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The response of the quasi-biennial oscillation (QBO) to an imposed mean upwelling with a periodic modulation is studied, by modeling the dynamics of the zero wind line at the equator using a class of equations known as descent rate models. These are simple mathematical models that capture the essence of QBO synchronization by focusing on the dynamics of the height of the zero wind line. A heuristic descent rate model for the zero wind line is described and is shown to capture many of the synchronization features seen in previous studies of the QBO. It is then demonstrated using a simple transformation that the standard Holton–Lindzen model of the QBO can itself be put into the form of a descent rate model if a quadratic velocity profile is assumed below the zero wind line. The resulting nonautonomous ordinary differential equation captures much of the synchronization behavior observed in the full Holton–Lindzen partial differential equation. The new class of models provides a novel framework within which to understand synchronization of the QBO, and we demonstrate a close relationship between these models and the circle map well known in the mathematics literature. Finally, we analyze reanalysis datasets to validate some of the predictions of our descent rate models and find statistically significant evidence for synchronization of the QBO that is consistent with model behavior.

Jupiter’s turbulent weather layer contains phenomena of many different sizes, from local storms up to the Great Red Spot and banded jets. The global circulation is driven by complex interactions with (as yet uncertain) small-scale processes. We have calculated structure functions and kinetic energy spectral fluxes from Cassini observations over a wide range of length scales in Jupiter’s atmosphere. We found evidence for an inverse cascade of kinetic energy from length scales comparable to the first baroclinic Rossby deformation radius up to the global jet scale, but also a forward cascade of kinetic energy from the deformation radius to smaller scales. This second result disagrees with the traditional picture of Jupiter’s atmospheric dynamics, but has some similarities with mesoscale phenomena in the Earth’s atmosphere and oceans. We conclude that the inverse cascade driving Jupiter’s jets may have a dominant energy source at scales close to the deformation radius, such as baroclinic instability. The Jovian atmosphere is highly turbulent due to processes happening on a wide range of length scales. Cassini spacecraft data now suggest the presence of kinetic energy cascades over different length scales — a likely origin of Jupiter’s turbulence.

The weather layers of the gas giant planets, Jupiter and Saturn, comprise the shallow atmospheric layers that are influenced energetically by a combination of incoming solar radiation and localised latent heating of condensates, as well as by upwelling heat from their planetary interiors. They are also the most accessible regions of those planets to direct observations. Recent analyses in Oxford of cloud-tracked winds on Jupiter have demonstrated that kinetic energy is injected into the weather layer at scales comparable to the Rossby radius of deformation and cascades both upscale, mostly into the extra-tropical zonal jets, and downscale to the smallest resolvable scales in Cassini images. The large-scale flow on both Jupiter and Saturn appears to equilibrate towards a state which is close to marginal instability according to Arnol’d’s 2nd stability theorem. This scenario is largely reproduced in a hierarchy of numerical models of giant planet weather layers, including relatively realistic models which seek to predict thermal and dynamical structures using a full set of parameterisations of radiative transfer, interior heat sources and even moist convection. Such models include (amongst others) the Jason GCM, developed in Oxford, which also represents the formation of (energetically passive) clouds of NH3, NH4SH and H2O condensates and the transport of condensable tracers. Recent results show some promise in comparison with observations from the Cassini and Juno missions, but some observed features (such as Jupiter’s Great Red Spot and other compact ovals) are not yet captured spontaneously by most weather layer models. We review recent work in this vein and discuss a number of open questions for future study.

This paper describes laboratory observations of inertia–gravity waves emitted from balanced fluid flow. In a rotating two-layer annulus experiment, the wavelength of the inertia–gravity waves is very close to the deformation radius. Their amplitude varies linearly with Rossby number in the range 0.05–0.14, at constant Burger number (or rotational Froude number). This linear scaling challenges the notion, suggested by several dynamical theories, that inertia–gravity waves generated by balanced motion will be exponentially small. It is estimated that the balanced flow leaks roughly 1% of its energy each rotation period into the inertia–gravity waves at the peak of their generation. The findings of this study imply an inevitable emission of inertia–gravity waves at Rossby numbers similar to those of the large-scale atmospheric and oceanic flow. Extrapolation of the results suggests that inertia–gravity waves might make a significant contribution to the energy budgets of the atmosphere and ocean. In particular, emission of inertia–gravity waves from mesoscale eddies may be an important source of energy for deep interior mixing in the ocean.

