scholarly journals A Turbulence Closure for the Convective Boundary Layer Based on a Two-Scale Mass-Flux Approach

2002 ◽  
Vol 59 (18) ◽  
pp. 2729-2744 ◽  
Author(s):  
Vladimir M. Gryanik ◽  
Jörg Hartmann
Keyword(s):  
Boundary Layer ◽  
Mass Flux ◽  
Convective Boundary Layer ◽  
Turbulence Closure ◽  
Convective Boundary

A Thermal Plume Model for the Convective Boundary Layer: Representation of Cumulus Clouds

2008 ◽  
Vol 65 (2) ◽  
pp. 407-425 ◽  
Author(s):  
Catherine Rio ◽  
Frédéric Hourdin
Keyword(s):  
Boundary Layer ◽  
Mass Flux ◽  
Convective Boundary Layer ◽  
Turbulent Transport ◽  
Thermal Plume ◽  
Cumulus Clouds ◽  
Convective Boundary ◽  
Near Surface ◽  
Plume Model ◽  
Surface Drying

Abstract The “thermal plume model,” a mass-flux scheme combined with a classical diffusive approach, originally developed to represent turbulent transport in the dry convective boundary layer, is extended here to the representation of cloud processes. The modified parameterization is validated in a 1D configuration against results of large eddy simulations (LES), as well as in a 3D configuration against in situ measurements, for a series of cases of dry and cloudy convective boundary layers. Accounting for coherent structures of the mixed layer with the mass-flux scheme improves the representation of the diurnal cycle of the boundary layer, particularly its progressive deepening during the day and the associated near-surface drying. Results also underline the role of the prescription of the mixing of air between the plume and its environment, and of submean-plume fluctuations.

scholarly journals On a solution of the closure problem for dry convective boundary layer turbulence and beyond

2021 ◽  
Keyword(s):  
Boundary Layer ◽  
Convective Boundary Layer ◽  
Higher Order ◽  
Turbulence Closure ◽  
Analytical Models ◽  
Central Feature ◽  
Closure Problem ◽  
Convective Boundary ◽  
Higher Order Moments ◽  
Closure Models

Abstract We consider the closure problem of representing the higher order moments (HOMs) in terms of lower-order moments, a central feature in turbulence modelling based on the Reynolds-Averaged Navier-Stokes (RANS) approach. Our focus is on models suited for the description of asymmetric, non-local and semi-organized turbulence in the dry atmospheric convective boundary layer (CBL). We establish a multivariate probability density function (PDF) describing populations of plumes which are embedded in a sea of weaker randomly spaced eddies, and apply an assumed Delta-PDF approximation. The main content of this approach consists of capturing the bulk properties of the PDF. We solve the closure problem analytically for all relevant higher order moments (HOMs) involving velocity components and temperature and establish a hierarchy of new non-Gaussian turbulence closure models of different content and complexity ranging from analytical to semi-analytical. All HOMs in the hierarchy have a universal and simple functional form. They refine the widely used Millionshchikov closure hypothesis and generalize the famous quadratic skewness-kurtosis relationship to higher-order. We examine the performance of the new closures by comparison with measurement, LES and DNS data and derive empirical constants for semi-analytical models, which are best for practical applications. We show that the new models have a good skill in predicting the HOMs for atmospheric CBL. Our closures can be implemented in second-, third- and fourth-order RANS turbulence closure models of bi-, tri-and four-variate levels of complexity. Finally, several possible generalizations of our approach are discussed.

scholarly journals Quantifying horizontal and vertical tracer mass fluxes in an idealized valley during daytime

2016 ◽  
Vol 16 (20) ◽  
pp. 13049-13066 ◽  
Author(s):  
Daniel Leukauf ◽  
Alexander Gohm ◽  
Mathias W. Rotach
Keyword(s):  
Boundary Layer ◽  
Mass Flux ◽  
Convective Boundary Layer ◽  
Transport Processes ◽  
Surface Heating ◽  
Convective Boundary ◽  
Mass Fluxes ◽  
Initial Stability ◽  
Slope Wind ◽  
Stable Core

