dc.contributor.author | Vallis, GK | |
dc.contributor.author | Parker, D | |
dc.contributor.author | Tobias, S | |
dc.date.accessioned | 2018-11-21T14:35:43Z | |
dc.date.issued | 2019-01-09 | |
dc.description.abstract | Rayleigh–Bénard convection is one of the most well-studied models in fluid mechanics.
Atmospheric convection, one of the most important components of the climate system, is by
comparison complicated and poorly understood. A key attribute of atmospheric convection
is the buoyancy source provided by the condensation of water vapour, but the presence
of radiation, compressibility, liquid water and ice further complicate the system and our
understanding of it. In this paper we present an idealized model of moist convection by
taking the Boussinesq limit of the ideal gas equations and adding a condensate that obeys a
simplified Clausius–Clapeyron relation. The system allows moist convection to be explored at
a fundamental level and reduces to the classical Rayleigh–Bénard model if the latent heat
of condensation is taken to be zero. The model has an exact, Rayleigh-number independent
‘drizzle’ solution in which the diffusion of water vapour from a saturated lower surface is
balanced by condensation, with the temperature field (and so the saturation value of the
moisture) determined self-consistently by the heat released in the condensation. This state
is the moist analogue of the conductive solution in the classical problem. We numerically
determine the linear stability properties of this solution as a function of Rayleigh number
and a nondimensional latent-heat parameter. We also present some two-dimensional, timedependent,
nonlinear solutions at various values of Rayleigh number and the nondimensional
condensational parameters. At sufficiently low Rayleigh number the system converges to the
drizzle solution, and we find no evidence that two-dimensional self-sustained convection
can occur when that solution is stable. The flow transitions from steady to turbulent as the
Rayleigh number or the effects of condensation are increased, with plumes triggered by gravity
waves emanating from other plumes. The interior dries as the level of turbulence increases,
because the plumes entrain more dry air and because the saturated boundary layer at the
top becomes thinner. The flow develops a broad relative humidity minimum in the domain
interior, only weakly dependent on Rayleigh number when that is high. | en_GB |
dc.description.sponsorship | This work was funded by
NERC under the Paracon Program via grants to the Universities of Exeter and Leeds. | en_GB |
dc.identifier.citation | Vol. 862, pp. 162-199. | en_GB |
dc.identifier.doi | 10.1017/jfm.2018.954 | |
dc.identifier.uri | http://hdl.handle.net/10871/34844 | |
dc.language.iso | en | en_GB |
dc.publisher | Cambridge University Press (CUP) | en_GB |
dc.rights.embargoreason | Under embargo until 09 July 2019 in compliance with publisher policy. | en_GB |
dc.rights | © Cambridge University Press 2019. | |
dc.subject | Convection | en_GB |
dc.subject | atmospheric flows | en_GB |
dc.subject | condensation/evaporation | en_GB |
dc.title | A Simple System for Moist Convection: The Rainy-Benard Model | en_GB |
dc.type | Article | en_GB |
dc.identifier.issn | 0022-1120 | |
dc.description | This is the author accepted manuscript. The final version is available from Cambridge University Press via the DOI in this record. | en_GB |
dc.identifier.journal | Journal of Fluid Mechanics | en_GB |