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

Abstract

Abstract

Steady Rayleigh–Bénard convection between stress-free boundaries

“…We have carried out computations using spectral methods over eight orders of magnitude in Ra, four orders of magnitude in Pr and more than an order of magnitude in the aspect ratio Γ , defined as the width-to-height ratio of a pair of rolls. As in the no-slip case, our steady states share many features with time-dependent simulations between stress-free boundaries (Paul et al 2012;Wang et al 2020). Moreover, the results verify predictions about the Ra → ∞ limit made by Chini & Cox (2009) who extended an approach initiated by Robinson (1967) to construct matched asymptotic approximations of steady rolls between stress-free boundaries.…”

“…The Re = O(Ra 2/3 ) scaling found at large Ra for steady rolls and approximately evidenced in the DNS of Wang et al (2020) means that buoyancy forces can sustain substantially faster-than-free-fall velocities. Indeed, if flow speeds were limited by the maximum buoyancy acceleration acting across the layer height then dimensional characteristic velocities could not be of larger order than √ gαΔh, and Re could not be larger than O(Ra 1/2 ).…”

“…The steady rolls we have computed share many features with unsteady flows from DNS of Rayleigh-Bénard convection with isothermal stress-free boundary conditions. In recent simulations, Wang et al (2020) found multistability between unsteady states exhibiting various numbers of roll pairs in wide 2-D domains. Each of the coexisting states suggested scalings approaching the Nu = O(Ra 1/3 ) and Re = O(Ra 2/3 ) asymptotic behaviour of steady rolls.…”

The effect of Prandtl number on turbulent sheared thermal convection

“…(2020) and Wang et al. (2020 b ) for thermal convection with rotation or Chong & Xia (2016) for severe lateral confinement, although the exact interplays between the forces in these cases are different.

Figure 3.( a ) Value of versus for varying .

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Sheared Rayleigh-Bénard turbulence

“…In both cases the effects of the momentum transfer are enhanced by the high Prandtl number. We mention that the non-monotonic behavior of the Nusselt number observed here is a frequently occurring feature of flows in which more than one parameter concur to determine the value of the heat transfer; other known cases have been reported by [155] and [129] for Poiseuille-RB flow, [180] and [181] for thermal convection with rotation or [182] for severe lateral confinement, though the exact interplay between the forces in these cases are different.…”