transition from the strong lithosphere to the convecting asthenosphere may become unstable, detach, and sink into the asthenosphere, to be replaced by hotter asthenospheric material. We have studied the instability of a thickened boundary layer for a range of physical parameters (Rayleigh number), amounts of thickening, and boundary conditions. In all cases the fluid was overlain by a rigid, conducting layer. Extensive numerical experiments were made for fluids with stress-free boundary conditions, heated either from below or from within. From a simple physical description of the observed pattern of flow we derived expressions that related the growth of the instability and the time needed to remove the thickened boundary layer as a function of the amount of horizontal shortening (f), the Rayleigh number (R), and the ratio (a/d) of the thicknesses of the rigid and fluid layers. In our opinion, observations and theory agree well (within 10% for R > 105) and show that the speed with which the thickened boundary layer is removed increases with increasing f, R, and a/d. A limited series of runs with no-slip boundary conditions suggests approximately the same functional relationships but with the process 0–30% slower than with stress-free boundaries. For Rayleigh numbers comparable to those appropriate for upper mantle convection (105–107) the removal of the boundary layer occurs rapidly, in times less than the thermal time constant of the overlying rigid plate. Using typical values for the physical parameters in the earth, the boundary layer is removed in times less than the duration of deformation in some collision zones (30–50 m.y.). Thus we suspect that often the lower lithosphere is removed during the process of crustal shortening, causing the overlying crust and uppermost mantle to warm rapidly. This process is likely to contribute to the development of regional metamorphism and to the generation of latetectonic or posttectonic granites. We suspect, in fact, that in some cases the entire mantle lithosphere may detach from the lower crust during crustal shortening, exposing the crust to asthenospheric temperatures.

New aspects of turbulent boundary-layer structure

Abstract: Flow visualization studies of the zero-pressure-gradient turbulent boundary layer over the Reynolds-number range 500 2000, say) the layer appears to consist very largely of elongated hairpin vortices or vortex pairs, originating in the wall region and extending through a large part of the boundary-layer thickness or beyond it; they are for the most part inclined to the wall at a characteristic angle in the region of 40–50°. Large-scale features, which exhibit a slow overturning motion, appear to consist mainly of random arrays of such hairpin vortices, although there is some evidence of more systematic structures.At low Reynolds numbers (Reθ < 800, say) the hairpin vortices are very much less elongated and are better described as horseshoe vortices or vortex loops; large-scale features now consist simply of isolated vortex loops (at the very lowest Reynolds numbers), or of several such loops interacting strongly, and show a relatively brisk rate of rotation.

Organized Motion in Turbulent Flow

Abstract: A review of organized motion in turbulent flow indicates that the transport properties of most shear flows are dominated by large-scale vortex nonrandom motions. The mean velocity profile of a turbulent boundary layer consists of a viscous sublayer, buffer layer, and a logarithmic outer layer; an empirical formula of Coles (1956) applies to various pressure gradients. The boundary layer coherent structure was isolated by the correlation methods of Townsend (1956) and flow visualization by direct observations of complex unsteady turbulent motions. The near-wall studies of Willmart and Wooldridge (1962) used the space-time correlation for pressure fluctuations at the wall under a thick turbulent boundary layer; finally, organized motion in free shear flows and transition-control of mixing demonstrated that the Reynolds number invariance of turbulence shows wide scatter.

