Large Rossby Number Research Articles

Dynamics of a stratified vortex under the complete Coriolis force: two-dimensional three-components evolution

We study the dynamics of an initially axisymmetric and vertical Lamb–Oseen vortex in a stratified-rotating fluid under the complete Coriolis force on the $f$ plane, i.e. in the presence of a background rotation both along the vertical and horizontal directions. By a combination of direct numerical simulations and asymptotic analyses for small horizontal background rotation, we show that a critical layer appears at the radius where the angular velocity of the vortex is equal to the buoyancy frequency when the Froude number is larger than unity. This critical layer generates a vertical velocity that is invariant along the vertical and which first increases linearly with time and then saturates at an amplitude scaling like $Re^{1/3}/\widetilde{Ro}$ , where $Re$ is the Reynolds number and $\widetilde {Ro}$ the non-traditional Rossby number based on the horizontal component of the background rotation. In turn, a quasi-axisymmetric anomaly of vertical vorticity is produced at the critical radius through the non-traditional Coriolis force. Below a critical $\widetilde {Ro}$ depending on $Re$ , the Rayleigh's inflectional criterion is satisfied and a shear instability is subsequently triggered rendering the vertical vorticity fully non-axisymmetric. The decay of the angular velocity is then enhanced until it is everywhere lower than the buoyancy frequency. A theoretical criterion derived from the Rayleigh condition predicts well the instability. It shows that this phenomenon can occur even for a large non-traditional Rossby number $\widetilde {Ro}$ for large $Re$ . Hence, the non-traditional Coriolis force might have much more impact on geophysical vortices than anticipated by considering the order of magnitude of $\widetilde {Ro}$ .

On the spinup and spreadout of a Cartesian gravity current on a slope in a rotating system

Ocean gravity currents flow along the inclined ocean floor for long times compared to the planet's rotation period. Their shape and motion is governed by the gravity buoyancy, Coriolis acceleration and friction-induced Ekman-layer spinup circulation. In order to understand this process, we consider the flow of a dense-fluid Boussinesq gravity current of fixed volume over an inclined bottom in a rotating system, in the framework of Cartesian 2.5-dimensional geometry (no dependency on the lateral direction $y$ , but with a non-trivial $y$ -component velocity $v$ due to Coriolis coupling with the main $u$ along the bottom $x$ ). After release from rest in a lock (co-rotating, with two gates creating propagation in ${\pm }x$ -directions), the current forms a quasi-steady geostrophic ‘vein’ of parabolic height profile with a significant lateral velocity $v$ . Subsequently, a spinup process, driven by the Ekman layers on the bottom and interface, appears and prevails for many revolutions, during which $v$ decays and the shape of the interface changes dramatically. We investigate the spinup motion, using an approximate model, for the case of large Rossby number, small Ekman number and small slope $\gamma$ (relevant to oceanic currents). We show that the initial shape of the natural geostrophic vein can be calculated rigorously (not an arbitrary parabola), and the initial lateral velocity $v(x,t=0)$ is counter-rotation about a fixed point (pivot) $x_{\rm \pi}$ at which $v(x_{\rm \pi},t) =0$ (at the beginning and during spinup). This point is placed excentrically, in the upper part, and this excentre, $\propto \gamma$ , plays a significant role in the process. The spinup in a rigid container is developed as the prototype process; an essential component is the edge (outer wall) where the flux of the Ekman layer is arrested (and then returned to the centre via the inviscid core). While the upper part of the vein adopts this spinup pattern, the lower part (most of the vein, $x< x_{\rm \pi}$ ) develops a leak (drainage) at the edge that (a) modifies the spinup of the vein, and (b) generates a thin tail extension downslope. The tail consists of two merged non-divergent Ekman layers, which chokes the drainage flow rate. The present model provides clear-cut insights and some quantitative predictions of the major spinup stage by analytical algebraic solutions. A comparison with a previously published simple model (Wirth, Ocean Dyn., vol. 59, 2009, pp. 551–563) is presented. We also discuss briefly stability of the initial vein.

