Laboratory studies of the entrainment zone of a convectively mixed layer
TL;DR: In this article, the entrainment zone of simulated atmospheric mixed layers is investigated from measurements of horizontally averaged temperature and buoyancy flux, and from visual observations of penetrating thermals using a spread laser beam.
Abstract: In laboratory experiments of simulated atmospheric mixed layers the entrainment zone is investigated from measurements of horizontally averaged temperature and buoyancy flux, and from visual observations of penetrating thermals using a spread laser beam. The region of negative buoyancy flux of entrainment is found to be confined between the outermost height reached by the few most vigorous penetrating parcels, and by the lesser height where mixed-layer fluid occupies, usually, some 90 to 95% of the total area. The height of most negative buoyancy flux of entrainment is found to agree roughly with the level at which mixed-layer fluid occupies half the area.The thickness of the entrainment zone, relative to the depth of the well-mixed layer just beneath, is found to be quite substantial (0·2 to 0·4), and apparently decreases only asymptotically with increasing ‘overall’ Richardson number, Ri*. The thickness is not well predicted by parcel theory.Extensive detrainment is found to occur within the entrainment zone, and adds to the difficulty in defining the position of the local interface between mixed-layer fluid and unmodified fluid.For typical Ri* values occurring in the atmosphere, the dimensionless entrainment rate is found to be given satisfactorily by 0·25(Ri*)−1, although an dependence cannot be ruled out by the present data. Entrainment into a neutral layer in the absence of a capping inversion is found to proceed at the expected rate.
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TL;DR: In this article, the authors review what is known about the convective process in the open ocean, in which the properties of large volumes of water are changed by intermittent, deep-reaching convection, triggered by winter storms.
Abstract: We review what is known about the convective process in the open ocean, in which the properties of large volumes of water are changed by intermittent, deep-reaching convection, triggered by winter storms. Observational, laboratory, and modeling studies reveal a fascinating and complex interplay of convective and geostrophic scales, the large-scale circulation of the ocean, and the prevailing meteorology. Two aspects make ocean convection interesting from a theoretical point of view. First, the timescales of the convective process in the ocean are sufficiently long that it may be modified by the Earth's rotation; second, the convective process is localized in space so that vertical buoyancy transfer by upright convection can give way to slantwise transfer by baroclinic instability. Moreover, the convective and geostrophic scales are not very disparate from one another. Detailed observations of the process in the Labrador, Greenland, and Mediterranean Seas are described, which were made possible by new observing technology. When interpreted in terms of underlying dynamics and theory and the context provided by laboratory and numerical experiments of rotating convection, great progress in our description and understanding of the processes at work is being made.
1,098 citations
Cites background from "Laboratory studies of the entrainme..."
...This may result in entrainment of fluid from below and a reverse buoyancy flux at the base of the convective zone [Deardorff et al., 1980]....
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TL;DR: The entrainment assumption, relating the inflow velocity to the local mean velocity of a turbulent flow, has been used successfully to describe natural phenomena over a wide range of scales as mentioned in this paper.
Abstract: The entrainment assumption, relating the inflow velocity to the local mean velocity of a turbulent flow, has been used successfully to describe natural phenomena over a wide range of scales. Its first application was to plumes rising in stably stratified surroundings, and it has been extended to inclined plumes (gravity currents) and related problems by adding the effect of buoyancy forces, which inhibit mixing across a density interface. More recently, the influence of viscosity differences between a turbulent flow and its surroundings has been studied. This paper surveys the background theory and the laboratory experiments that have been used to understand and quantify each of these phenomena, and discusses their applications in the atmosphere, the ocean and various geological contexts.
784 citations
TL;DR: In this paper, the authors compared the TM model and the K-profile model of the planetary boundary layer (PBL) and found that the TM models gave too high PBL heights in the PBL with strong shear, and too low heights for the convection-dominated PBL, which caused unrealistic heat flux profiles.
Abstract: Modifications of the widely used K-profile model of the planetary boundary layer (PBL), reported by Troen and Mahrt (TM) in 1986, are proposed and their effects examined by comparison with large eddy simulation (LES) data. The modifications involve three parts. First, the heat flux from the entrainment at the inversion layer is incorporated into the heat and momentum profiles, and it is used to predict the growth of the PBL directly. Second, profiles of the velocity scale and the Prandtl number in the PBL are proposed, in contrast to the constant values used in the TM model. Finally, non-local mixing of momentum was included. The results from the new PBL model and the original TM model are compared with LES data. The TM model was found to give too high PBL heights in the PBL with strong shear, and too low heights for the convection-dominated PBL, which causes unrealistic heat flux profiles. The new PBL model improves the predictability of the PBL height and produces profiles that are more realistic. Moreover, the new PBL model produces more realistic profiles of potential temperature and velocity. We also investigated how each of these three modifications affects the results, and found that explicit representation of the entrainment rate is the most critical.
