Zonostrophic Beta-plumes, Breaking Waves and Zonal Jets in
Locally-forced, Large-Scale Shallow Water Experiments
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 ~
(Πε/β3)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.