From zonal flow to convection rolls in Rayleigh-Bénard convection with free-slip plates

Abstract

Rayleigh-Bénard (RB) convection with free-slip plates and horizontally periodic boundary conditions is investigated using direct numerical simulations. Two configurations are considered, one is two-dimension (2D) RB convection and the other one three-dimension (3D) RB convection with a rotating axis parallel to the plate. We explore the parameter range of Rayleigh numbers Ra from $10^{7}to$10^9$andPrandtlnumbers$Pr$from$1$to$100$.Weshowthatzonalflow,whichwasobserved,forexample,byGoluskin\text{et al}.\text{J. Fluid. Mech.}759,360-385(2014)for$Γ=2$,isonlystablewhen$Γ$issmallerthanacriticalvalue,whichdependson$Ra$and$Pr$.Withincreasing$Γ$,wefindasecondregimeinwhichbothzonalflowanddifferentconvectionrollstatescanbestatisticallystable.Forevenlarger$Γ$,inathirdregime,onlyconvectionrollstatesarestatisticallystableandzonalflowisnotsustained.Forthe3Dsimulations,wefix$Ra=10^7$and$Pr=0.71$,andcomparetheflowfor$Γ=8$and$Γ= 16$.Wedemonstratethatwithincreasingaspectratio$Γ$,zonalflow,whichwasobservedforsmall$Γ=2π$byvonHardenberg\text{et al}.\text{Phys. Rev. Lett.}15,134501(2015),completelydisappearsfor$Γ=16$.Forsuchlarge$Γ$onlyconvectionrollstatesarestatisticallystable.Inbetween,hereformediumaspectratio$Γ= 8$, the convection roll state and the zonal flow state are both statistically stable. What state is taken depends on the initial conditions, similarly as we found for the 2D case.

arXiv comment26 pages, 12 figures

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Cited by in corpus (2)

• Multiple states in turbulent large-aspect ratio thermal convection: What determines the number of convection rolls?
• The effect of Prandtl number on turbulent sheared thermal convection