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Dynamics of potential vorticity staircase evolution and step mergers in a reduced model of beta-plane turbulence

M. A. Malkov1 and P. H. Diamond1,2

  • 1CASS and Department of Physics, University of California, San Diego, California 92093, USA
  • 2Center for Fusion Sciences, Southwestern Institute of Physics, Chengdu, Sichuan 610041, People's Republic of China

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Phys. Rev. Fluids 4, 044503 – Published 22 April, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.044503

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, ɛ. 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 ɛ-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. 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.

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Phys. Rev. Fluids 4, 044503– Published 22 April, 2019
  • Received 30 November 2018
Article part of CHORUS
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