Abstract. The transport and mixing of pollution during the daytime evolution of a valley boundary layer is studied in an idealized way. The goal is to quantify horizontal and vertical tracer mass fluxes between four different valley volumes: the convective boundary layer, the slope wind layer, the stable core, and the atmosphere above the valley. For this purpose, large eddy simulations (LES) are conducted with the Weather Research and Forecasting (WRF) model for a quasi-two-dimensional valley. The valley geometry consists of two slopes with constant slope angle and is homogeneous in the along-valley direction. The surface sensible heat flux is horizontally homogeneous and prescribed by a sine function. The initial sounding is characterized by an atmosphere at rest and a constant Brunt–Väisälä frequency. Various experiments are conducted for different combinations of surface heating amplitudes and initial stability conditions. A passive tracer is released with an arbitrary but constant rate at the valley floor and resulting tracer mass fluxes are evaluated between the aforementioned volumes.As a result of the surface heating, a convective boundary layer is established in the lower part of the valley with a stable layer on top – the so-called stable core. The height of the slope wind layer, as well as the wind speed within, decreases with height due to the vertically increasing stability. Hence, the mass flux within the slope wind layer decreases with height as well. Due to mass continuity, this along-slope mass flux convergence leads to a partial redirection of the flow from the slope wind layer towards the valley centre and the formation of a horizontal intrusion above the convective boundary layer. This intrusion is associated with a transport of tracer mass from the slope wind layer towards the valley centre. A strong static stability and/or weak forcing lead to large tracer mass fluxes associated with this phenomenon. The total export of tracer mass out of the valley atmosphere increases with decreasing stability and increasing forcing. The effects of initial stability and forcing can be combined to a single parameter, the breakup parameter B. An analytical function is presented that describes the exponential decrease of the percentage of exported tracer mass with increasing B. This study is limited by the idealization of the terrain shape, stratification, and forcing, but quantifies transport processes for a large range of forcing amplitudes and atmospheric stability.

scholarly journals Mass-Flux Characteristics of Reactive Scalars in the Convective Boundary Layer

1999 ◽  
Vol 56 (1) ◽  
pp. 37-56 ◽  
Author(s):  
Arthur C. Petersen ◽  
Cees Beets ◽  
Han van Dop ◽  
Peter G. Duynkerke ◽  
A. Pier Siebesma
Keyword(s):  
Boundary Layer ◽  
Mass Flux ◽  
Convective Boundary Layer ◽  
Convective Boundary ◽  
Reactive Scalars

A Combined Eddy-Diffusivity Mass-Flux Approach for the Convective Boundary Layer

2007 ◽  
Vol 64 (4) ◽  
pp. 1230-1248 ◽  
Author(s):  
A. Pier Siebesma ◽  
Pedro M. M. Soares ◽  
João Teixeira
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Mass Flux ◽  
Convective Boundary Layer ◽  
Weather Prediction ◽  
Eddy Diffusivity ◽  
Moist Convection ◽  
Convective Boundary ◽  
New Approach ◽  
Convective Boundary Layers

Abstract A better conceptual understanding and more realistic parameterizations of convective boundary layers in climate and weather prediction models have been major challenges in meteorological research. In particular, parameterizations of the dry convective boundary layer, in spite of the absence of water phase-changes and its consequent simplicity as compared to moist convection, typically suffer from problems in attempting to represent realistically the boundary layer growth and what is often referred to as countergradient fluxes. The eddy-diffusivity (ED) approach has been relatively successful in representing some characteristics of neutral boundary layers and surface layers in general. The mass-flux (MF) approach, on the other hand, has been used for the parameterization of shallow and deep moist convection. In this paper, a new approach that relies on a combination of the ED and MF parameterizations (EDMF) is proposed for the dry convective boundary layer. It is shown that the EDMF approach follows naturally from a decomposition of the turbulent fluxes into 1) a part that includes strong organized updrafts, and 2) a remaining turbulent field. At the basis of the EDMF approach is the concept that nonlocal subgrid transport due to the strong updrafts is taken into account by the MF approach, while the remaining transport is taken into account by an ED closure. Large-eddy simulation (LES) results of the dry convective boundary layer are used to support the theoretical framework of this new approach and to determine the parameters of the EDMF model. The performance of the new formulation is evaluated against LES results, and it is shown that the EDMF closure is able to reproduce the main properties of dry convective boundary layers in a realistic manner. Furthermore, it will be shown that this approach has strong advantages over the more traditional countergradient approach, especially in the entrainment layer. As a result, this EDMF approach opens the way to parameterize the clear and cumulus-topped boundary layer in a simple and unified way.

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