Non-Linear Processes in the Gironde River Plume (North-East Atlantic): Instabilities and Mixing

Instability and mixing are ubiquitous processes in river plumes but their small spatial and temporal scales often limit their observation and analysis. We investigate flow instability and mixing processes in the Gironde river plume (Bay of Biscay, North-East Atlantic ocean) in response to air-sea fluxes, tidal currents, and winds. High-resolution numerical simulations are conducted in March (average river discharge) and in August (low discharge) to explore such processes. Two areas of the Gironde river plume (the bulge and the coastal current) experience different instabilities: barotropic, baroclinic, symmetric, and/or vertical shear instabilities. Energy conversion terms reveal the coexistence of barotropic and baroclinic instabilities in the bulge and in the coastal current during both months. These instabilities are intensified over the whole domain in August and over the inner-shelf in March. The Hoskins criterion indicates that symmetric instability exists in most parts of the plume during both periods. The evolution of the Gironde plume with the summer stratification, tidal currents and winds favors its development. During both seasons, ageostrophic flow and large Rossby numbers characterize rapidly-growing and small-scale frontal baroclinic and symmetric instabilities. The transition between these instabilities is investigated with an EKE decomposition on the modes of instability. In the frontal region of the plume, during both months, symmetric instabilities grow first followed by baroclinic and mixed ones, during wind bursts and/or high discharge events. In contrast, when the wind is weak or relaxing, baroclinic instabilities grow first followed by symmetric and then mixed ones. Their growth periods range from a few hours to a few days. Mixing at the ocean surface is analyzed via Potential Vorticity (PV) fluxes. The net injection of PV at the ocean surface occurs at submesoscale buoyant fronts of the Gironde plume during both months. Vertical mixing at these fronts has similar magnitude as the wind-driven and surface buoyancy fluxes. During both months, the frontal region of the plume is restratified during wind relaxation events and/or high river discharge events through frontogenetic processes. Conversely, wind bursts destratify the frontal plume interior through non-conservative PV fluxes.

Estimating Ocean Surface Currents With Machine Learning

Global surface currents are usually inferred from directly observed quantities like sea-surface height, wind stress by applying diagnostic balance relations (like geostrophy and Ekman flow), which provide a good approximation of the dynamics of slow, large-scale currents at large scales and low Rossby numbers. However, newer generation satellite altimeters (like the upcoming SWOT mission) will capture more of the high wavenumber variability associated with the unbalanced components, but the low temporal sampling can potentially lead to aliasing. Applying these balances directly may lead to an incorrect un-physical estimate of the surface flow. In this study we explore Machine Learning (ML) algorithms as an alternate route to infer surface currents from satellite observable quantities. We train our ML models with SSH, SST, and wind stress from available primitive equation ocean GCM simulation outputs as the inputs and make predictions of surface currents (u,v), which are then compared against the true GCM output. As a baseline example, we demonstrate that a linear regression model is ineffective at predicting velocities accurately beyond localized regions. In comparison, a relatively simple neural network (NN) can predict surface currents accurately over most of the global ocean, with lower mean squared errors than geostrophy + Ekman. Using a local stencil of neighboring grid points as additional input features, we can train the deep learning models to effectively “learn” spatial gradients and the physics of surface currents. By passing the stenciled variables through convolutional filters we can help the model learn spatial gradients much faster. Various training strategies are explored using systematic feature hold out and multiple combinations of point and stenciled input data fed through convolutional filters (2D/3D), to understand the effect of each input feature on the NN's ability to accurately represent surface flow. A model sensitivity analysis reveals that besides SSH, geographic information in some form is an essential ingredient required for making accurate predictions of surface currents with deep learning models.

Observations of a Deep Submesoscale Cyclonic Vortex in the Arabian Sea

AbstractSubmesoscale coherent vortices (SCVs) are numerous in high‐resolution numerical simulations, but their observations are scarce. Among the few in situ available measurements of SCVs, a vast majority concern anticyclones. No cyclonic SCV with large dynamical Rossby number (|ζ/f| > 1) has ever been sampled. This suggested that such small cyclones may lack robustness. Here, we present in situ measurements of an intense cyclonic SCV in the Arabian Sea. This eddy lay at 600 m depth, with a Rossby number and a dynamical Rossby number |ζ/f| > 1.5. This cyclone was most likely generated at the mouth of the Gulf of Aden. It trapped and advected Red Sea Water, from there on. This highlights the role of deep SCVs in the spreading of salty waters across the Arabian Sea.

