For any aspect ratio Ro/Ri of the cylinder radii, the non-linear stability of the steady 2D-solutions of the non-linear Stokes system, which is an approximation of the Oberbeck-Boussinesq system, is theoretically studied. The sufficient condition for the stability shows a critical Ra which is a function of the aspect ratio. It is the same of the associated homogeneous linear problem and it can be found by looking for the largest eigenvalue of a suitable symmetric operator. The critical Ra so defined proves to be uniformly bounded from below in the space of dimensionless parameters, while it is non-uniformly bounded from above for the aspect ratio going to infinity. A scheme to evaluate it as a function of the aspect ratio is given. The results do not depend on the Prandtl number Pr.

A theoretical study of the first transition for the non-linear Stokes problem in a horizontal annulus

FERRARIO, Carlo;PASSERINI, Arianna
2016

Abstract

For any aspect ratio Ro/Ri of the cylinder radii, the non-linear stability of the steady 2D-solutions of the non-linear Stokes system, which is an approximation of the Oberbeck-Boussinesq system, is theoretically studied. The sufficient condition for the stability shows a critical Ra which is a function of the aspect ratio. It is the same of the associated homogeneous linear problem and it can be found by looking for the largest eigenvalue of a suitable symmetric operator. The critical Ra so defined proves to be uniformly bounded from below in the space of dimensionless parameters, while it is non-uniformly bounded from above for the aspect ratio going to infinity. A scheme to evaluate it as a function of the aspect ratio is given. The results do not depend on the Prandtl number Pr.
2016
Ferrario, Carlo; Passerini, Arianna
File in questo prodotto:
File Dimensione Formato  
1-s2.0-S0020746215001432-main.pdf

solo gestori archivio

Tipologia: Full text (versione editoriale)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 363.46 kB
Formato Adobe PDF
363.46 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
1-s2.0-S0020746215001432-main (1).pdf.pdf

solo gestori archivio

Tipologia: Altro materiale allegato
Licenza: DRM non definito
Dimensione 296.29 kB
Formato Adobe PDF
296.29 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
RaAppr.pdf

accesso aperto

Descrizione: Pre print
Tipologia: Pre-print
Licenza: PUBBLICO - Pubblico con Copyright
Dimensione 133.02 kB
Formato Adobe PDF
133.02 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2359581
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 5
social impact