695 citations
Cites background from "Laboratory studies of the entrainme..."
...According to Deardorff et al. (1980), the thickness of the entrainment zone, δ, can be estimated as δ/h = d1 + d2Ri−1∗ , (17) where Ri∗(= (g/T0)h)θ/w2∗) is the convective Richardson number, and d1 and d2 are constants....
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TL;DR: In this article, large-eddy simulation (LES) is used to investigate entrainment and structure of the inversion layer of a clear convectively driven planetary boundary layer (PBL) over a range of bulk Richardson numbers, Ri.
Abstract: The authors use large-eddy simulation (LES) to investigate entrainment and structure of the inversion layer of a clear convectively driven planetary boundary layer (PBL) over a range of bulk Richardson numbers, Ri. The LES code uses a nested grid technique to achieve fine resolution in all three directions in the inversion layer. Extensive flow visualization is used to examine the structure of the inversion layer and to illustrate the temporal and spatial interaction of a thermal plume and the overlying inversion. It is found that coherent structures in the convective PBL, that is, thermal plumes, are primary instigators of entrainment in the Ri range 13.6 # Ri # 43.8. At Ri 5 13.6, strong horizontal and downward velocities are generated near the inversion layer because of the plume‐interface interaction. This leads to folding of the interface and hence entrainment of warm inversion air at the plume’s edge. At Ri 5 34.5, the inversion’s strong stability prevents folding of the interface but strong horizontal and downward motions near the plume’s edge pull down pockets of warm air below the nominal inversion height. These pockets of warm air are then scoured off by turbulent motions and entrained into the PBL. The structure of the inversion interface from LES is in good visual agreement with lidar measurements in the PBL obtained during the Lidars in Flat Terrain field experiment. A quadrant analysis of the buoyancy flux shows that net entrainment flux (or average minimum buoyancy flux wu min) is identified with quadrant IV w2u1 , 0 motions, that is, warm air moving downward. Plumes generate both large negative quadrant II w1u2 , 0 and positive quadrant III w2u2 . 0 buoyancy fluxes that tend to cancel. The maximum vertical gradient in potential temperature at every (x, y) grid point is used to define a local PBL height, zi(x, y). A statistical analysis of zi shows that skewness of zi depends on the inversion strength. Spectra of zi exhibit a sensitivity to grid resolution. The normalized entrainment rate we/w * , where we and w * are entrainment and convective velocities, varies as ARi21 with A 0.2 in the range 13.6 # Ri # 43.8 and is in good agreement with convection tank measurements. For a clear convective PBL, the authors found that the finite thickness of the inversion layer needs to be considered in an entrainment rate parameterization derived from a jump condition.
378 citations
Cites background or methods or result from "Laboratory studies of the entrainme..."
...For Ri values typical of the atmosphere Deardorff et al. (1980) found the dimensionless entrainment rate to vary as w Ae 5 , (3) w Ri* where we is the entrainment velocity and A is a parameter in the range 0.1 , A , 0.2....
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...This definition of the PBL height was introduced by Deardorff et al. (1980) and is often used in LES....
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...Comparison of entrainment rate vs Ri21 from current LES calculations and convection tank measurements (Deardorff et al. 1980)....
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...The thermally driven convection tank simulations of Deardorff et al. (1980), obtained at larger Reynolds number, are a closer analog to PBL turbulence....
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...6 and 7 are remarkably similar to the flow visualization pictures taken by Deardorff et al. (1980) in a convection tank using a dye tracer....
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TL;DR: This work presents methods suited for precise determination of the ABL structure's temporal evolution in a dynamic environment as complex as the Paris area and compares commonly used methods that permit ABL height retrievals from backscatter lidar signals under different meteorological conditions.
Abstract: The Paris area is strongly urbanized and is exposed to atmospheric
pollution events. To understand the chemical and physical processes
that are taking place in this area it is necessary to describe
correctly the atmospheric boundary-layer (ABL) dynamics and the ABL
height evolution. During the winter of 1994–1995, within the
framework of the Etude de la Couche Limite Atmospherique en
Agglomeration Parisienne (ECLAP) experiment, the vertical
structure of the ABL over Paris and its immediate suburbs was
extensively documented by means of lidar measurements. We present
methods suited for precise determination of the ABL structure’s
temporal evolution in a dynamic environment as complex as the Paris
area. The purpose is to identify a method that can be used on a
large set of lidar data. We compare commonly used methods that
permit ABL height retrievals from backscatter lidar signals under
different meteorological conditions. Incorrect tracking of the ABL
depth’s diurnal cycle caused by limitations in the methods is
analyzed. The study uses four days of the ECLAP experiment
characterized by different meteorological and synoptic
conditions.
327 citations
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TL;DR: In this article, a three-dimensional model using 64000 grid points within a volume 5 km on a side and 2 km deep was used to study the heated boundary layer for DAY 33 of the Wangara data of southeast Australia.