Assessment of Critical Convection and Associated Rotation States in Models of Sun-like Stars Including a Stable Layer

Abstract Recent numerical simulations of rotating stellar convection have suggested the possible existence of retrograde (slow equator, fast poles) or so-called antisolar differential rotation states in slowly rotating stars possessing a large Rossby number. We aim to understand whether such rotational states exist from the onset of convective instability or are the outcome of complex nonlinear interactions in the turbulent convective envelope. To this end, we have made a systematic linear analysis of the critical state of convection in a series of 15 numerical simulations published in Brun et al. We have assessed their degree of supercriticality and most-unstable mode properties, and computed the second-order mean zonal flow response. We find that none of the linear critical cases show a retrograde state at the onset of convection even when their nonlinear counterparts do. We also find that the presence of a stably stratified layer coupled to the convectively unstable upper layer leads to interesting gravity-wave excitation and angular momentum transport. We conclude that retrograde states of differential rotation are probably the outcome of complex mode–mode interactions in the turbulent convection layer and are, as a consequence, likely to exist in real stars.

Influence of Coriolis Force Upon Bottom Boundary Layers in a Large‐Scale Gravity Current Experiment: Implications for Evolution of Sinuous Deep‐Water Channel Systems

AbstractOceanic density currents in many deep‐water channels are strongly influenced by the Coriolis force. The dynamics of the bottom boundary layer in large geostrophic flows and low Rossby number turbidity currents are very important for determining the erosion and deposition of sediment in channelized contourite currents and many large‐scale turbidity currents. However, these bottom boundary layers are notoriously difficult to resolve with oceanic field measurements or in previous small‐scale rotating laboratory experiments. We present results from a large, 13‐m diameter, rotating laboratory platform that is able to achieve both stratified and highly turbulent flows in regimes where the rotation is sufficiently rapid that the Coriolis force can potentially dominate. By resolving the dynamics of the turbulent bottom boundary in straight and sinuous channel sections, we find that the Coriolis force can overcome centrifugal force to switch the direction of near‐bed flows in channel bends. This occurs for positive Rossby numbers less than +0.8, defined as RoR = /Rf, where is the depth and time‐averaged velocity, R is the radius of channel curvature, and f is the Coriolis parameter. Density and velocity fields decoupled in channel bends, with the densest fluid of the gravity current being deflected to the outer bend of the channel by the centrifugal force, while the location of velocity maximum shifted with the Coriolis force, leading to asymmetries between left‐ and right‐turning bends. These observations of Coriolis effects on gravity currents are synthesized into a model of how sedimentary structures might evolve in sinuous turbidity current channels at various latitudes.

Energetic Submesoscale Dynamics in the Ocean Interior

AbstractSubmesoscale ocean processes, characterized by order-1 Rossby and Richardson numbers, are currently thought to be mainly confined to the ocean surface mixed layer, whereas the ocean interior is commonly assumed to be in quasigeostrophic equilibrium. Here, a realistic numerical simulation in the Antarctic Circumpolar Current, with a 1/48° horizontal resolution and tidal forcing, is used to demonstrate that the ocean interior departs from the quasigeostrophic regime down to depths of 900 m, that is, well below the mixed layer. Results highlight that, contrary to the classical paradigm, the ocean interior is strongly ageostrophic, with a pronounced cyclone–anticyclone asymmetry and a dominance of frontogenesis over frontolysis. Numerous vortices and filaments, from the surface down to 900 m, are characterized by large Rossby and low Richardson numbers, strong lateral gradients of buoyancy, and vigorous ageostrophic frontogenesis. These deep submesoscales fronts are only weakly affected by internal gravity waves and drive intense upward vertical heat fluxes, consistent with recent observations in the Antarctic Circumpolar Current and the Gulf Stream. As such, deep submesoscale fronts are an efficient pathway for the transport of heat from the ocean interior to the surface, suggesting the presence of an intensified oceanic restratification at depth.

The Impact of Metallicity on the Evolution of the Rotation and Magnetic Activity of Sun-like Stars

