Simplified two-layer models of precipitating atmosphere and their properties

Lambaerts, Julien; Lapeyre, Guillaume; Zeitlin, Vladimir; Bouchut, François

doi:10.1063/1.3582356

Cited by 30 publications

(54 citation statements)

References 32 publications

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“…It should also be pointed out that among the first class of multi-layer models (i.e. between pairs of nonmiscible materials), some authors recently introduced new models that handle with some mass exchange, see for example [20,19]. These models remain different from the models of the second class that are considered in the current study since the exchange takes place between physically distinguished materials.…”

Section: Introductionmentioning

confidence: 62%

A fast finite volume solver for multi-layered shallow water flows with mass exchange

Audusse¹,

Benkhaldoun²,

Sari³

et al. 2014

Journal of Computational Physics

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(2014) 'A fast nite volume solver for multi-layered shallow water ows with mass exchange.', Journal of computational physics., 272 . pp. 23-45. Further information on publisher's website:http://dx.doi.org/10.1016/j.jcp.2014.04.026Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Journal of Computational Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. A denitive version was subsequently published in Journal of Computational Physics, 272, 2014Physics, 272, , 10.1016Physics, 272, /j.jcp.2014 Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractA fast finite volume solver for hydrostatic multi-layered shallow water flows with mass exchange is investigated. In contrast to many models for multi-layered hydrostatic shallow water flows where the immiscible suppression is assumed, the present model allows for mass exchange between the layers. The multi-layered shallow water equations form a system of conservation laws with source terms for which the computation of the eigenvalues is not trivial. For most practical applications, complex eigenvalues may arise in the system and the multi-layered shallow water equations are not hyperbolic any more. This property makes the application of conventional finite volume methods difficult or even impossible for those methods which require in their formulation the explicit computation of the eigenvalues. In the current study, we propose a finite volume method that avoids the solution of Riemann problems. At each time step, the method consists of two stages to update the new solution. In the first stage, the multilayered shallow water equations are rewritten in a non-conservative form and the intermediate solutions are calculated using the method of characteristics. In the second stage, the numerical fluxes are reconstructed from the intermediate solutions in the first stage and used in the conservative form of the multi-layered shallow water equations. The proposed method is simple to implement, satisfies the conservation property and is suitable for multi-layered shallow water equations on non-flat topography. The proposed finite volume solver is verified against several benchmark tests and it shows good agreement with analytical solutions of the incompressible hydrostat...

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Section: Introductionmentioning

confidence: 62%

A fast finite volume solver for multi-layered shallow water flows with mass exchange

Audusse¹,

Benkhaldoun²,

Sari³

et al. 2014

Journal of Computational Physics

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“…Notation for the simplified two‐layer scheme with mass flux across material surfaces. From Lambaerts et al (), with permission of AIP…”

Section: Derivation Of the Improved Mcrswmentioning

confidence: 99%

“…The model is based on vertically averaged primitive equations with pseudo‐height as vertical coordinate. Instead of proceeding by a direct averaging of the complete system of equations with full thermodynamics and microphysics, which necessitates a series of specific ad hoc hypotheses, a hybrid approach is used, consisting in combination of vertical averaging between pairs of isobaric surfaces and Lagrangian conservation of the equivalent potential temperature (Bouchut et al ; Lambaerts et al ). Technically, convective fluxes, i.e.…”

Section: Introductionmentioning

confidence: 99%

An improved moist‐convective rotating shallow‐water model and its application to instabilities of hurricane‐like vortices

Rostami

Zeitlin

2018

Quart J Royal Meteoro Soc

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We show how the two-layer moist-convective rotating shallow-water model (mcRSW), which proved to be a simple and robust tool for studying effects of moist convection for large-scale atmospheric motions, can be improved. The improvement is achieved by including, in addition to the water vapour, precipitable water, and the effects of vaporization, entrainment, and precipitation, rendering the model cloud-resolving. It is applied, as an illustration, to model the development of instabilities of tropical cyclone-like vortices.

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“…The system is not supposed to model the whole troposphere but rather its lower part. A more realistic model contains two or more layers with convective exchanges between them and will be presented elsewhere (Lambaerts et al 2011). One can show that the one-layer model below results, as it should, from the two-layer one in the limit of infinitely thick second layer.…”

Section: The Mcrsw Modelmentioning

confidence: 99%

Moist versus Dry Barotropic Instability in a Shallow-Water Model of the Atmosphere with Moist Convection

Lambaerts

Lapeyre

Zeitlin

2011

Journal of the Atmospheric Sciences

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Dynamical influence of moist convection upon development of the barotropic instability is studied in the rotating shallow-water model. First, an exhaustive linear ''dry'' stability analysis of the Bickley jet is performed, and the most unstable mode identified in this way is used to initialize simulations to compare the development and the saturation of the instability in dry and moist configurations. High-resolution numerical simulations with a well-balanced finite-volume scheme reveal substantial qualitative and quantitative differences in the evolution of dry and moist-convective instabilities. The moist effects affect both balanced and unbalanced components of the flow. The most important differences between dry and moist evolution are 1) the enhanced efficiency of the moist-convective instability, which manifests itself by the increase of the growth rate at the onset of precipitation, and by a stronger deviation of the end state from the initial one, measured with a number of different norms; 2) a pronounced cyclone-anticyclone asymmetry during the nonlinear evolution of the moist-convective instability, which leads to an additional, with respect to the dry case, geostrophic adjustment, and the modification of the end state; and 3) an enhanced ageostrophic activity in the precipitation zones but also in the nonprecipitating areas because of the secondary geostrophic adjustment.

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Simplified two-layer models of precipitating atmosphere and their properties

Cited by 30 publications

References 32 publications

A fast finite volume solver for multi-layered shallow water flows with mass exchange

A fast finite volume solver for multi-layered shallow water flows with mass exchange

An improved moist‐convective rotating shallow‐water model and its application to instabilities of hurricane‐like vortices

Moist versus Dry Barotropic Instability in a Shallow-Water Model of the Atmosphere with Moist Convection

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