Entraining Plume Model Research Articles

A Multiple Mass-Flux Parameterization for the Surface-Generated Convection. Part I: Dry Plumes

Abstract The present study introduces a parameterization for the mixing in the surface-generated free convection regime (including dry and moist convection cases). The parameterization explicitly represents the plumes that drive the convective turbulence. Ascending parcels that have similar properties in the surface layer are grouped into updrafts, with a determined fractional area. The updrafts ascend according to an entraining plume model, and may eventually overturn. The plume model can either use a time or a length scale for the lateral entrainment closure. The plumes' environment is assumed to be horizontally uniform. A one-dimensional framework is used to evaluate the parameterization in the case of a dry convective boundary layer (CBL). The predicted variances are underestimated (presumably due to the uniform environment assumption). The contrast between the strong upward motions and the compensating subsidence is simulated, and the skewness of w increases realistically with height. The plumes' dyn...

Episodic Mixing and Buoyancy-Sorting Representations of Shallow Convection: A Diagnostic Study

Episodic mixing and buoyancy-sorting (EMBS) models have been proposed as a physically more realistic alternative to entraining plume models of cumulus convection. Applying these models to shallow nonprecipitating clouds requires assumptions about the rate at which undilute subcloud air is eroded into the environment, an algorithm to calculate the eventual detrainment level of cloud‐environment mixtures, and the probability distribution of mixing fraction. A diagnostic approach is used to examine the sensitivity of an EMBS model to these three closure assumptions, given equilibrium convection with known large-scale forcings taken from phase III of the Barbados Oceanographic Meteorological Experiment (BOMEX). The undilute eroding rate (UER) is retrieved and found to decrease exponentially with height above cloud base, suggesting a strong modulation by the cloud size distribution. The EMBS model is also used to calculate convective transport by individual clouds of varying thickness. No single cloud from this ensemble can balance the large-scale BOMEX forcing; the observed equilibrium requires a population of clouds with a cloud size distribution that is maximum for small clouds and decreases monotonically with cloud size. The EMBS model depends sensitively on the assumptions governing the detrainment of positively buoyant mixtures. In particular, given the requirement that positively buoyant mixtures detrain at their neutral buoyancy level, there is no positive definite undilute eroding rate that is consistent with the BOMEX forcing. The model is less sensitive to the assumed distribution of cloud‐environment mixtures, given a multiple mixing treatment of positively buoyant parcels and detrainment at the unsaturated neutral buoyancy level.

Two-dimensional plumes in stratified environments

Laboratory experiments on the flow of negatively buoyant two-dimensional plumes adjacent to a wall in a density-stratified environment are described. The flow passes through several stages, from an inertial jet to a buoyant plume, to a neutrally buoyant jet, and then a negatively buoyant plume when it overshoots its equilibrium density. This fluid then ‘springs back’ and eventually occupies an intermediate range of heights. The flow is primarily characterized by the initial value of the buoyancy number, B0 = Q0N3/g′02, where Q0 is the initial volume flux per unit width, g′0 is the initial buoyancy and N is the buoyancy frequency of the environment. Scaled with the initial equilibrium depth D of the in flowing fluid, the maximum depth of penetration increases with B0, as does the width of the initial down flow, which is observed to increase very slowly with distance downward. Observations are made of the profiles of flow into and away from the plume as a function of height. Various properties of the flow are compared with predictions from the ‘standard’ two-dimensional entraining plume model, and this shows generally consistent agreement, although there are differences in magnitudes and in details. This flow constrasts with flows down gentle slopes into stratified environments, where two-way exchange of fluid occurs.

Vertical transport by convection plumes: modification by rotation

Convection, generated by destabilising buoyancy forcing, is a significant source of vertical mixing in the ocean and atmosphere. Ensembles of convective elements or plumes transport buoyancy and tracers across the convective layer. Here we examine numerical simulations of turbulent convection to identify the modifications to the vertical transports induced by strong rotation (typical of deep ocean convection). We extract the typical convection plumes from the numerical simulations using a conditional sampling compositing technique. The plume budgets of mass, heat and momentum are then compared with an entraining plume model. In the presence of strong rotation the vertical transports are significantly reduced by vigorous lateral mixing, which dilutes plume anomalies. This mixing is generated by the energetic cyclonic vortices associated with the individual plumes and the interaction between the many vortices in the plume ensemble.

