Rayleigh-Bénard convection with phase changes in a Galerkin model

Thomas Weidauer, Olivier Pauluis, Jörg Schumacher

Research output: Contribution to journalArticle

Abstract

The transition to turbulence in Rayleigh-Bénard convection with phase changes and the resulting convective patterns are studied in a three-dimensional Galerkin model. Our study is focused on the conditionally unstable regime of moist convection in which the stratification is stable for unsaturated air parcels and unstable for saturated parcels. We perform a comprehensive statistical analysis of the transition to convection that samples the dependence of attractors (or fixed points) in the phase space of the model on the dimensionless parameters. Conditionally unstable convection can be initiated either from a fully unsaturated linearly stable equilibrium or a fully saturated linearly unstable equilibrium. Highly localized moist convection can be found in a steady state, in an oscillating recharge-discharge regime, or turbulent in dependence of the aspect ratio and the degree of stable stratification of the unsaturated air. Our phase-space analysis predicts parameter ranges for which self-sustained convective regimes in the case of subcritical conditional instability can be observed. The observed regime transitions for moist convection bear some similarities to transitions to turbulence in simple shear flows.

Original languageEnglish (US)
Article number046303
JournalPhysical Review E
Volume84
Issue number4
DOIs
StatePublished - Oct 6 2011

Fingerprint

Phase Change
Rayleigh
Galerkin
Convection
convection
Unstable
Transition to Turbulence
Stratification
stratification
Phase Space
Linearly
turbulence
Model
air
Shear Flow
bears
shear flow
Dimensionless
Aspect Ratio
statistical analysis

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Rayleigh-Bénard convection with phase changes in a Galerkin model. / Weidauer, Thomas; Pauluis, Olivier; Schumacher, Jörg.

In: Physical Review E, Vol. 84, No. 4, 046303, 06.10.2011.

Research output: Contribution to journalArticle

Weidauer, Thomas ; Pauluis, Olivier ; Schumacher, Jörg. / Rayleigh-Bénard convection with phase changes in a Galerkin model. In: Physical Review E. 2011 ; Vol. 84, No. 4.
@article{d1db469682af4e89b702c4495817a2a5,
title = "Rayleigh-B{\'e}nard convection with phase changes in a Galerkin model",
abstract = "The transition to turbulence in Rayleigh-B{\'e}nard convection with phase changes and the resulting convective patterns are studied in a three-dimensional Galerkin model. Our study is focused on the conditionally unstable regime of moist convection in which the stratification is stable for unsaturated air parcels and unstable for saturated parcels. We perform a comprehensive statistical analysis of the transition to convection that samples the dependence of attractors (or fixed points) in the phase space of the model on the dimensionless parameters. Conditionally unstable convection can be initiated either from a fully unsaturated linearly stable equilibrium or a fully saturated linearly unstable equilibrium. Highly localized moist convection can be found in a steady state, in an oscillating recharge-discharge regime, or turbulent in dependence of the aspect ratio and the degree of stable stratification of the unsaturated air. Our phase-space analysis predicts parameter ranges for which self-sustained convective regimes in the case of subcritical conditional instability can be observed. The observed regime transitions for moist convection bear some similarities to transitions to turbulence in simple shear flows.",
author = "Thomas Weidauer and Olivier Pauluis and J{\"o}rg Schumacher",
year = "2011",
month = "10",
day = "6",
doi = "10.1103/PhysRevE.84.046303",
language = "English (US)",
volume = "84",
journal = "Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics",
issn = "1063-651X",
publisher = "American Physical Society",
number = "4",

}

TY - JOUR

T1 - Rayleigh-Bénard convection with phase changes in a Galerkin model

AU - Weidauer, Thomas

AU - Pauluis, Olivier

AU - Schumacher, Jörg

PY - 2011/10/6

Y1 - 2011/10/6

N2 - The transition to turbulence in Rayleigh-Bénard convection with phase changes and the resulting convective patterns are studied in a three-dimensional Galerkin model. Our study is focused on the conditionally unstable regime of moist convection in which the stratification is stable for unsaturated air parcels and unstable for saturated parcels. We perform a comprehensive statistical analysis of the transition to convection that samples the dependence of attractors (or fixed points) in the phase space of the model on the dimensionless parameters. Conditionally unstable convection can be initiated either from a fully unsaturated linearly stable equilibrium or a fully saturated linearly unstable equilibrium. Highly localized moist convection can be found in a steady state, in an oscillating recharge-discharge regime, or turbulent in dependence of the aspect ratio and the degree of stable stratification of the unsaturated air. Our phase-space analysis predicts parameter ranges for which self-sustained convective regimes in the case of subcritical conditional instability can be observed. The observed regime transitions for moist convection bear some similarities to transitions to turbulence in simple shear flows.

AB - The transition to turbulence in Rayleigh-Bénard convection with phase changes and the resulting convective patterns are studied in a three-dimensional Galerkin model. Our study is focused on the conditionally unstable regime of moist convection in which the stratification is stable for unsaturated air parcels and unstable for saturated parcels. We perform a comprehensive statistical analysis of the transition to convection that samples the dependence of attractors (or fixed points) in the phase space of the model on the dimensionless parameters. Conditionally unstable convection can be initiated either from a fully unsaturated linearly stable equilibrium or a fully saturated linearly unstable equilibrium. Highly localized moist convection can be found in a steady state, in an oscillating recharge-discharge regime, or turbulent in dependence of the aspect ratio and the degree of stable stratification of the unsaturated air. Our phase-space analysis predicts parameter ranges for which self-sustained convective regimes in the case of subcritical conditional instability can be observed. The observed regime transitions for moist convection bear some similarities to transitions to turbulence in simple shear flows.

UR - http://www.scopus.com/inward/record.url?scp=80054869860&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80054869860&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.84.046303

DO - 10.1103/PhysRevE.84.046303

M3 - Article

C2 - 22181257

AN - SCOPUS:80054869860

VL - 84

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 4

M1 - 046303

ER -