Abstract: The heated boundary layer for DAY 33 of the Wangara data of southeast Australia (Clarke et al., 1971) is studied numerically with a three-dimensional model using 64000 grid points within a volume 5 km on a side and 2 km deep. Subgrid-scale transport equations were utilized in place of eddy-coefficient formulations. The rate of growth of the mixed layer is examined and parameterized, and the vertical profiles of heat flux, moisture flux and momentum fluxes are examined. The momentum boundary layer is found to coincide essentially with the mixed layer, and to grow with the latter during the hours of solar heating of the surface.
573 citations
TL;DR: In this article, a constant stress is applied to the surface of an initially quiescent tank of fluid with a uniform density gradient, and the development of the turbulent layer by entrainment of the underlying fluid is described.
Abstract: An experiment is described in which a constant stress is applied to the surface of an initially quiescent tank of fluid with a uniform density gradient. The development of the turbulent layer by entrainment of the underlying fluid is described and it is found that the entrainment coefficient E, the ratio of the entrainment velocity ue to the friction velocity u* is given in terms of the depth D of the mixed layer and the density jump δρ across the entrainment interface by the relation
\[
E = \frac{u_e}{U_{*}} = 2.5\frac{\rho_0u^2_{*}}{g\delta\rho D}.
\]
The rate of increase of potential energy of the stratified fluid was found to be proportional to the rate of dissipation of kinetic energy per unit area in the turbulent layer. The form of these results is consistent with those found by Turner with an agitation tank, but the parameters used here allow direct application to entrainment in the ocean.
479 citations
TL;DR: In this paper, the authors discussed the thermodynamic transport of heat, liquid water and (briefly) water vapour by non-precipitating cumulus convection.
Abstract: This paper discusses the thermodynamic transports of heat, liquid water and (briefly) water vapour by non-precipitating cumulus convection. It is shown that because of the irreversible mixing between cloud and environment, there is a downward transport of enthalphy in the cumulus layer. A lapse-rate adjustment model relates stratification to the life-cycle of a model cloud parcel. A sub-cloud layer model specifies the lower boundary of the lapse-rate model, and the convective transports through cloud-base. Budget equations together with the lapse-rate model, and its time dependent boundary conditions, predict the time development of the cumulus layer, and show the dependence on large-scale mean vertical motion, cloud-base variations, and the surface sensible heat flux.
452 citations
TL;DR: In this paper, a laboratory model of the unstable planetary boundary layer is presented and compared with atmospheric observations, showing that good agreement exists between the model measurements and the atmospheric observations when the variables are appropriately scaled with the depth of the mixed layer zi, and the convective velocity and temperature scales w* and T *.
Abstract: Experimental details of a laboratory model of the unstable planetary boundary layer are given. Measurements of vertical profiles of mean temperature and heat flux, and of velocity and temperature fluctuations are presented and compared with atmospheric observations. Good agreement exists between the model measurements and the atmospheric observations when the variables are appropriately scaled with the depth of the mixed layer zi, and the convective velocity and temperature scales w* and T*. Turbulence kinetic energy budgets for the mixed layer turbulence are presented. The buoyant energy production decreases nearly linearly with height, while the rate of dissipation of kinetic energy is found to be about constant with height. Horizontal temperature spectra at three heights are presented. The temperature spectrum for a height neat the middle of the mixed layer suggests the existence of an inertial subrange as well as a viscous-convective subrange. The temperature spectrum calculated from horizont...
392 citations
TL;DR: In this article, the rate of mixing across a density interface between two layers of liquid has been measured in a laboratory experiment which allows a direct comparison between heat and salinity transports over the same range of density differences.
Abstract: The rate of mixing across a density interface between two layers of liquid has been measured in a laboratory experiment which allows a direct comparison between heat and salinity transports over the same range of density differences. Low Reynolds number turbulence was produced by stirring mechanically at a fixed distance from the interface, either in one or in both layers, and the results for these two sets of experiments are also compared. The measurements cover a factor of two in stirring rate and twenty in density. Over this range of conditions the ratio of entrainment velocity to stirring velocity can be expressed as functions of an overall Richardson number Ri, and in this form the results of the one and two stirred layer experiments are indistinguishable from one another. For density differences produced by heat alone, the functional dependence is close to Ri−1 except at small values of Ri where it approaches a finite limit. For experiments with a salinity difference across the interface, the mixing rate is the same as in the heat experiments at low values of Ri, but falls progressively below this as Ri is increased, with the approximate form .An interpretation of these results has been attempted, using a dimensional analysis and qualitative mechanistic arguments about the nature of the motion. The Ri−1 dependence implies a rate of change of potential energy proportional to the rate of working by the stirrer. The decreased mixing rates for salt have been attributed to a slower rate of incorporation of an entrained element into its surroundings by diffusion, which increases the tendency for it to return to the interface and dissipate energy in wave-like motions.
305 citations