Plumes in rotating convection. Part 1. Ensemble statistics and dynamical balances

Atmospheric and oceanic convection often occurs over areas occupied by many localized circulation elements known as plumes. The convective transports therefore may depend not only on the individual elements, but also on the interactions between plumes and the turbulent environment created by other plumes. However, many attempts to understand these plumes focus on individual isolated elements, and the behaviour of an ensemble is not understood. Geophysical convection may be influenced by rotation when the transit time of a convecting element is long compared to an inertial period (for example in deep oceanic convection). Much recent attention has been given to the effect of rotation on individual plumes, but the role of rotation in modifying the behaviour of an ensemble is not fully understood. Here we examine the behaviour of plumes within an ensemble, both with and without rotation, to identify the influence of rotation on ensemble plume dynamics.We identify the coherent structures (plumes) present in numerical solutions of turbulent Rayleigh–Bénard convection, a canonical example of a turbulent plume ensemble. We use a conditional sampling compositing technique to extract the typical structure in both non-rotating and rotating solutions. The dynamical balances of these composite plumes are evaluated and compared with entraining plume models. We find many differences between non-rotating and rotating plumes in their transports of mass, buoyancy and momentum. As shown in previous studies, the expansion of the turbulent plume by entrainment of exterior fluid is suppressed by strong rotation. Our most significant new result is quantification of the continuous mixing between the plume and ambient fluid which occurs at high rotation without any net changes in plume volume. This mixing is generated by the plume–plume interactions and acts to reduce the buoyancy anomaly of the plume. By contrast, in the non-rotating case, no such loss of buoyancy by mixing occurs. As a result, the total buoyancy transport by upwardly moving plumes diminishes across the layer in the rotating case, while remaining approximately constant in the non-rotating case. At high values of rotation, the net vertical acceleration is considerably reduced compared to the non-rotating case due to loss of momentum through entrainment and mixing and a decelerating pressure gradient which partially balances the buoyancy-driven acceleration of plumes. As a result of the dilution of buoyancy, the pressure-gradient deceleration and the loss of momentum due to mixing with the environment in the rotating solutions, the conversion of potential energy to kinetic energy is significantly less than that of non-rotating plumes.The combination of efficient lateral mixing and slow vertical movement by the plumes accounts for the unstable mean temperature gradient that occurs in rotating Rayleigh–Bénard convection, while the less penetrative convection found at low Rossby number is a consequence of the reduced kinetic energy transport. Within the ensemble of plumes identified by the conditional sampling algorithm, distributions of vertical velocity, buoyancy and vorticity mimic those of the volume as a whole. Plumes cover a small fraction of the total area, yet account for most of the vertical heat flux.

The Macroscopic Entrainment Processes of Simulated Cumulus Ensemble. Part II: Testing the Entraining-Plume Model

Abstract According to Part I of this paper, it seems that ignoring the contribution from descendent cloud air in a cloud model for cumulus parameterization (CMCP), such as the spectral cumulus ensemble model in the Arakawa–Schubert parameterization, is an acceptable simplification for tropical deep convection. Since each subensemble in the spectral cumulus ensemble model is formally analogous to an entraining plume, the latter is examined using the simulated data from a cloud-resolving model (CRM). The authors first follow the analysis procedure of Warner. With the data from a nonprecipitating experiment, the authors show that the entraining-plume model cannot simultaneously predict the mean liquid water profile and cloud top height of the clouds simulated by the CRM. However, the mean properties of active elements of clouds, which are characterized by strong updrafts, can be described by an entraining plume of similar top height. With the data from a precipitating experiment, the authors examine the spec...

Vertical Mass Flux Calculations in Hawaiian Trade Cumulus Clouds from Dual-Doppler Radar

Abstract Two ground-based Doppler radars and an instrumented aircraft provided a means for computing the vertical mass flux in trade wind cumulus clouds that formed east of the island of Hawaii dining the Hawaiian Rainband Project of 1990. This study compares the mass fluxes of small isolated cells with larger groups of clouds and rainbands. Because of excellent sensitivity, the 5.5-cm wavelength radars were capable of detecting Bragg backscatter, which extended the measurements to include some precipitation-free air within and surrounding the clouds. The shape of the vertical profile of vertical mass flux within shallow cumulus clouds and cloud groups varied considerably over the cloud's life cycle but was comparatively independent of cloud size. The early stages of convection displayed a mass flux profile that resembled those produced by buoyancy sorting and entraining plume models, but the mature and later stages were considerably more affected by precipitation-driven down-drafts and included mean down...