The global superrotation index S compares the integrated axial angular momentum of the atmosphere to that of a state of solid-body corotation with the underlying planet. The index S is similar to a zonal Rossby number, which suggests it may be a useful indicator of the circulation regime occupied by a planetary atmosphere. We investigate the utility of S for characterizing regimes of atmospheric circulation by running idealized Earthlike general circulation model experiments over a wide range of rotation rates Ω, 8Ω E to Ω E /512, where Ω E is Earth’s rotation rate, in both an axisymmetric and three-dimensional configuration. We compute S for each simulated circulation, and study the dependence of S on Ω. For all rotation rates considered, S is on the same order of magnitude in the 3D and axisymmetric experiments. For high rotation rates, S ≪ 1 and S ∝ Ω −2 , while at low rotation rates S ≈ 1/2 = constant. By considering the limiting behavior of theoretical models for S , we show how the value of S and its local dependence on Ω can be related to the circulation regime occupied by a planetary atmosphere. Indices of S ≪ 1 and S ∝ Ω −2 define a regime dominated by geostrophic thermal wind balance, and S ≈ 1/2 = constant defines a regime where the dynamics are characterized by conservation of angular momentum within a planetary-scale Hadley circulation. Indices of S ≫ 1 and S ∝ Ω −2 define an additional regime dominated by cyclostrophic balance and strong equatorial superrotation that is not realized in our simulations.

We present a numerical study of axisymmetric flow in a rotating annulus in which local thermal forcing, via a heated annular ring on the outside of the base and a cooled circular disk in the centre of the top surface, drives convection. This new configuration is a variant of the classical thermally-driven annulus, where uniform heating and cooling are applied through the outer and inner sidewalls respectively. The annulus provides an analogue to a planetary circulation and the new configuration, with its more relaxed vertical thermal boundary conditions, is expected to better emulate vigorous convection in the tropics and polar regions as well as baroclinic instability in the mid-latitude baroclinic zone. Using the Met Office/Oxford Rotating Annulus Laboratory (MORALS) code, we have investigated a series of equilibrated, two dimensional axisymmetric flows across a large region of parameter space. These are characterized in terms of their velocity and temperature fields. When rotation is applied several distinct flow regimes may be identified for different rotation rates and strengths of differential heating. These regimes are defined as a function of the ratio of the horizontal Ekman layer thickness to the non-rotating thermal boundary layer thickness and are found to be similar to those identified in previous annulus experiments. Convection without rotation is also considered and the scaling of the heat transport with Rayleigh number is calculated. This is then compared with existing work on the classical annulus as well as horizontal and Rayleigh-Bénard convection. As with previous studies on both rotating and non-rotating convection the system’s behaviour is found to be aspect ratio dependent. This dependence is seen in the scaling of the non-rotating Nusselt number and in transitions between regimes in the rotating case although further investigation is required to fully explain these observations.

Three-dimensional direct numerical simulations (DNS) of the nonlinear dynamics and a route to chaos in a rotating fluid subjected to lateral heating are presented here and discussed in the context of laboratory experiments in the baroclinic annulus. Following two previous preliminary studies, the fluid used is air rather than a liquid as used in all other previous work. This study investigates a bifurcation sequence from the axisymmetric flow to a number of complex flows. The transition sequence, on increase of the rotation rate, from the axisymmetric solution via a steady fully developed baroclinic wave to chaotic flow, followed a variant of the classical quasi-periodic bifurcation route, starting with a subcritical Hopf and associated saddle-node bifurcation. This was followed by a sequence of two supercritical Hopf-type bifurcations, first to an amplitude vacillation, then to a three-frequency quasi-periodic modulated amplitude vacillation (MAV), and finally to a chaotic (MAV). In the context of the baroclinic annulus this sequence is unusual as the vacillation is usually found on decrease of the rotation rate from the steady wave flow. Further transitions of a steady wave with a higher wavenumber pointed to the possibility that a barotropic instability of the sidewall boundary layers and the subsequent breakdown of these barotropic vortices may play a role in the transition to structural vacillation and, ultimately, geostrophic turbulence.

