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Inherent thermal convection in a granular gas inside a box under a gravity field

Published online by Cambridge University Press:  16 November 2018

Francisco Vega Reyes Open the ORCID record for Francisco Vega Reyes [Opens in a new window] ,
Andrea Puglisi ,
Giorgio Pontuale  and
Andrea Gnoli
Francisco Vega Reyes*
Affiliation:
Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06071 Badajoz, Spain
Andrea Puglisi
Affiliation:
Istituto dei Sistemi Complessi, CNR and Dipartimento di Fisica, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Rome, Italy
Giorgio Pontuale
Affiliation:
Istituto dei Sistemi Complessi, CNR and Dipartimento di Fisica, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Rome, Italy
Andrea Gnoli
Affiliation:
Istituto dei Sistemi Complessi, CNR and Dipartimento di Fisica, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Rome, Italy
*
†Email address for correspondence: [email protected]
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Abstract

We theoretically prove the existence in granular fluids of a thermal convection that is inherent in the sense that it is always present and has no thermal gradient threshold (convection occurs for all finite values of the Rayleigh number). More specifically, we study a gas of inelastic smooth hard disks enclosed in a rectangular region under a constant gravity field. The vertical walls act as energy sinks (i.e. inelastic walls that are parallel to gravity), whereas the other two walls are perpendicular to gravity and act as energy sources. We show that this convection is due to the combined action of dissipative lateral walls and a volume force (in this case, gravitation). Hence, we call it dissipative lateral walls convection (DLWC). Our theory, which also describes the limit case of elastic collisions, shows that inelastic particle collisions enhance the DLWC. We perform our study via numerical solutions (volume-element method) of the corresponding hydrodynamic equations in an extended Boussinesq approximation. We show that our theory describes the essentials of the results for similar (but more complex) laboratory experiments.

JFM classification

Convection: Buoyancy-driven instability Convection: Convection Granular media: Granular media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 160 - 173
Copyright
© 2018 Cambridge University Press 

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