Entrainment in Cumulus Clouds

Abstract Entrainment of dry air into cumulus clouds influences the development of the clouds in a major way. The many aspects of the entrainment process are examined in this paper by critically reviewing the literature from the time when investigations began. It is an interesting time in the evolution of the study of cumulus clouds with the advent of different models and several new instruments. Traditional entraining plume and thermal models that received considerable attention during the early years are being replaced by episodic-type mixing models. Recent observations of the source of entrained air are in part responsible for the new thinking, but the ideas really originate with the suggestion made by Squires more than 40 years age that vertical rather than horizontal mixing causes the dilution of cumuli by the process of penetrative downdrafts.

A One-Dimensional Entraining/Detraining Plume Model and Its Application in Convective Parameterization

Abstract A new one-dimensional cloud model, specifically designed for application in mesoscale convective parameterization schemes (CPSs), is introduced. The model is unique in its representation of environmental entrainment and updraft detrainment rates. In particular, the two-way exchange of mass between clouds and their environment is modulated at each vertical level by a buoyancy sorting mechanism at the interface of clear and cloudy air. The new entrainment/detrainment scheme allows vertical profiles of both updraft moisture detrainment and updraft vertical mass flux to vary in a physically realistic way as a function of the cloud-scale environment. These performance characteristics allow the parameterized vertical distribution of convective heating and drying to be much more responsive to environmental conditions than is possible with a traditional one-dimensional entraining plume model. The sensitivities of the new model to variations in environmental convective available potential energy and verti...

Diagnosis of Convective and Mesoscale Motions During Phase IH of Gate

Abstract Observational evidence from GATE suggests that a significant fraction of precipitation in tropical disturbances over the eastern Atlantic occurs beneath anvil-type mesoscale convective systems that are frequently associated with intense cumulonimbus convection. A diagnostic model is developed that includes heat, moisture and mass transports by both the convective-scale and mesoscale components of these systems. An entraining plume model is used for individual convective-scale elements yielding a spectral distribution of cumulus sizes. Mesoscale downdrafts are modeled using a bulk cloud model. A parameterization links properties of the mesoscale systems to those of associated deep convective-scale (cumulonimbus) clouds. A method based on a subjective comparison of model results to observed cloud cover is used to determine mesoscale downdraft areas in relation to cumulonimbus areas. For this reason only qualitative results derived from application of the theory can be considered reliable. The model...

The Entrainment Mechanism in Colorado Cumuli

Abstract Cloud air and clear air properties are analyzed to determine the altitude from where the entrained air originates. This is done using two parameters that are conserved with adiabatic altitude changes and that mix in a nearly linear manner. The method employed is only applicable to cloud regions that do not contain significant amounts of ice or precipitation size drops. The analysis shows that most of the entrained air originates several kilometers above the observation level. The mixed regions are typically found in downdrafts and the weaker updraft regions. The present results are inconsistent with the laterally entraining plume model. The results indicate that mixing of dry environmental air with cloud air produces sufficient evaporative cooling to create downdrafts that penetrate several kilometers into the cloud. The updraft air is diluted primarily through mixing with nearby downdraft air.

Sensitivity Analysis and Application of an Entraining Plume Model

Abstract Data derived from radiosonde soundings and stereoscopic photographs collected during a field experiment were input to a steady-state entraining plume cloud model to predict cumulus cloud development. The basic data input requirements of the model include cloud-base height, vertical profiles of temperature and dew point, and initial radius and vertical velocity at cloud base. The model was used to simulate convection on three different days, using the average of each day's measured cloud-base heights, its radiosonde data, and each of four combinations of initial cloud radius and vertical velocity. The dimensions of the four clouds predicted for each day were compared with dimensions of the photogrammetrically observed clouds that formed over mountainous terrain. Variability of measured cloud-top heights corresponded closely with model predictions from three of the combinations of initial radius and vertical velocity for each day's medium and large sized clouds. A sensitivity analysis of the model ...