A two‐fluid single‐column model of the dry, shear‐free, convective boundary layer

Thuburn, John; Efstathiou, Georgios A.; Beare, Robert J.

doi:10.1002/qj.3510

Cited by 14 publications

(74 citation statements)

References 45 publications

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“…The assumption that

w_{i j}^{T} = 0

does not imply anything about

b_{i j}^{T}

. In the absence of knowledge of the subfilter‐scale variability, the buoyancy transferred follows Thuburn et al (2019)

b_{i j}^{T} = θ_{b} b_{i} + false(1 - θ_{b} false) b_{j} .

…”

Section: The Multifluid Boussinesq Equationsmentioning

confidence: 99%

“…Thuburn et al (2019) and Weller and McIntyre (2019) presented solutions of two‐fluid equations using the same pressure for both fluids. Thuburn et al (2019) showed that these equations are in fact unstable and can be stabilized by diffusion of vertical velocity whereas Weller and McIntyre (2019) stabilized the equations with diffusion and drag between fluids. Neither of these stabilization techniques are acceptable; sufficient diffusion to stabilize the multifluid equations may smooth out real features of the flow, and the diffusion between fluids and drag used by Weller and McIntyre (2019) meant that both fluids tended to move together rather than through each other.…”

Section: Introductionmentioning

confidence: 99%

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Multifluids for Representing Subgrid‐Scale Convection

Weller

McIntyre

Shipley

2020

J Adv Model Earth Syst

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Traditional parameterizations of convection are a large source of error in weather and climate prediction models, and the assumptions behind them become worse as resolution increases. Multifluid modeling is a promising new method of representing subgrid‐scale and near‐grid‐scale convection allowing for net mass transport by convection and nonequilibrium dynamics. The air is partitioned into two or more fluids, which may represent, for example, updrafts and the nonupdraft environment. Each fluid has its own velocity, temperature, and constituents with separate equations of motion. This paper presents two‐fluid Boussinesq equations for representing subgrid‐scale dry convection with sinking and w = 0 air in Fluid 0 and rising air in Fluid 1. Two vertical slice test cases are developed to tune parameters and to evaluate the two‐fluid equations: a buoyant rising bubble and radiative convective equilibrium. These are first simulated at high resolution with a single‐fluid model and conditionally averaged based on the sign of the vertical velocity. The test cases are next simulated with the two‐fluid model in one column. A model for entrainment and detrainment based on divergence leads to excellent representation of the convective area fraction. Previous multifluid modeling of convection has used the same pressure for both fluids. This is shown to be a bad approximation, and a model for the pressure difference between the fluids based on divergence is presented.

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“…The assumption that

w_{i j}^{T} = 0

does not imply anything about

b_{i j}^{T}

. In the absence of knowledge of the subfilter‐scale variability, the buoyancy transferred follows Thuburn et al (2019)

b_{i j}^{T} = θ_{b} b_{i} + false(1 - θ_{b} false) b_{j} .

…”

Section: The Multifluid Boussinesq Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multifluids for Representing Subgrid‐Scale Convection

Weller

McIntyre

Shipley

2020

J Adv Model Earth Syst

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“…Alternatively, Holm and Kupershmidt (1984) regularized these equations using multiple pressures for problems with surface tension. Thuburn et al (2019) are also working on a single-column solution of conditionally averaged equations and show that the incompressible conditionally averaged equations are unstable without additional coupling between the fluids.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of the conditionally averaged equations for representing net mass flux due to convection