A simple global model of plate dynamics and mantle convection

Abstract: Cooling and thickening of lithospheric plates with age and subduction result in large-scale horizontal density contrasts tending to drive plate motions and mantle flow. We quantify the driving forces associated with these density contrasts to determine if they can drive the observed plate motions. First, two-dimensional models are computed to evaluate the effects of assumed rheologies and boundary conditions. We are unable to obtain platelike behavior in viscous models with traction-free boundary conditions. The piecewise uniform velocities distinctive of plate motion can be imposed as boundary conditions and the dynamic consistency of the models evaluated by determining if the net force on each vanishes. If the lithosphere has a Newtonian viscous rheology, the net force on any plate is a strong function of the effective grid spacing used, leading to ambiguities in interpretation. Incorporating a rigid-plastic lithosphere, which fails at a critical yield stress, into the otherwise viscous model removes these ambiguities. The model is extended to the actual three-dimensional (spherical) plate geometry. The observed velocities of rigid-plastic plates are matched to the solution of the viscous Stokes equation at the lithosphere-asthenosphere boundary. Body forces from the seismically observed slabs, from the thickening of the lithosphere obtained from the actual lithospheric ages, and from the differences in structure between continents and oceans are included. Interior density contrasts such as those resulting from upwellings from a hot bottom boundary layer are assumed to occur on a scale small compared to plate dimensions and are not included. The driving forces from the density contrasts within the plates are calculated and compared to resisting forces resulting from viscous drag computed from the three-dimensional global return flow and resistance to deformation at converging boundaries; the rms residual torque is ∼30% of the driving torque. The density contrasts within the plates themselves can reasonably account for plate motions. Body forces from convection in the interior may provide only a small net force on the plates. At converging boundaries the lithosphere has a yield stress of ∼100 bars; drag at the base of the plates is ∼5 bars and resists plate motion. The net driving forces from subducting slabs and collisional resistance are localized and approximately balance. Driving forces from lithospheric thickening are distributed over the areas of the plates, as is viscous drag. The approximate balance of these two forces predicts plate velocities uncorrelated with plate area, as observed. The model represents a specific case of boundary layer convection; the dynamical results are consistent with either upper mantle or mantle-wide convection.

Experiments in nearly homogenous turbulent shear flow with a uniform mean temperature gradient. Part 1

Abstract: A reasonably uniform mean temperature gradient has been superimposed upon a nearly homogeneous turbulent shear flow in a wind tunnel. The overheat is small enough to have negligible effect on the turbulence. Away from the wind-tunnel entrance, the transverse statistical homogeneity is good and the temperature fluctuations and their integral scales grow monotonically like the corresponding velocity fluctuations (Harris, Graham & Corrsin 1977). Measurements of several moments, one- and two-point correlation functions, spectra, integral scales, microscales, probability densities, and joint probability densities of the turbulent velocities, temperature fluctuations, and temperature-velocity products are reported. The heat-transport characteristics are much like those of momentum transport, with the turbulent Prandtl number nearly 1. The temperature fluctuation is better correlated with the streamwise than the transverse velocity component, and the cross-component D12 of the turbulent diffusivity tensor has sign opposite to and about twice the magnitude of the diagonal component D22. Some resemblance of directional properties (relative magnitudes of correlation functions, integral scales, microscales) of the temperature with those of the streamwise velocity is also observed. Comparisons of the present data with measurements in the inner part of a heated boundary layer and a fully turbulent pipe flow (x2/d = 0·25) show comparable magnitudes of temperature-velocity correlation coefficients, turbulent Prandtl numbers and ratios of turbulent diffusivities, and show similar shapes of two-point correlation functions.

Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers

Abstract: Quadrant analysis has been used to investigate the events contributing to the Reynolds shear stress in zero-pressure-gradient turbulent boundary layers over regularly arrayed rough surfaces of several different densities, and over a smooth surface. By partitioning the stress into ejections, sweeps, and inward and outward interactions, it is shown that sweeps account for most of the stress close to rough surfaces, and that the relative magnitude of the sweep component increases both with surface roughness and with proximity to the surface. The sweep-dominated region delineates a ‘roughness sublayer’ with a depth of up to several roughness element heights, in which the turbulence characteristics depend explicitly on the roughness. In the remainder of the inner (or constant-stress) layer, and in the outer layer, the flow obeys familiar similarity laws with respect to surface roughness.The difference ΔS0 between the fractional contributions of sweeps and ejections to the stress is shown to be well related everywhere to the third moments of the streamwise and normal velocity fluctuations. Experimental proportionalities are established between the third moments and δS0, and are shown to agree with predictions made from cumulant-discard theory.The time scale for the passage of large coherent structures past a fixed point, T, is assumed proportional to the mean time between occurrences in a specified quadrant of an instantaneous stress u'w’ at least H times the local mean stress u'w’, where H is a threshold level. For both the ejection and sweep quadrants and for any choice of H, it is found that T scales with the friction velocity u* and the boundary-layer thickness δ, such that Tu*/δ is invariant with change of surface roughness.

