Mixed baroclinic convection in a cavity

Research output: Contribution to journalArticle

Abstract

We study the convective patterns that arise in a nearly semi-cylindrical cavity fed in with hot fluid at the upper boundary, bounded by a cold, porous semi-circular boundary at the bottom, and infinitely extended in the third direction. While this configuration is relevant to continuous casting processes that are significantly more complex, we focus on the flow patterns associated with the particular form of mixed convection that arises in it. Linear stability analysis and direct numerical simulations (DNS) are conducted, using the spectral element method to identify observable states. The nature of the bifurcations is determined through Stuart–Landau analysis for completeness. The base flow consists of two counter-rotating rolls driven by the baroclinic imbalance due to the curved isothermal boundary. These are however suppressed by the through-flow, which is found to have a stabilising influence as soon as the Reynolds number Re based on the through-flow exceeds 25. For a sufficiently high Rayleigh number, this base flow is linearly unstable to three different modes, depending on Re. For Re ≤ 75, the rolls destabilise through a supercritical bifurcation into a travelling wave. For 100 ≤ Re ≤ 110, a subcritical bifurcation leads to a standing oscillatory mode, whereas for Re ≥ 150, the unstable mode is non-oscillatory and grows out of a supercritical bifurcation. The direct numerical simulations confirm that in all cases, the dominant mode returned by the linear stability analysis precisely matches the topology and evolution of the flow patterns that arise out of the fully nonlinear dynamics.
Original languageEnglish
Article numberA40
Number of pages31
JournalJournal of Fluid Mechanics
Volume885
Early online date7 Jan 2020
DOIs
Publication statusE-pub ahead of print - 7 Jan 2020

Fingerprint

Linear stability analysis
Mixed convection
Direct numerical simulation
Flow patterns
convection
base flow
cavities
Bifurcation (mathematics)
Continuous casting
direct numerical simulation
flow distribution
Reynolds number
Topology
Fluids
completeness
Rayleigh number
traveling waves
counters
topology
fluids

Keywords

  • baroclinic flows
  • buoyancy-driven instability

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Mixed baroclinic convection in a cavity. / Kumar, Abhishek; Potherat, Alban.

In: Journal of Fluid Mechanics, Vol. 885, A40, 25.02.2020.

Research output: Contribution to journalArticle

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