The non-axisymmetric structure of an unstable Stewartson shear layer generated via a differential rotation between flush disks and a cylindrical enclosure is investigated numerically using both three-dimensional direct numerical simulation and a quasi-two-dimensional model. Previous literature has only considered the depth-independent quasi-two-dimensional model due to its low computational cost. The three-dimensional model implemented here highlights the supercritical instability responsible for the polygonal deformation of the shear layer in the linear and nonlinear growth regimes and reveals that linear stability analysis is capable of accurately determining the preferred azimuthal wavenumber for flow conditions near the onset of instability. This agreement is lost for sufficiently forced flows where nonlinear effects encourage the coalescence of vortices towards lower-wavenumber structures. Time-dependent flows are found for large Reynolds numbers defined based on the Stewartson layer thickness and azimuthal velocity differential. However, this temporal behaviour is not solely characterized by Reynolds number but is rather a function of both the Rossby and Ekman numbers. At high Ekman and Rossby numbers, unsteady flow emerges through a small-scale azimuthal destabilization of the axial jets within the Stewartson layers; at low Ekman numbers, unsteady flow emerges through a modulation in the strength of one of the axial vortices rolled up by non-axisymmetric instability of the Stewartson layer.

Saturn's slow seasonal evolution was disrupted in 2010–2011 by the eruption of a bright storm in its northern spring hemisphere. Thermal infrared spectroscopy showed that within a month, the resulting planetary-scale disturbance had generated intense perturbations of atmospheric temperatures, winds, and composition between 20° and 50°N over an entire hemisphere (140,000 kilometers). The tropospheric storm cell produced effects that penetrated hundreds of kilometers into Saturn's stratosphere (to the 1-millibar region). Stratospheric subsidence at the edges of the disturbance produced \"beacons\" of infrared emission and longitudinal temperature contrasts of 16 kelvin. The disturbance substantially altered atmospheric circulation, transporting material vertically over great distances, modifying stratospheric zonal jets, exciting wave activity and turbulence, and generating a new cold anticyclonic oval in the center of the disturbance at 41°N.

The banded organization of clouds and zonal winds in the atmospheres of the outer planets has long fascinated observers. Several recent studies in the theory and idealized modeling of geostrophic turbulence have suggested possible explanations for the emergence of such organized patterns, typically involving highly anisotropic exchanges of kinetic energy and vorticity within the dissipationless inertial ranges of turbulent flows dominated (at least at large scales) by ensembles of propagating Rossby waves. The results from an attempt to reproduce such conditions in the laboratory are presented here. Achievement of a distinct inertial range turns out to require an experiment on the largest feasible scale. Deep, rotating convection on small horizontal scales was induced by gently and continuously spraying dense, salty water onto the free surface of the 13-m-diameter cylindrical tank on the Coriolis platform in Grenoble, France. A “planetary vorticity gradient” or “β effect” was obtained by use of a conically sloping bottom and the whole tank rotated at angular speeds up to 0.15 rad s−1. Over a period of several hours, a highly barotropic, zonally banded large-scale flow pattern was seen to emerge with up to 5–6 narrow, alternating, zonally aligned jets across the tank, indicating the development of an anisotropic field of geostrophic turbulence. Using particle image velocimetry (PIV) techniques, zonal jets are shown to have arisen from nonlinear interactions between barotropic eddies on a scale comparable to either a Rhines or “frictional” wavelength, which scales roughly as (β/Urms)−1/2. This resulted in an anisotropic kinetic energy spectrum with a significantly steeper slope with wavenumber k for the zonal flow than for the nonzonal eddies, which largely follows the classical Kolmogorov k−5/3 inertial range. Potential vorticity fields show evidence of Rossby wave breaking and the presence of a “hyperstaircase” with radius, indicating instantaneous flows that are supercritical with respect to the Rayleigh–Kuo instability criterion and in a state of “barotropic adjustment.” The implications of these results are discussed in light of zonal jets observed in planetary atmospheres and, most recently, in the terrestrial oceans.