Structure of the low‐latitude boundary layer

Abstract: Observations at high temporal resolution of the frontside magnetopause and plasma boundary layer, made with the LASL/MPE fast plasma analyzer onboard the ISEE 1 and 2 spacecraft, revealed a complex quasiperiodic structure of some of the observed boundary layers. A cool tailward streaming boundary layer plasma was seen intermittently, with intervening periods of hot tenuous plasma which has properties similar to the magnetospheric population. While individual encounters with the boundary layer plasma last only a few minutes, the total observation time may extend over one hour or more.

Turbulent boundary layer at low Reynolds number

Abstract: The results of an experimental investigation of a turbulent boundary layer with zero‐pressure gradient directed toward extending the data base at low Reynolds numbers are presented. The data obtained are concerned primarily with mean‐velocity distributions, skin‐friction coefficients, and distributions of intensity of the longitudinal‐component of the turbulent‐velocity fluctuations for Reynolds numbers based on momentum thickness as low as 465. The validity, at low Reynolds numbers, of the semi‐empirical laws characterizing the inner and outer regions of the boundary layer is examined.

Wave-induced responses in a fluid-filled poro-elastic solid with a free surface : A boundary layer theory

Abstract: Summary. Wave-induced stress in a porous elastic medium is studied on the basis of Biot's linearized theory which is a special case of the mixture theory. For sufficiently high frequencies which are pertinent to ocean waves and seismic waves, a boundary layer of Stokes' type is shown to exist near the free surface of the solid. Outside the boundary layer, fluid and the solid skeleton move together according to the laws of classical elasticity for a single phase. This division simplifies the analysis of the equations governing the two phases; and several examples of potential interest to geophysics and foundation mechanics are treated analytically.

The structure of a separating turbulent boundary layer. Part 1. Mean flow and Reynolds stresses

Abstract: The problem of turbulent-boundary-layer separation due to an adverse pressure gradient is an old but still important problem in many fluid flow devices. Until recent years little quantitative experimental information was available on the flow structure downstream of separation because of the lack of proper instrumentation. The directionally sensitive laser anemometer provides the ability to measure the instantaneous flow direction and magnitude accurately. The experimental results described here are concerned with a nominally two-dimensional, separating turbulent boundary layer for an airfoil-type flow in which the flow was accelerated and then decelerated until separation. Upstream of separation single and cross-wire hot-wire anemometer measurements are also presented. Measurements in the separated zone with a directionally sensitive laser-anemometer system were obtained for U, V , $\overline{u^2}, \overline{v^2}, - \overline{uv}$ , the fraction of time that the flow moves downstream, and the fraction of time that the flow moves away from the wall. In addition to confirming the earlier conclusions of Simpson, Strickland & Barr (1977) regarding a separating airfoil-type turbulent boundary layer, much new information about the separated region has been gathered. (1) The backflow mean velocity profile scales on the maximum negative mean velocity U N and its distance from the wall N . A U + vs. y + law-of-the-wall velocity profile is not consistent with this result. (2) The turbulent velocities are comparable with the mean velocity in the backflow, although low turbulent shearing stresses are present. (3) Mixing length and eddy viscosity models are physically meaningless in the backflow and have reduced values in the outer region of the separated flow. Downstream of fully developed separation, the mean backflow appears to be divided into three layers: a viscous layer nearest the wall that is dominated by the turbulent flow unsteadiness but with little Reynolds shearing stress effects; a rather flat intermediate layer that seems to act as an overlap region between the viscous wall and outer regions; and the outer backflow region that is really part of the large-scaled outer region flow. The Reynolds shearing stress must be modelled by relating it to the turbulence structure and not to local mean velocity gradients. The mean velocities in the backflow are the results of time averaging the large turbulent fluctuations and are not related to the source of the turbulence.

Diurnal Boundary-Layer Development over Sloping Terrain

Abstract: A one-dimensional prognostic model of the atmospheric boundary layer coupled to a surface energy budget is described which utilizes a profile formulation (non-local) for exchange coefficients in the daytime convective boundary layer and an exchange coefficient scheme based on local Richardson number for the stable nocturnal boundary layer. This combined local and non-local model is used to simulate the full diurnal cycle of the boundary-layer behavior of days 33–34 of the Wangara experiment. Results of the simulation indicate that these simplified exchange coefficient schemes simulate the mean features of the boundary layer as well as the more complex and computationally expensive higher order closure models. This diurnal boundary-layer formulation is incorporated into a two-dimensional mesoscale model employing a terrain-following coordinate system to examine boundary-layer behavior over sloping terrain similar to that of the Great Plains of the United States. Particular emphasis is placed on th...

