A heuristic framework for next-generation models of geostrophic convective turbulence

Abstract

Many geophysical and astrophysical phenomena are driven by turbulent fluid dynamics, containing behaviors separated by tens of orders of magnitude in scale. While direct simulations have made large strides toward understanding geophysical systems, such models still inhabit modest ranges of the governing parameters that are difficult to extrapolate to planetary settings. The canonical problem of rotating Rayleigh-Bénard convection provides an alternate approach -isolating the fundamental physics in a reduced setting. Theoretical studies and asymptotically-reduced simulations in rotating convection have unveiled a variety of flow behaviors likely relevant to natural systems, but still inaccessible to direct simulation. In lieu of this, several new large-scale rotating convection devices have been designed to characterize such behaviors. It is essential to predict how this potential influx of new data will mesh with existing results. Surprisingly, a coherent framework of predictions for extreme rotating convection has not yet been elucidated. In this study, we combine asymptotic predictions, laboratory and numerical results, and experimental constraints to build a heuristic framework for cross-comparison between a broad range of rotating convection studies. We categorize the diverse field of existing predictions in the context of asymptotic flow regimes. We then consider the physical constraints that determine the points of intersection between flow behavior predictions and experimental accessibility. Applying this framework to several upcoming devices demonstrates that laboratory studies may soon be able to characterize geophysically-relevant flow regimes. These new data may transform our understanding of geophysical and astrophysical turbulence, and the conceptual framework developed herein should provide the theoretical infrastructure needed for meaningful discussion of these results. ARTICLE HISTORY

Ocean Dynamics of Outer Solar System Satellites

“…For Rayleigh numbers greater than Ra UNR , the influence of rotation is lost globally ("NR" regime). As reviewed by Cheng et al (2018), significant debate exists in the community on the scaling laws for Ra GTU and Ra UNR . Rather than assume a single scaling law for each Ekman number, E = ∕2 D 2 10 −10 -10 −11 10 −11 -10 −12 10 −12 10 −10 -10 −13…”

“…Implications for icy satellites are explored in section 4, and the challenges of extrapolating to realistic ocean conditions are discussed in section 5. Cheng et al (2018) with superimposed parameter estimates for Enceladus (magenta), Titan (gray), Europa (cyan), and Ganymede (blue) superimposed (see Table 1). Our numerical simulations are denoted by stars, where interior color denotes Ekman number and exterior color denotes Rayleigh number.…”

Scaling Laws in Rayleigh‐Bénard Convection

“…The Rossby number is limited as well by its relation to E and Ra such that the Rossby numbers achievable are typically (Cheng et al, ). Current efforts to build larger laboratory tanks should extend this range (Cheng et al, ).…”

Turbulent rotating convection confined in a slender cylinder: The sidewall circulation

“…cylinder and periodic layer), roughly a factor two in magnitude. This discrepancy is unexpected: as the cylindrical domains in experiments were always wide enough to accommodate many times the characteristic horizontal convective scale [1], no confinement effects were anticipated.…”