Abstract The rotation rates and magnetic activity of Sun-like and low-mass (≲1.4M ⊙) main-sequence stars are known to decline with time, and there now exist several models for the evolution of rotation and activity. However, the role that chemical composition plays during stellar spin-down has not yet been explored. In this work, we use a structural evolution code to compute the rotational evolution of stars with three different masses (0.7, 1.0, and 1.3 M ⊙) and six different metallicities, ranging from [Fe/H] = −1.0 to [Fe/H] = +0.5. We also implement three different wind-braking formulations from the literature (two modern and one classical) and compare their predictions for rotational evolution. The effect that metallicity has on stellar structural properties, and in particular the convective turnover timescale, leads the two modern wind-braking formulations to predict a strong dependence of the torque on metallicity. Consequently, they predict that metal-rich stars spin down more effectively at late ages (≳1 Gyr) than metal-poor stars, and the effect is large enough to be detectable with current observing facilities. For example, the formulations predict that a Sun-like (solar-mass and solar-aged) star with [Fe/H] = −0.3 will have a rotation period of less than 20 days. Even though old, metal-poor stars are predicted to rotate more rapidly at a given age, they have larger Rossby numbers and are thus expected to have lower magnetic activity levels. Finally, the different wind-braking formulations predict quantitative differences in the metallicity dependence of stellar rotation, which may be used to test them.

Baroclinic Instability with a Simple Model for Vertical Mixing

AbstractHere, we examine baroclinic instability in the presence of vertical mixing in an idealized setting. Specifically, we use a simple model for vertical mixing of momentum and buoyancy and expand the buoyancy and vorticity in a series for small Rossby numbers. A flow in subinertial mixed layer (SML) balance (see the study by Young in 1994) exhibits a normal mode linear instability, which is studied here using linear stability analysis and numerical simulations. The most unstable modes grow by converting potential energy associated with the basic state into kinetic energy of the growing perturbations. However, unlike the inviscid Eady problem, the dominant energy balance is between the buoyancy flux and the energy dissipated by vertical mixing. Vertical mixing reduces the growth rate and changes the orientation of the most unstable modes with respect to the front. By comparing with numerical simulations, we find that the predicted scale of the most unstable mode matches the simulations for small Rossby numbers while the growth rate and orientation agree for a broader range of parameters. A stability analysis of a basic state in SML balance using the inviscid QG equations shows that the angle of the unstable modes is controlled by the orientation of the SML flow, while stratification associated with an advection/diffusion balance controls the size of growing perturbations for small Ekman numbers and/or large Rossby numbers. These results imply that baroclinic instability can be inhibited by small-scale turbulence when the Ekman number is sufficiently large and might explain the lack of submesoscale eddies in observations and numerical models of the ocean surface mixed layer during summer.

Do Non-dipolar Magnetic Fields Contribute to Spin-down Torques?

Abstract Main-sequence low-mass stars are known to spin down as a consequence of their magnetized stellar winds. However, estimating the precise rate of this spin-down is an open problem. The mass-loss rate, angular momentum loss rate, and magnetic field properties of low-mass stars are fundamentally linked, making this a challenging task. Of particular interest is the stellar magnetic field geometry. In this work, we consider whether non-dipolar field modes contribute significantly to the spin-down of low-mass stars. We do this using a sample of stars that have all been previously mapped with Zeeman–Doppler imaging. For a given star, as long as its mass-loss rate is below some critical mass-loss rate, only the dipolar fields contribute to its spin-down torque. However, if it has a larger mass-loss rate, higher-order modes need to be considered. For each star, we calculate this critical mass-loss rate, which is a simple function of the field geometry. Additionally, we use two methods of estimating mass-loss rates for our sample of stars. In the majority of cases, we find that the estimated mass-loss rates do not exceed the critical mass-loss rate; hence, the dipolar magnetic field alone is sufficient to determine the spin-down torque. However, we find some evidence that, at large Rossby numbers, non-dipolar modes may start to contribute.

Plumes in a rotating two-layer stratified fluid

Laboratory experiments are conducted to examine a descending plume in a rotating two-layer stratified ambient fluid such that the plume at the interface has moderate to large Rossby number. While the source fluid is more dense than the lower layer, the experiments are designed so that the mean density of the plume fluid impinging upon the interface is less than the lower layer density, as represented by a buoyancy parameter, $$\varLambda $$, being less than unity. In such cases, the discharged plume fluid spreads radially at the interface in the form of an intrusive gravity current at early times. At later times, this intrusion evolves to form an anticyclonic lens due to the influence of the Coriolis force. The measured radial position of the intrusion front, R(t), follows different power law relationships at early and late times during the spread of the intrusion: at early times when rotation does not play a significant role the power law exponent lies between 0.5 and 1.1; at late times when the intrusion acts as a rotationally influenced expanding lens the power law exponent ranges between 0.15 and 0.5, with generally smaller values for larger $$\varLambda $$. The plume fluid reaching the interface progressively increases in density due to re-entraining relatively dense fluid as the plume descends within the thickening lens. Consequently, the plume eventually penetrates through the interface and descends to the bottom of the tank. Faster rotation makes the lens thicker and hence increases the volume of the re-entrained lens-fluid, which decreases the time for the onset of penetration. The penetration time normalized by the rotation rate is found to hold a simple power law relationship with $$\varLambda $$.

