Another look at zonal flows: Resonance, shearing, and frictionless saturation

Journal Article · 23 April 2018 · Physics of Plasmas

DOI: https://doi.org/10.1063/1.5027107 · OSTI ID:1540198

Li, J. C.  ^[1]; Diamond, P. H. ^[2]

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1. Univ. of California, San Diego, CA (United States). Center for Astrophysics & Space Sciences (CASS); DOE/OSTI
2. Univ. of California, San Diego, CA (United States). Center for Astrophysics & Space Sciences (CASS)

We show that shear is not the exclusive parameter that represents all aspects of flow structure effects on turbulence. Rather, wave-flow resonance enters turbulence regulation, both linearly and nonlinearly. Resonance suppresses the linear instability by wave absorption. Flow shear can weaken the resonance, and thus destabilize drift waves, in contrast to the near-universal conventional shear suppression paradigm. Furthermore, consideration of wave-flow resonance resolves the long-standing problem of how zonal flows (ZFs) saturate in the limit of weak or zero frictional drag, and also determines the ZF scale. We show that resonant vorticity mixing, which conserves potential enstrophy, enables ZF saturation in the absence of drag, and so is effective at regulating the Dimits up-shift regime. Vorticity mixing is incorporated as a nonlinear, self-regulation effect in an extended 0D predator-prey model of drift-ZF turbulence. This analysis determines the saturated ZF shear and shows that the mesoscopic ZF width scales as L_ZF~f^3/16(1-$$f$$)^1/8ρ $$^{5/8}_s$$ $$l^{3/8}_0$$in the (relevant) adiabatic limit (i.e., τ_ckk$$2\atop{||}$$ D_||$$\gg$$1). $$f$$ is the fraction of turbulence energy coupled to ZF and l₀ is the base state mixing length, absent ZF shears. We calculate and compare the stationary flow and turbulence level in frictionless, weakly frictional, and strongly frictional regimes. In the frictionless limit, the results differ significantly from conventionally quoted scalings derived for frictional regimes. To leading order, the flow is independent of turbulence intensity. The turbulence level scales as E~(γ_L/ε_c)², which indicates the extent of the “near-marginal” regime to be γ_L<ε_c, for the case of avalanche-induced profile variability. Here, ε_c is the rate of dissipation of potential enstrophy and γ_L is the characteristic linear growth rate of fluctuations. The implications for dynamics near marginality of the strong scaling of saturated E with γ_L are discussed.

• Research Organization: Univ. of California, San Diego, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: FG02-04ER54738
• OSTI ID: 1540198
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 4 Vol. 25; ISSN 1070-664X
• Publisher: American Institute of Physics (AIP)Copyright Statement
• Country of Publication: United States
• Language: English