Propagating substorm injection fronts

Abstract: It is argued that a series of two-satellite observations leads to a clarification of substorm plasma injection, in which boundary motion plays a major role. Emphasis is put on a type of event characterized by abrupt, dispersionless changes in electron intensity and a coincident perturbation that consists of both a field magnitude increase and a small rotation toward more dipolar orientation. Comparing plasma observations at two points, it is found that in active, preinjection conditions the two most important features of the plasma sheet are: (1) the low-energy convection boundary for near-zero energy particles, determined by the magnitude of the large-scale convection electric field; and (2) the precipitation-flow boundary layer between the hot plasma sheet and the atmospherically contaminated inner plasma sheet.

On the growth of turbulent regions in laminar boundary layers

Abstract: Turbulent spots evolving in a laminar boundary layer on a nominally zero pressure gradient flat plate are investigated. The plate is towed through an 18 m water channel, using a carriage that rides on a continuously replenished oil film giving a vibrationless tow. Turbulent spots are initiated using a solenoid valve that ejects a small amount of fluid through a minute hole on the working surface. A novel visualization technique that utilizes fluorescent dye excited by a sheet of laser light is employed. Some new aspects of the growth and entrainment of turbulent spots, especially with regard to lateral growth, are inferred from the present experiments. To supplement the information on lateral spreading, a turbulent wedge created by placing a roughness element in the laminar boundary layer is also studied both visually and with probe measurements. The present results show that, in addition to entrainment, another mechanism is needed to explain the lateral growth characteristics of a turbulent region in a laminar boundary layer. This mechanism, termed growth by destabilization, appears to be a result of the turbulence destabilizing the unstable laminar boundary layer in its vicinity. To further understand the growth mechanisms, the turbulence in the spot is modulated using drag-reducing additives and salinity stratification.

Air flow over a two-dimensional hill: studies of velocity speed-up, roughness effects and turbulence

Abstract: Wind tunnel measurements have been made of the streamwise mean and turbulent velocities over a rough, bell-shaped, two-dimensional hill, with height h and maximum slope 0.26, placed in a neutrally stable boundary layer of thickness 10 h and roughness length zo = 0.02 h. Close agreement is found between the mean velocity and predictions obtained from Taylor's (1977) computational model and Jackson and Hunt's (1975) analytical linearized model, for locations at or upwind of the hill top but not in the wake. Examination of the models shows that the shear stresses are only important in an inner region close to the hill surface, so that, as suggested by Jackson and Hunt (1975), the perturbation to the mean flow outside this region is essentially inviscid. the theory shows that over very rough surfaces, such as wooded or urban terrain, the height of this inner region can be of the same order as the height of the roughness elements (so that in our experiments no measurements could be made in this region). In a second experiment flow over a smooth hill on a rough surface was studied. the additional increase of wind speed over the hill top can be estimated by assuming a linear superposition of the velocity changes produced by the changes in elevation and in surface roughness (in this case rough to smooth). In the lee of a hill, however, the change in roughness significantly alters the flow with flow separation being suppressed and here a linear superposition is not appropriate. Finally we consider why observed changes in turbulence structure close to the surface differ from those well above the surface. Calculations of these changes based on the simple theoretical arguments of equilibrium shear layers and rapidly distorted turbulent flows agree well with turbulence measurements in wind tunnels and in the field.

Instability and transition in rotating disk flow

Abstract: The stability of three dimensional rotating disk flow and the effects of Coriolis forces and streamline curvature were investigated It was shown that this analysis gives better growth rates than Orr-Sommerfeld equation Results support the numerical prediction that the number of stationary vortices varies directly with the Reynolds number

Turbulence structure of a reattaching mixing layer

Abstract: Hot-wire measurements of second- and third-order mean products of velocity fluctuations have been made in the flow behind a backward-facing step with a thin, laminar boundary layer at the top of the step. Measurements extend to a distance of about 12 step heights downstream of the step, and include parts of the recirculating-flow region: approximate limits of validity of hot-wire results are given. The Reynolds number based on step height is about 105, the mixing layer being fully turbulent (fully three-dimensional eddies) well before reattachment, and fairly close to self-preservation in contrast to the results of some previous workers. Rapid changes in turbulence quantities occur in the reattachment region: Reynolds shear stress and triple products decrease spectacularly, mainly because of the confinement of the large eddies by the solid surface. The terms in the turbulent energy and shear stress balances also change rapidly but are still far from the self-preserving boundary-layer state even at the end of the measurement region.

