Boussinesq wave theory in fluid mixtures with application to the cloudy atmosphere

Bois, Pierre-Antoine

doi:10.1016/0020-7225(94)90007-8

Cited by 3 publications

(2 citation statements)

References 11 publications

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“…3, the linearized gravity wave equation governing the motions is derived. The study is made using the asymptotic frame of the Boussinesq approximation already used in previous papers (Bois, 1991(Bois, , 1994. The use of this approximation first implies the existence of a particular solution describing a static state of the medium, depicted with the help of unique variable (the altitude referred to the "dry" atmospheric scale).…”

Section: Introductionmentioning

confidence: 99%

A theoretical model for double diffusive phenomena in cloudy convection

Bois¹,

Kubicki²

2003

Ann. Geophys.

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Abstract. Using classical rheological principles, a model is proposed to depict the molecular diffusion in a moistsaturated dissipative atmosphere: due to the saturation condition existing between water vapor and liquid water in the medium, the equations are those of a double diffusive phenomenon with Dufour effect. The double diffusivity is important because of the huge diffusivity difference between the liquid phase and the gaseous phase. Reduced equations are constructed and are then applied to describe the linear free convection of a thin cloudy layer bounded by two free surfaces. The problem is solved with respect to two destabilizing parameters, a Rayleigh number R a and a moist Rayleigh number R h . Two instabilities may occur: (i) oscillatory modes, which exist for sufficiently large values of the Rayleigh number: these modes generalize the static instability of the medium; (ii) stationary modes, which mainly occur when the moist Rayleigh number is negative. These modes are due to the molecular diffusion, and exist even when the medium is statically stable: the corresponding motions describe, in the moist-saturated air, configurations such as "fleecy clouds". Growth rates are determined at the instability threshold for the two modes of instability occurring in the process. The case of vanishing moisture concentration is considered: the oscillatory unstable case appears as a singular perturbation (due to the moisture) of the stationary unstable state of the Rayleigh-Bénard convection in pure fluid, and, more generally, as the dynamical perturbation of the static instability. The convective behaviour of a cloud in the air at rest is then examined: the instability of the cloud is mainly due to moisture, while the instability of the surrounding air is mainly due to heating.

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Section: Introductionmentioning

confidence: 99%

A theoretical model for double diffusive phenomena in cloudy convection

Bois¹,

Kubicki²

2003

Ann. Geophys.

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“…The study is made using the asymptotic framework of the Boussinesq approximation already used in previous papers [Bois, 1991[Bois, , 1994. In shallow convection, this assumption implies the existence of a (known) static state of the medium.…”

Section: Introductionmentioning

confidence: 99%

Double diffusive aspects of the convection in moist-saturated air

Bois

Kubicki

Solid Mechanics and Its Applications

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Abstract. -Equations of fluid mixtures are used in order to derive a set of equations governing the motion of a moist, viscous and heat conducting, saturated air in presence of gravity. From these equations, a model is constructed to exhibit the double diffusive behaviour of this system. As application, we consider free convection in a shallow layer, by assuming small water concentration : the medium is, in general, linearly stable, but two instability cases are exhibited : stationary instability exists for negative Rayleigh number, and oscillatory instability can exist for negative moist Rayleigh number. In realistic cases, where the moist Rayleigh number is always small, the stationary instability is the only occurring instability. Following the description of the problem of thermohaline convection, this instability may be interpreted as moisture fingers in the medium.

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Deep gravity waves in moist-saturated atmospheric air

Bois

Kubicki

2001

Mechanics Research Communications

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Boussinesq wave theory in fluid mixtures with application to the cloudy atmosphere

Cited by 3 publications

References 11 publications

A theoretical model for double diffusive phenomena in cloudy convection

A theoretical model for double diffusive phenomena in cloudy convection

Double diffusive aspects of the convection in moist-saturated air

Deep gravity waves in moist-saturated atmospheric air

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