Critical Rossby number for the inverse cascade in rotating turbulence · revision history

Revision 2

Accepted · core change · record

Changes against revision 1:

Title
Critical Rossby number for the inverse cascade in rotating turbulence
Plain
Rapid rotation makes turbulence nearly two-dimensional and can reverse the direction of energy flow, sending energy to large scales. The rotation rate at which this switch happens, and whether it is sharp like a phase transition, are unsettled.
Precise · changed · core
Revision 1: In forced rotating turbulence with rotation rate $\Omega$, forcing scale $\ell_f$ and Rossby number $\mathrm{Ro} = u_f/(2\Omega \ell_f)$, an upscale energy flux appears below a critical $\mathrm{Ro}_c$. Determine Ro_c in the limits $\mathrm{Re} \to \infty$ and $\text{domain size} \to \infty$, the scaling of the upscale flux fraction near $\mathrm{Ro}_c$, and whether the transition is continuous with critical exponents or discontinuous with hysteresis.
Revision 2: In forced rotating turbulence with rotation rate $\Omega$, forcing scale $\ell_f$ and Rossby number $\mathrm{Ro} = u_f/(2\Omega \ell_f)$, an upscale energy flux appears below a critical $\mathrm{Ro}_c$. Determine $\mathrm{Ro}_{c}$ in the limits $\mathrm{Re} \to \infty$ and $\text{domain size} \to \infty$, the scaling of the upscale flux fraction near $\mathrm{Ro}_c$, and whether the transition is continuous with critical exponents or discontinuous with hysteresis.
Settled by
DNS at increasing Re and domain size showing convergence of $\mathrm{Ro}_{c}$ and of the exponent of the upscale flux near $\mathrm{Ro}_{c}$.
Kind
well-posed
Answer type
value
References
(empty)
Literature status
partially-resolved
Status note
Simulations find a transition with hysteresis and metastable flux-loop states (Clark di Leoni, Alexakis, Biferale, Buzzicotti 2020); the large-Re, large-domain limit is not settled.
Posed since
(empty)

Decisions