Effects of weak planetary rotation on the stability and dynamics of internal stratified jets

This study explores the stability characteristics and nonlinear evolution of internal jets in rotating stratified fluids using a combination of direct numerical simulations and linear instability analyses. Our ultimate goal is the assessment of the potential impact of the Earth’s rotation on relatively small-scale structures, exemplified by turbulent wakes generated by propagating bluff objects in the ocean. We question the popular notion that ascribes a secondary role to the Coriolis effects in large Rossby number (Ro) systems. It is shown that the Earth’s rotation can substantially influence circulation patterns with Rossby numbers as high as Ro ∼ 103. Therefore, such effects must be taken into account in the numerical and theoretical models of finescale (∼10–100 m) processes in the ocean. We present a series of examples in which planetary rotation controls flows with large but finite values of Ro through centrifugal destabilization. These calculations reveal that centrifugal instabilities can affect fluid motion either directly, by modifying the basic state, or indirectly, by preferentially eliminating anticyclonic coherent vortices that form in the course of dynamic destabilization of jets. The results of this study have potentially significant geophysical implications in terms of elucidating mechanisms of energy cascade to progressively smaller scales. In the naval context, we anticipate that our investigation could influence the development of algorithms for detection and analysis of late wakes, generated by propagating submersibles in the ocean.

The Finite-Amplitude Evolution of Mixed Kelvin–Rossby Wave Instability and Equatorial Superrotation in a Shallow-Water Model and an Idealized GCM

Abstract An instability involving the resonant interaction of a Rossby wave and a Kelvin wave has been proposed to drive equatorial superrotation in planetary atmospheres with a substantially smaller radius or a smaller rotation rate than Earth, that is, with a large thermal Rossby number. To pursue this idea, this paper investigates the equilibration mechanism of Kelvin–Rossby instability by simulating the unforced initial-value problem in a shallow-water model and in a multilevel primitive equation model. Although the instability produces equatorward momentum fluxes in both models, only the multilevel model is found to superrotate. It is argued that the shortcoming of the shallow-water model is due to its difficulty in representing Kelvin wave breaking and dissipation, which is crucial for accelerating the flow in the tropics. In the absence of dissipation, the zonal momentum fluxed into the tropics is contained in the eddy contribution to the mass-weighted zonal wind rather than the zonal-mean zonal flow itself. In the shallow-water model, the zonal-mean zonal flow is only changed by the eddy potential vorticity flux, which is very small in our flow in the tropics and can only decelerate the flow in the absence of external vorticity stirring.

Gulf Stream Transport and Mixing Processes via Coherent Structure Dynamics

AbstractThe Gulf Stream has been characterized as either a barrier or blender to fluid transfer, a duality relevant to gyre‐scale climate adjustment. However, previous characterization depended on relatively sparse, Lagrangian in situ observations. The finite‐time Lyapunov exponent (FTLE) is calculated from satellite altimetry to identify Lagrangian coherent structures (LCS) in the Gulf Stream region. These LCS provide dense sampling of flow and capture distinct regions associated with mixing. Independent observations of ocean color contain similar flow‐dependent structures, providing verification of the method and highlighting transport and mixing processes that influence sea surface temperature and chlorophyll, among other water properties. Diagnosed LCS support the existing Bower kinematic model of the Gulf Stream, but also highlight novel behavior of comparable importance. These include vortex pinch‐off and formation of spiral eddies, clearly identified by LCS and which may be explained by considering changes to flow topology and the dynamics of shear‐flow instability at both small and large Rossby number. Such processes, seen though LCS, may further enable validation of climate models. The spatial distribution of these intermittent processes is characterized in terms of the criticality of jet dynamics with respect to Rossby wave propagation, and whether the jet is in an unstable or wave‐maker regime. The generation and connectivity of hyperbolic trajectories in the flow appears to play an important role in governing large‐scale transport and mixing across the Gulf Stream.

Enhanced Stellar Activity for Slow Antisolar Differential Rotation?

