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Zonostrophic Beta-plumes, Breaking Waves and Zonal Jets in Locally-forced, Large-Scale Shallow Water Experiments
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  • Peter Read,
  • Roland Young,
  • Hélène Scolan,
  • Enrico Ferrero,
  • Boris Galperin,
  • Federica Ive,
  • Massimilano Manfrin,
  • Stefania Espa,
  • Simon Cabanes
Peter Read
University of Oxford

Corresponding Author:[email protected]

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Roland Young
UAE University
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Hélène Scolan
Université Lyon, Université Claude Bernard Lyon 1, Ecole Centrale de Lyon, INSA Lyon, CNRS
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Enrico Ferrero
Università del Piemonte Orientale
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Boris Galperin
University of South Florida St. Petersburg
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Federica Ive
Università degli Studi di Torino
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Massimilano Manfrin
Università degli Studi di Torino
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Stefania Espa
Sapienza Università di Roma
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Simon Cabanes
Sapienza Università di Roma
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Abstract

Eddy-driven zonal jets and Rossby waves are common features of planetary atmospheres and oceans, organising the large-scale flow and influencing the dispersion and transport of material tracers and constituents. In the presence of relatively weak friction and forcing, zonal jets form a dominant component of the flow in a regime known as “zonostrophic”, characterized by strongly anisotropic energy spectra and the formation of slowly evolving systems of alternating zonal jets. This regime is characterized by two scales, Lβ ~ (Πε3)1/5 and LR ~ (Urms/β)1/2, where Πε is the transfer rate of the inverse energy cascade and β is the radial gradient of the Coriolis parameter. Their ratio is known as the zonostrophy index, Rβ = LR/Lβ. Zonal jets become discernible at Rβ ≥ 1.5 but are much stronger for Rβ > 2. Achieving such high values of Rβ in a laboratory is non-trivial, however. The atmospheres of gas giant planets are probably well within such a regime with Rβ ~ 5 [Galperin et al. Icarus 2014], though the Earth’s atmosphere and oceans are in a more friction-dominated state where Rβ ~ 1.5 – 1.8. In this study we have investigated the flow obtained in a rapidly rotating fluid on a topographic beta-plane in a cylindrical tank, subject to localised, periodic mechanical forcing along a radius. The experiments were carried out in the 5 m diameter rotating tank at the Turlab facility in Turin, Italy under the European High-Performance Infrastructures in Turbulence (EUHiT) programme. Velocity measurements were obtained using PIV in a horizontal plane a short distance below the free surface, while discrete particles floating on the surface were tracked to obtained their Lagrangian trajectories. The flow exhibited the spontaneous formation of persistent zonal jets, nonlinear topographic Rossby waves and intense vortical eddies (see image below). The large-scale flow was found to lie within the zonostrophic regime with Rβ ≥ 2.4. Diagnostics indicate the presence of an anisotropic dual (inverse/direct) KE cascade. The KE spectrum, however, seems unexpectedly consistent with recent f-plane turbulence models based on Quasi-Normal Scale Elimination [Galperin & Sukoriansky Phys. Rev. Fluids 2020], the implications of which will be discussed in the presentation.