Dynamics of potential vorticity staircase evolution and step mergers in a reduced model of beta-plane turbulence
Abstract
A two-field model of potential vorticity (PV) staircase structure and dynamics relevant to both beta-plane and drift-wave plasma turbulence is studied numerically and analytically. The model evolves averaged PV whose flux is both driven by and regulates a potential enstrophy field, ε. The model employs a closure using a mixing length model. Its link to bistability, vital to staircase generation, is analyzed and verified by integrating the equations numerically. Long-time staircase evolution consistently manifests a pattern of metastable quasiperiodic configurations, lasting for hundreds of time units, yet interspersed with abrupt ( Δt << 1 ) mergers of adjacent steps in the staircase. The mergers occur at the staircase lattice defects where the pattern has not completely relaxed to a strictly periodic solution that can be obtained analytically. Other types of stationary solutions are solitons and kinks in the PV gradient and ε-profiles. The waiting time between mergers increases strongly as the number of steps in the staircase decreases. This is because of an exponential decrease in interstep coupling strength with growing spacing. The long-time staircase dynamics is shown numerically be determined by local interaction with adjacent steps. In conclusion, mergers reveal themselves through the explosive growth of the turbulent PVmore »
- Authors:
-
- Univ. of California, San Diego, CA (United States)
- Univ. of California, San Diego, CA (United States); Southwestern Inst. of Physics, Sichuan (China)
- Publication Date:
- Research Org.:
- Univ. of California, San Diego, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1609563
- Alternate Identifier(s):
- OSTI ID: 1508188
- Grant/Contract Number:
- FG02-04ER54738
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Fluids
- Additional Journal Information:
- Journal Volume: 4; Journal Issue: 4; Journal ID: ISSN 2469-990X
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; physics; boundary layers; drift waves; flow instability; geophysical fluid dynamics; magnetic confinement fusion; mixing in geophysical flows; turbulence; turbulent mixing
Citation Formats
Malkov, M. A., and Diamond, P. H. Dynamics of potential vorticity staircase evolution and step mergers in a reduced model of beta-plane turbulence. United States: N. p., 2019.
Web. doi:10.1103/physrevfluids.4.044503.
Malkov, M. A., & Diamond, P. H. Dynamics of potential vorticity staircase evolution and step mergers in a reduced model of beta-plane turbulence. United States. https://doi.org/10.1103/physrevfluids.4.044503
Malkov, M. A., and Diamond, P. H. Mon .
"Dynamics of potential vorticity staircase evolution and step mergers in a reduced model of beta-plane turbulence". United States. https://doi.org/10.1103/physrevfluids.4.044503. https://www.osti.gov/servlets/purl/1609563.
@article{osti_1609563,
title = {Dynamics of potential vorticity staircase evolution and step mergers in a reduced model of beta-plane turbulence},
author = {Malkov, M. A. and Diamond, P. H.},
abstractNote = {A two-field model of potential vorticity (PV) staircase structure and dynamics relevant to both beta-plane and drift-wave plasma turbulence is studied numerically and analytically. The model evolves averaged PV whose flux is both driven by and regulates a potential enstrophy field, ε. The model employs a closure using a mixing length model. Its link to bistability, vital to staircase generation, is analyzed and verified by integrating the equations numerically. Long-time staircase evolution consistently manifests a pattern of metastable quasiperiodic configurations, lasting for hundreds of time units, yet interspersed with abrupt ( Δt << 1 ) mergers of adjacent steps in the staircase. The mergers occur at the staircase lattice defects where the pattern has not completely relaxed to a strictly periodic solution that can be obtained analytically. Other types of stationary solutions are solitons and kinks in the PV gradient and ε-profiles. The waiting time between mergers increases strongly as the number of steps in the staircase decreases. This is because of an exponential decrease in interstep coupling strength with growing spacing. The long-time staircase dynamics is shown numerically be determined by local interaction with adjacent steps. In conclusion, mergers reveal themselves through the explosive growth of the turbulent PV flux, which, however, abruptly drops to its global constant value once the merger is completed.},
doi = {10.1103/physrevfluids.4.044503},
journal = {Physical Review Fluids},
number = 4,
volume = 4,
place = {United States},
year = {Mon Apr 22 00:00:00 EDT 2019},
month = {Mon Apr 22 00:00:00 EDT 2019}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 5 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Homogenization of potential vorticity in planetary gyres
journal, September 1982
- Rhines, Peter B.; Young, William R.
- Journal of Fluid Mechanics, Vol. 122, Issue -1
Mesoscopic Transport Events and the Breakdown of Fick’s Law for Turbulent Fluxes
journal, September 2018
- Hahm, T. S.; Diamond, P. H.
- Journal of the Korean Physical Society, Vol. 73, Issue 6
Finding the Elusive Staircase in Magnetized Plasmas
journal, February 2015
- Dif-Pradalier, G.; Hornung, G.; Ghendrih, Ph.
- Physical Review Letters, Vol. 114, Issue 8
Turbulent-driven low-frequency sheared E × B flows as the trigger for the H-mode transition
journal, July 2013
- Tynan, G. R.; Xu, M.; Diamond, P. H.
- Nuclear Fusion, Vol. 53, Issue 7
Multiple Jets as PV Staircases: The Phillips Effect and the Resilience of Eddy-Transport Barriers
journal, March 2008
- Dritschel, D. G.; McIntyre, M. E.
- Journal of the Atmospheric Sciences, Vol. 65, Issue 3
A comparison of adaptive software for 1D parabolic PDEs
journal, August 2004
- Wang, Rong; Keast, Patrick; Muir, Paul
- Journal of Computational and Applied Mathematics, Vol. 169, Issue 1
Magnetohydrodynamic Turbulence Revisited
journal, August 1997
- Goldreich, P.; Sridhar, S.
