Abstract
Using direct numerical simulations of rotating Rayleigh–Bénard convection, we explore the transitions between turbulent states from a three-dimensional (3-D) flow state towards a quasi-2-D condensate known as the large-scale vortex (LSV). We vary the Rayleigh number $Ra$ as control parameter and study the system response (strength of the LSV) in terms of order parameters, assessing the energetic content in the flow and the upscale energy flux. By sensitively probing the boundaries of the region of existence of the LSV in parameter space, we find discontinuous transitions and we identify the presence of a hysteresis loop as well as a memoryless abrupt growth dynamics. We show furthermore that the creation of the condensate state coincides with a discontinuous transition of the energy transport into the largest mode of the system.
Highlights
A hallmark feature of three-dimensional (3-D) turbulence is the forward energy cascade, transporting kinetic energy from large scales to ever smaller scales, as described by the celebrated theory of Kolmogorov (1941)
The different components of kinetic energy are provided over the range of considered Ra, crossing both large-scale vortex (LSV) transitions
From the 2-D energy that captures the LSV, we find a substantial discontinuity at both boundaries of the LSV state
Summary
A hallmark feature of three-dimensional (3-D) turbulence is the forward energy cascade, transporting kinetic energy from large scales to ever smaller scales, as described by the celebrated theory of Kolmogorov (1941). Hickel 2019; van Kan & Alexakis 2020), rendering the flow quasi-two-dimensional This leads to the development of an inverse energy flux, akin to fully 2-D turbulence (Kraichnan 1967; Batchelor 1969), transporting energy from smaller to larger scales. This can lead to accumulation of kinetic energy at the largest available scales, followed by condensation into a vertically coherent large-scale vortex (LSV) structure at the domain size (see Alexakis & Biferale (2018) for a recent review). This categorisation of the transition into the condensate state has shown to be an insightful approach in various other quasi-2-D flow systems (Alexakis 2015; Yokoyama & Takaoka 2017; Seshasayanan & Alexakis 2018; van Kan & Alexakis 2019)
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