Another look at zonal flows: Resonance, shearing, and frictionless saturation
Abstract
We show that shear is not the exclusive parameter that represents all aspects of flow structure effects on turbulence. Rather, waveflow 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 nearuniversal conventional shear suppression paradigm. Furthermore, consideration of waveflow resonance resolves the longstanding 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 upshift regime. Vorticity mixing is incorporated as a nonlinear, selfregulation effect in an extended 0D predatorprey model of driftZF turbulence. This analysis determines the saturated ZF shear and shows that the mesoscopic ZF width scales as L_{ZF}~f^{3/16}(1$$f$$)^{1/8}ρ $$^{5/8}_s$$ $$l^{3/8}_0$$in the (relevant) adiabatic limit (i.e., τ_{ck}k$$2\atop{}$$ D_{}$$\gg$$1). $$f$$ is the fraction of turbulence energy coupled to ZF and l_{0} 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 “nearmarginal” regime to be γ_{L}<ε_{c}, for the case of avalancheinduced 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.
 Authors:

 Univ. of California, San Diego, CA (United States). Center for Astrophysics & Space Sciences (CASS)
 Publication Date:
 Research Org.:
 Univ. of California, San Diego, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 1540198
 Alternate Identifier(s):
 OSTI ID: 1434357
 Grant/Contract Number:
 FG0204ER54738
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 25; Journal Issue: 4; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Physics
Citation Formats
Li, J. C., and Diamond, P. H. Another look at zonal flows: Resonance, shearing, and frictionless saturation. United States: N. p., 2018.
Web. doi:10.1063/1.5027107.
Li, J. C., & Diamond, P. H. Another look at zonal flows: Resonance, shearing, and frictionless saturation. United States. https://doi.org/10.1063/1.5027107
Li, J. C., and Diamond, P. H. Mon .
"Another look at zonal flows: Resonance, shearing, and frictionless saturation". United States. https://doi.org/10.1063/1.5027107. https://www.osti.gov/servlets/purl/1540198.
@article{osti_1540198,
title = {Another look at zonal flows: Resonance, shearing, and frictionless saturation},
author = {Li, J. C. and Diamond, P. H.},
abstractNote = {We show that shear is not the exclusive parameter that represents all aspects of flow structure effects on turbulence. Rather, waveflow 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 nearuniversal conventional shear suppression paradigm. Furthermore, consideration of waveflow resonance resolves the longstanding 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 upshift regime. Vorticity mixing is incorporated as a nonlinear, selfregulation effect in an extended 0D predatorprey model of driftZF turbulence. This analysis determines the saturated ZF shear and shows that the mesoscopic ZF width scales as LZF~f3/16(1$f$)1/8ρ $^{5/8}_s$ $l^{3/8}_0$in the (relevant) adiabatic limit (i.e., τckk$2\atop{}$ 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~(γL/εc)2, which indicates the extent of the “nearmarginal” regime to be γL<εc, for the case of avalancheinduced profile variability. Here, εc is the rate of dissipation of potential enstrophy and γL is the characteristic linear growth rate of fluctuations. The implications for dynamics near marginality of the strong scaling of saturated E with γL are discussed.},
doi = {10.1063/1.5027107},
journal = {Physics of Plasmas},
number = 4,
volume = 25,
place = {United States},
year = {2018},
month = {4}
}
Web of Science
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