- The Astrophysical Journal, Vol. 485, Issue 2
Zonal flow as pattern formation
journal, October 2013
- Parker, Jeffrey B.; Krommes, John A.
- Physics of Plasmas, Vol. 20, Issue 10
Theory of the spatiotemporal dynamics of transport bifurcations
journal, April 1997
- Lebedev, V. B.; Diamond, P. H.
- Physics of Plasmas, Vol. 4, Issue 4
Zonal flows and pattern formation
journal, July 2015
- Gürcan, Ö D.; Diamond, P. H.
- Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue 29
Eddy Motion in the Atmosphere
journal, January 1915
- Taylor, G. I.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 215, Issue 523-537
On the validity of the local diffusive paradigm in turbulent plasma transport
journal, August 2010
- Dif-Pradalier, G.; Diamond, P. H.; Grandgirard, V.
- Physical Review E, Vol. 82, Issue 2
Nonperturbative mean-field theory for minimum enstrophy relaxation
journal, May 2015
- Hsu, Pei-Chun; Diamond, P. H.; Tobias, S. M.
- Physical Review E, Vol. 91, Issue 5
Self-organization of electrostatic turbulence in a cylindrical plasma
journal, October 1987
- Hasegawa, Akira; Wakatani, Masahiro
- Physical Review Letters, Vol. 59, Issue 14
Pseudo-three-dimensional turbulence in magnetized nonuniform plasma
journal, January 1978
- Hasegawa, Akira; Mima, Kunioki
- Physics of Fluids, Vol. 21, Issue 1
How mesoscopic staircases condense to macroscopic barriers in confined plasma turbulence
journal, November 2016
- Ashourvan, Arash; Diamond, P. H.
- Physical Review E, Vol. 94, Issue 5
Drift hole structure and dynamics with turbulence driven flows
journal, July 2012
- Kosuga, Y.; Diamond, P. H.
- Physics of Plasmas, Vol. 19, Issue 7
Turbulence in a strongly stratified fluid—is it unstable?
journal, January 1972
- Phillips, O. M.
- Deep Sea Research and Oceanographic Abstracts, Vol. 19, Issue 1
Dynamics of interfaces and layers in a stratified turbulent fluid
journal, January 1998
- Balmforth, N. J.; Llewellyn Smith, Stefan G.; Young, W. R.
- Journal of Fluid Mechanics, Vol. 355
A review of theories of the L-H transition
journal, December 1999
- Connor, J. W.; Wilson, H. R.
- Plasma Physics and Controlled Fusion, Vol. 42, Issue 1
Analytic theory of L→H transition, barrier structure, and hysteresis for a simple model of coupled particle and heat fluxes
journal, December 2008
- Malkov, M. A.; Diamond, P. H.
- Physics of Plasmas, Vol. 15, Issue 12
On the emergence of macroscopic transport barriers from staircase structures
journal, January 2017
- Ashourvan, Arash; Diamond, P. H.
- Physics of Plasmas, Vol. 24, Issue 1
Introduction to Drift Wave Turbulence Modelling
journal, February 2008
- Garbet, X.
- Fusion Science and Technology, Vol. 53, Issue 2T
Jets
journal, June 1994
- Rhines, Peter B.
- Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 4, Issue 2
Zonal flows in plasma—a review
journal, April 2005
- Diamond, P. H.; Itoh, S-I; Itoh, K.
- Plasma Physics and Controlled Fusion, Vol. 47, Issue 5
Role of Zonal Flow Predator-Prey Oscillations in Triggering the Transition to H-Mode Confinement
journal, April 2012
- Schmitz, L.; Zeng, L.; Rhodes, T. L.
- Physical Review Letters, Vol. 108, Issue 15
Spatial Localization in Dissipative Systems
journal, March 2015
- Knobloch, E.
- Annual Review of Condensed Matter Physics, Vol. 6, Issue 1
Effects of E×B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices
journal, May 1997
- Burrell, K. H.
- Physics of Plasmas, Vol. 4, Issue 5
Thermal confinement bifurcation and the L‐ to H‐mode transition in tokamaks
journal, March 1991
- Hinton, F. L.
- Physics of Fluids B: Plasma Physics, Vol. 3, Issue 3
Zonostrophic Instability
journal, May 2012
- Srinivasan, Kaushik; Young, W. R.
- Journal of the Atmospheric Sciences, Vol. 69, Issue 5
Regime of Improved Confinement and High Beta in Neutral-Beam-Heated Divertor Discharges of the ASDEX Tokamak
journal, November 1982
- Wagner, F.; Becker, G.; Behringer, K.
- Physical Review Letters, Vol. 49, Issue 19
Wave-number spectrum of dissipative drift waves and a transition scale
journal, September 2015
- Ghantous, K.; Gürcan, Ö. D.
- Physical Review E, Vol. 92, Issue 3
Scaling laws and Diffuse Locality of Balanced and Imbalanced Magnetohydrodynamic Turbulence
journal, September 2010
- Beresnyak, A.; Lazarian, A.
- The Astrophysical Journal, Vol. 722, Issue 1
Waves and turbulence on a beta-plane
journal, June 1975
- Rhines, Peter B.
- Journal of Fluid Mechanics, Vol. 69, Issue 3
Works referencing / citing this record:
Scale selection and feedback loops for patterns in drift wave-zonal flow turbulence
journal, August 2019
- Guo, Weixin; Diamond, Patrick H.; Hughes, David W.
- Plasma Physics and Controlled Fusion, Vol. 61, Issue 10