Weller

McIntyre

2019

Quart J Royal Meteoro Soc

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The representation of subgrid‐scale convection is a weak aspect of weather and climate prediction models and the assumption that no net mass is transported by convection in parametrizations is increasingly unrealistic as models enter the grey zone, partially resolving convection. The solution of conditionally averaged equations of motion (multifluid equations) is proposed in order to avoid this assumption. Separate continuity, temperature, and momentum equations are solved for inside and outside convective plumes, which interact via mass‐transfer terms, drag, and by a common pressure. This is not a convection scheme that can be used with an existing dynamical core—this requires a whole new model. This article presents stable numerical methods for solving the multifluid equations, including large transfer terms between the environment and plume fluids. Without transfer terms, the two fluids are not sufficiently coupled and solutions diverge. Two transfer terms are presented, which couple the fluids together in order to stabilize the model: diffusion of mass between the fluids (similar to turbulent entrainment) and drag between the fluids. Transfer terms are also proposed to move buoyant air into the plume fluid and vice versa as would be needed to represent initialization and termination of subgrid‐scale convection. The transfer terms are limited (clipped in size) and solved implicitly in order to achieve bounded, stable solutions. Results are presented for a well‐resolved warm bubble with rising air being transferred to the plume fluid. For stability, equations are formulated in advective rather than flux form and solved using bounded finite‐volume methods. Discretization choices are made to preserve boundedness and conservation of momentum and energy when mass is transferred between fluids. The formulation of transfer terms in order to represent subgrid convection is the subject of future work.

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“…This behaviour is probably related to the entrainment-detrainment processes and the continuous exchange of particles between fluid 2 and fluid 1. Furthermore, Lagrangian particle tracking is known to produce excessive switching of particle labels between the coherent structures and their environment (see Yeo and Romps 2013;Thuburn et al 2019).…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

“…Others (e.g., Angevine 2005) calculate the profile of σ via a vertical integral of the updraft mass budget. More recently, EDMF-like schemes have been introduced in which updraft properties including w, θ , and the area fraction are prognostic variables (Tan et al 2018;Thuburn et al 2019). For all of these schemes, information on the profile of σ and other updraft properties from high-resolution reference simulations is essential either as direct input to the scheme or for calibration and validation.…”

Section: Introductionmentioning

confidence: 99%

Diagnosing Coherent Structures in the Convective Boundary Layer by Optimizing Their Vertical Turbulent Scalar Transfer

Efstathiou

Thuburn

Beare

2019

Boundary-Layer Meteorol

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A new method is introduced to identify coherent structures in the convective boundary layer, based on optimizing the vertical scalar flux in a two-fluid representation of turbulent motions as simulated by a large-eddy simulation. The new approach partitions the joint frequency distribution (JFD) of the vertical velocity and a transported scalar into coherent structures (fluid 2) and their environment (fluid 1) by maximizing that part of the scalar flux resolved by the mean properties in fluid 2 and fluid 1. The proposed method does not rely on any a priori criteria for the partitioning of the flow nor any pre-assumptions about the shape of the JFD. Different flavours of the optimization approach are examined based on maximizing either the total (fluid 1 + fluid 2) or the fluid-2 resolved scalar flux, and on whether all possible partitions or only a subset are considered. These options can result in different derived area fractions for the coherent structures. The properties of coherent structures diagnosed by the optimization method are compared to the conditional sampling of a surface-emitted decaying tracer, in which coherent structures are defined as having tracer perturbation greater than some height-dependent threshold. Results show that the optimization method is able to smoothly define coherent thermal structures in both the horizontal and the vertical. Moreover, optimizing the turbulent transfer by the fluid-2 resolved flux produces very similar coherent structures to the tracer threshold method, especially in terms of their area fraction and updraft velocities. Nonetheless, further analysis of the partitioning of the JFD reveals that, even though the area fraction of coherent structures might be similar, their definition can occupy different quadrants of the JFD, implying the contribution of different physical mechanisms to the turbulent transfer in the boundary layer. Finally, the kinematic and thermodynamic characteristics of the coherent structures are examined based on their definition criteria.

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A two‐fluid single‐column model of the dry, shear‐free, convective boundary layer

Cited by 14 publications

References 45 publications

Multifluids for Representing Subgrid‐Scale Convection

Multifluids for Representing Subgrid‐Scale Convection

Numerical solution of the conditionally averaged equations for representing net mass flux due to convection

Diagnosing Coherent Structures in the Convective Boundary Layer by Optimizing Their Vertical Turbulent Scalar Transfer

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