# Simplified two-layer models of precipitating atmosphere and their properties

@article{Lambaerts2011SimplifiedTM, title={Simplified two-layer models of precipitating atmosphere and their properties}, author={Julien Lambaerts and Guillaume Lapeyre and Vladimir Zeitlin and François Bouchut}, journal={Physics of Fluids}, year={2011}, volume={23}, pages={046603} }

We derive a two-layer rotating shallow-water model for a moist atmosphere with water vapor condensation and related diabatic heating. Moist convection is represented by additional mass exchanges between the layers, which are determined from the moist enthalpy conservation principle, and related to the precipitation. Various boundary conditions at the lower and upper boundaries may be used. We show that the model reproduces in appropriate limits the main simplified models used previously in the…

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## References

SHOWING 1-10 OF 44 REFERENCES

Fronts and nonlinear waves in a simplified shallow-water model of the atmosphere with moisture and convection

- Environmental Science, Physics
- 2009

We describe a shallow-water type atmospheric model which includes the transport of moisture as well as related precipitation and convection effects. The model combines hydrodynamic nonlinearity of…

The Structure of Precipitation Fronts for Finite Relaxation Time

- Environmental Science, Physics
- 2006

When convection is parameterized in an atmospheric circulation model, what types of waves are supported by the parameterization? Several studies have addressed this question by finding the linear…

Precipitation fronts and the reflection and transmission of tropical disturbances

- Environmental Science, Physics
- 2008

This paper investigates the interactions between precipitation and the circulation in an idealized model for the tropical atmosphere where convection is represented by a quasi‐equilibrium closure.…

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

- Environmental Science, Physics
- 2011

AbstractDynamical 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…

Large Scale Dynamics of Precipitation Fronts in the Tropical Atmosphere: A Novel Relaxation Limit

- Environmental Science, Physics
- 2004

A simplifled set of equations is derived systematically below for the interaction of large scale ∞ow flelds and precipitation in the tropical atmosphere. These equations, the Tropical Climate Model,…

Studies of moisture effects in simple atmospheric models: The stable case

- Physics, Environmental Science
- 1982

Abstract The shallow-water equations are supplemented by a moisture equation in order to model effects of latent heat release on the horizontal propagation of disturbances. Since latent heating in…

Instabilities of buoyancy-driven coastal currents and their nonlinear evolution in the two-layer rotating shallow water model. Part 2. Active lower layer

- Environmental Science, PhysicsJournal of Fluid Mechanics
- 2010

This paper is the second part of the work on linear and nonlinear stability of buoyancy-driven coastal currents. Part 1, concerning a passive lower layer, was presented in the companion paper Gula &…

The role of moisture in the dynamics and energetics of turbulent baroclinic eddies

- Environmental Science, Physics
- 2004

The effects of moisture on nonlinear baroclinic eddies are examined in the context of a horizontally homogeneous two-layer quasigeostrophic model. Using an explicit equation for moisture and a simple…

Analytical and numerical results for flow and shock formation in two-layer gravity currents

- Environmental ScienceThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics
- 1998

Abstract Many gravity driven flows can be modelled as homogeneous layers of inviscid fluid with a hydrostatic pressure distribution. There are examples throughout oceanography, meteorology, and many…

Atmospheric Frontogenesis Models: Mathematical Formulation and Solution

- Physics, Environmental Science
- 1972

Abstract The approximation of geostrophic balance across a front is studied. Making this approximation, an analytic approach is made to a frontogenesis model based on the classic horizontal…