New, quasi-simultaneous method to calculate interacting boundary layers

Abstract: A quasi-simultan eous method is described to calculate laminar, incompressible boundary layers interacting with an inviscid outer flow. The essential feature of this method is an interactive boundary condition prescribing a linear combination of pressure and displacement thickness which models the behavior of the outer flow. This way the quasi-simultaneous method avoids difficulties incurred when either direct or inverse methods are used, resulting in fast convergence of the iterative procedure involved. The method is consistent with the asymptotic triple-deck theory. Results will be presented for two problems which exhibit strong interaction between the viscous and inviscid regions: a boundary layer with a separation bubble, and the flow near the trailing edge of a flat plate. fj Nomenclature cf = skin friction coefficient, cf-Re h = mesh size in x direction H = thickness of computational boundary-layer domain L = characteristic length M,N = number of grid points in y and x direction, respectively p = pressure RJ = remainder term in discrete interaction law Re = Reynolds number , Re = U0L I v u = component of flow velocity parallel to surface Ue>ue0 = value of u at edge of boundary layer with and

Steady flow in a channel or tube with an accelerating surface velocity. An exact solution to the Navier—Stokes equations with reverse flow

Abstract: An exact solution to the Navier–Stokes equations for the flow in a channel or tube with an accelerating surface velocity is presented. By means of a similarity transformation the equations of motion are reduced to a single ordinary differential equation for the similarity function which is solved numerically. For the two-dimensional flow in a channel, a single solution is found to exist when the Reynolds number R is less than 310. When R exceeds 310, two additional solutions appear and form a closed branch connecting two different asymptotic states at infinite R. The large R structure of the solutions consists of an inviscid fluid core plus an O(R−1) thin boundary layer adjacent to the moving wall. Matched-asymptotic-expansion techniques are used to construct asymptotic series that are consistent with each of the numerical solutions.For the axisymmetric non-swirling flow in a tube, however, the situation is quite different. For R [Lt ] 10[sdot ]25, two solutions exist which form a closed branch. Beyond 10[sdot ]25, no similarity solutions exist within the range 10[sdot ]25 0. These solutions, however, do not evolve from the R = 0 state nor do they bifurcate from the non-swirling solutions at any finite value of R.

Lagrangian and Eulerian Time-Scale Relations in the Daytime Boundary Layer

Abstract: Lagrangian (neutral balloon) and Eulerian (tower and aircraft) turbulence observations were made in the daytime mixed layer near Boulder, Colorado. Average sampling time was ∼25 min. Average Lagrangian time scale is ∼70 s and average ratio of Lagrangian to Eulerian time scales (β = TL/TE) is about 1.7. The ratio β is inversely proportional to turbulence intensity i. These data support the formula β = 0.7/i. Lagrangian time scale for the vertical component of turbulence at heights above ∼100 m is given by the formula TL = 0.17zi/σμ where zi is mixing depth. This formula is valid for the horizontal components of turbulence at all heights in the mixed layer. Lagrangian spectra in the inertial subrange are best represented by the formula Fr(n) = 0.2ϵn−2.

New, quasi-simultaneous method to calculate interacting boundary layers

Abstract: A quasi-simultan eous method is described to calculate laminar, incompressible boundary layers interacting with an inviscid outer flow. The essential feature of this method is an interactive boundary condition prescribing a linear combination of pressure and displacement thickness which models the behavior of the outer flow. This way the quasi-simultaneous method avoids difficulties incurred when either direct or inverse methods are used, resulting in fast convergence of the iterative procedure involved. The method is consistent with the asymptotic triple-deck theory. Results will be presented for two problems which exhibit strong interaction between the viscous and inviscid regions: a boundary layer with a separation bubble, and the flow near the trailing edge of a flat plate. fj Nomenclature cf = skin friction coefficient, cf-Re h = mesh size in x direction H = thickness of computational boundary-layer domain L = characteristic length M,N = number of grid points in y and x direction, respectively p = pressure RJ = remainder term in discrete interaction law Re = Reynolds number , Re = U0L I v u = component of flow velocity parallel to surface Ue>ue0 = value of u at edge of boundary layer with and

