Multiple Zonal Jets in a Differentially Heated Rotating Annulus

Abstract

A laboratory experiment of multiple baroclinic zonal jets is described, thought to be dynamically similar to flow observed in the Antarctic Circumpolar Current. Differential heating sets the overall temperature difference and drives unstable baroclinic flow, but the circulation is free to determine its own structure and local stratification; experiments were run to a stationary state and extend the dynamical regime of previous experiments. A topographic analog to the planetary β effect is imposed by the gradient of fluid depth with radius supplied by a sloping bottom and a parabolic free surface. New regimes of a low thermal Rossby number (RoT ~ 10−3) and high Taylor number (Ta ~ 1011) are explored such that the deformation radius Lρ is much smaller than the annulus gap width L and similar to the Rhines length. Multiple jets emerge in rough proportion to the smallness of the Rhines scale, relatively insensitive to the Taylor number; a regime diagram taking the β effect into account better reflects the emergence of the jets. Eddy momentum fluxes are consistent with an active role in maintaining the jets, and jet development appears to follow the Vallis and Maltrud phenomenology of anisotropic wave–turbulence interaction on a β plane. Intermittency and episodes of coherent meridional jet migration occur, especially during spinup.

A laboratory model for deep-seated jets on the gas giants

“…This small-scale turbulence is analogous to the convective turbulence that exists in deep planetary interiors 18,19 and constitutes an appropriate source of energy to supply deep jets 20 . Inspired by several preceding experimental attempts [10][11][12][13][14]21,22 this laboratory device bridges the gap to the planetary 'zonostrophic' regime and suggests the possibility of deep-seated jets on the gas planets.In natural settings, zonal jets develop from rapidly rotating turbulence in the presence of strong boundary curvature 23 . In particular, the Coriolis force must dominate the fluid's inertia (that is, low Rossby number Ro), which, in turn, must dominate the viscous dissipative effects (large Reynolds number Re and small Ekman number E) (see Supplementary Table 1).…”

“…This small-scale turbulence is analogous to the convective turbulence that exists in deep planetary interiors 18,19 and constitutes an appropriate source of energy to supply deep jets 20 . Inspired by several preceding experimental attempts [10][11][12][13][14]21,22 this laboratory device bridges the gap to the planetary 'zonostrophic' regime and suggests the possibility of deep-seated jets on the gas planets.…”

Complex environmental <i>β</i>-plane turbulence: laboratory experiments with altimetric imaging velocimetry

“…A classic model for a baroclinically unstable system is a rotating annulus where heating/cooling is provided at the outer wall/centre of the tank respectively. Different aspects of the dynamics of this system were studied in a number of experiments (Hide and Mason, 1975;Mason, 1975;Read, 1997, 1998;Wordsworth et al, 2008;Smith et al, 2014 Matulka and Afanasyev (2015). It was shown that the meridional scale of the jets is determined to a large extent by the radius of deformation and, at the same time, is in good agreement with the Rhines scale (Rhines, 1975).…”

The Dynamics of Baroclinic Zonal Jets*

“…These experiments used a gamma effect, with small-scale turbulence excited by electromagnetic Lorentz forces associated with a horizontal array of permanent magnets. Most recently, Smith et al (2014) identified multiple zonal jets in a differentially heated rotating annulus with an inner radius of 20.0 cm and an outer radius of 48.75 cm. This experiment used both a topographic beta effect and a gamma effect, with geostrophic turbulence excited by baroclinic instability.…”

“…There was clear evidence of zonal jet formation on the Rhines scale, although the jets meandered substantially and occasionally split and merged, unlike the relatively steady jets on Jupiter and Saturn. Most numerical and laboratory studies to date have focused on the special case of jets that are barotropic [see Lee (2005) and Smith et al (2014) for exceptions]. However, the planetary atmospheres and oceans that exhibit multiple alternating zonal jets are stratified fluids, with a spectrum of excited baroclinic modes in addition to the barotropic mode.…”