Competition between Ekman Plumes and Vortex Condensates in Rapidly Rotating Thermal Convection

Abstract

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The geostrophic regime of rapidly rotating turbulent convection

“…However, studies comparing no-slip and stress-free conditions could not see LSVs for no-slip plates at the same parameters where the stress-free case did display LSV formation [78,79], or only transiently would LSVs grow to be destroyed again shortly after [66]. By using higher Ra/Ra C values than before at small E, Aguirre Guzmán et al [80] have found stable LSVs in domains with no-slip plates at Pr = 5.2, E = 10 −7 , Ra/Ra C > 40, and at Pr = 0.1, 2 × 10 −7 ≤ E ≤ 5 × 10 −7 , Ra = 10 10 . Indeed, stronger buoyant forcing is required for the upscale energy transfer to withstand the Ekman-plume perturbations to the bulk from the no-slip boundaries and achieve LSV formation.…”

“…I thus introduce a 'rotation-affected' range 2a, and a 'rotation-dominated' range 2b. In range 2b, the flow state of geostrophic turbulence remains mostly out of reach at large Pr: asymptotic simulations at Pr = 3 have reported it; a recent DNS study [80] has observed LSVs at Pr = 5.2, where their generation mechanism of upscale energy transfer is a characteristic feature of geostrophic turbulence. It is not clear where to place the upper boundary of the geostrophic regime, that in fact encompasses all four flow types (cells, columns, plumes and geostrophic turbulence) and is indicated with the shaded area in Figure 2(b).…”

“…The turbulence is anisotropic. An interesting feature of this state is the occurrence of an inverse energy cascade from small to large spatial scales, resulting in the formation of large-scale vortices (LSVs) [26,[75][76][77][78][79][80]. I will return to the LSVs in more detail in Section 3.3.…”

“…It appears to be 'easier' to reach a state of geostrophic turbulence at low Pr (i.e. reached at smaller Ra/Ra C ) [26,80].…”

“…References: Stress-free conditions: Schmitz and Tilgner [111]; Julien et al [26,92]; Favier et al [76]; Guervilly et al [77]; Maffei et al [112]. Noslip conditions: King et al [48,94,96]; Plumley et al [66] Aguirre Guzmán et al [80]. Studies comparing both conditions: Julien et al [50]; Stellmach et al [78] and Kunnen et al (2016) [79].…”