Algebraic growth of disturbances in a laminar boundary layer

Abstract: The temporal evolution of small three‐dimensional disturbances with a large streamwise scale in viscous, parallel, semi‐bounded flows is studied. In the limit of the initial disturbance being independent of the streamwise coordinate, the vertical velocity component consists solely of a continuous spectrum part. Tollmien–Schlichting waves do not appear in this special case. The streamwise perturbation velocity is obtained by solving a forced initial value problem. While the vertical velocity remains constant for small times, the streamwise perturbation velocity exhibits a linear growth due to the forcing. Eventually, viscous dissipation becomes dominant and the disturbance decays. Asymptotic solutions valid for small and large times are presented. The relation of these results to the longitudinal streaky structure found in many shear flows is discussed.

Radiative Cooling Effects within and above the Nocturnal Boundary Layer

Abstract: For representative tropospheric profiles of water vapor, CO2 and temperature we have calculated in situ longwave radiative flux divergence for use in a simplified second-order closure model of nocturnal boundary-layer evolution. The time evolution of “bulk” boundary-layer parameters is little affected by radiational cooling, as seems to be the cast for stress, velocity variance and diffusivity profiles within this layer. In contrast the w′θ′ profile adjusts itself in response to radiative flux divergence which, within the surface layer, depends on surface emissivity, surface temperature and boundary-layer humidity. Under conditions of strong radiative cooling near the surface an elevated minimum in w′θ′ (at heights up to 0.1 h, h being boundary-layer height) exists, and the cooling produces significant effects on the nondimensional, surface-layer gradients ΦH and ΦM, particularly ΦM. Thermodynamically the boundary layer develops a three-layer structure—in the lowest (0.1 h thick) and uppermost (0...

Fully developed laminar convection from a helical coil

Abstract: A general correlating equation has been developed for all Prandtl and Dean numbers. This expression was constructed by joining the theoretical Nusselt number for a straight tube, a theoretical asymptote for the regime of creeping secondary flow, a semi-theoretical expression for the boundary layer regime and an asymptotic value of Nu for the intervening regime of flow.The arbitrary coefficients and exponents in the model were evaluated using experimental and numerically computed values. Slightly differing sets of coefficients are required for uniform wall temperature and longitudinally uniform heating with uniform peripheral wall temperature. All prior theoretical results were for toroidal flow (zero pitch). A numerical solution was developed for helical flow (finite pitch). These results confirm the validity of neglecting pitch for tightly wound coils but suggest a generalization of the correlating equation for large pitch.

Stalling Pressure Rise Capability of Axial Flow Compressor Stages

Abstract: A procedure for estimating the maximum pressure rise potential of axial flow compressor stages is presented. A simplified stage average pitchline approach is employed so that the procedure can be used during a preliminary design effort before detailed radial distributions of blading geometry and fluid parameters are established. Semi-empirical correlations of low speed experimental data are presented that relate the stalling static-pressure-rise coefficient of a compressor stage to cascade passage geometry, tip clearance, bladerow axial spacing and Reynolds number. Blading aspect ratio is accounted for through its effect on normalized clearances, Reynolds number and wall boundary layer blockage. An unexpectedly strong effect of airfoil stagger and of the resulting flow coefficient of the stage’s vector triangle is observed in the experimental data. This is shown to be caused by the differing ability of different types of stage vector triangles to re-energize incoming low-momentum fluid. Use of a suitable “effective” dynamic head in the pressure rise coefficient gives a good correlation of this effect. Stalling pressure rise data from a wide range of both low speed and high speed compressor stages are shown to be in good agreement with these correlations.

Modeling the Trade-Wind Cumulus Boundary Layer. Part I: Testing the Ensemble Cloud Relations Against Numerical Data.

Abstract: The possibility of studying the cloudy planetary boundary layer through one-dimensional modeling is investigated. The various possible parameterizations of mean liquid water content and correlations, in term of the known statistical properties of the conservative variables θ1, and qw are examined in comparison with the results of a three-dimensional numerical model. The “Gaussian” cloud model is removed and a simple, skew exponential distribution is found to be most efficient for parameterizing the turbulent kinetic energy buoyancy production by latent beat release, in the case of the trade-wind cumulus layer. This distribution fits well the histograms of conservative thermodynamic variables and vertical velocity, computed from the three-dimensional data.