Abstract High-precision photometry of solar-like members of the open cluster M67 with Kepler/K2 data has recently revealed enhanced activity for stars with a large Rossby number, which is the ratio of rotation period to the convective turnover time. Contrary to the well established behavior for shorter rotation periods and smaller Rossby numbers, the chromospheric activity of the more slowly rotating stars of M67 was found to increase with increasing Rossby number. Such behavior has never been reported before, although it was theoretically predicted to emerge as a consequence of antisolar differential rotation (DR) for stars with Rossby numbers larger than that of the Sun, because in those models the absolute value of the DR was found to exceed that for solar-like DR. Using gyrochronological relations and an approximate age of 4 Gyr for the members of M67, we compare with computed rotation rates using just the B − V color. The resulting rotation–activity relation is found to be compatible with that obtained by employing the measured rotation rate. This provides additional support for the unconventional enhancement of activity at comparatively low rotation rates and the possible presence of antisolar differential rotation.

Wake of inertial waves of a horizontal cylinder in horizontal translation

We analyze theoretically and experimentally the wake behind a horizontal cylinder of diameter $d$ horizontally translated at constant velocity $U$ in a fluid rotating about the vertical axis at a rate $\Omega$. Using particle image velocimetry measurements in the rotating frame, we show that the wake is stabilized by rotation for Reynolds number ${\rm Re}=Ud/\nu$ much larger than in a non-rotating fluid. Over the explored range of parameters, the limit of stability is ${\rm Re} \simeq (275 \pm 25) / {\rm Ro}$, with ${\rm Ro}=U/2\Omega d$ the Rossby number, indicating that the stabilizing process is governed by the Ekman pumping in the boundary layer. At low Rossby number, the wake takes the form of a stationary pattern of inertial waves, similar to the wake of surface gravity waves behind a ship. We compare this steady wake pattern to a model, originally developed by [Johnson, J. Fluid Mech. 120, 359 (1982)], assuming a free-slip boundary condition and a weak streamwise perturbation. Our measurements show a quantitative agreement with this model for ${\rm Ro}\lesssim 0.3$. At larger Rossby number, the phase pattern of the wake is close to the prediction for an infinitely small line object. However, the wake amplitude and phase origin are not correctly described by the weak-streamwise-perturbation model, calling for an alternative model for the boundary condition at moderate rotation rate.

The Life Cycle of Spontaneously Generated Internal Waves

AbstractRecent numerical modeling studies have suggested significant spontaneous internal wave generation near the ocean surface and energy transfers to and from these waves in the ocean interior. Spontaneous generation is the emission of waves by unbalanced, large Rossby number flows in the absence of direct forcing. Here, the authors’ previous work is extended to investigate where and how these waves exchange energy with the nonwave (mean) flow. A novel double-filtering technique is adopted to separate first the wave and nonwave fields, then the individual upward- and downward-propagating wave fields, and thereby identify the pathways of energy transfer. These energy transfers are dominated by the interaction of the waves with the vertical shear in the mean flow. Spontaneously generated waves are found to be oriented such that the downward-propagating wave is amplified by the mean shear. The internal waves propagate through the entire model depth while dissipating energy and reflect back upward. The now-upward-propagating waves have the opposite sign interaction with the mean shear and decay, losing most of their energy to the nonwave flow in the upper 500 m. Overall, in the simulations described here, approximately 30% of the wave energy is dissipated, and 70% is returned to the mean flow. The apparent preferential orientation of spontaneous generation suggests a potentially unique role for these waves in the ocean energy budget in uniformly drawing net energy from mean flow in the upper-ocean interior and transporting it to depth.

Submesoscale surface fronts and filaments: secondary circulation, buoyancy flux, and frontogenesis

Problems are posed and solved for upper-ocean submesoscale density fronts and filaments in the presence of surface wind stress and the associated boundary-layer turbulent mixing, their associated geostrophic and secondary circulations and their instantaneous buoyancy fluxes and frontogenetic evolutionary tendencies in both velocity and buoyancy gradients. The analysis is diagnostic rather than prognostic, and it is based on a momentum-balanced approximation that assumes the ageostrophic acceleration is negligible, although the Rossby number is finite and ageostrophic advection is included, justified by the quasi-steady, coherent-structure flow configurations of fronts and filaments. Across a wide range of wind and buoyancy-gradient parameters, the ageostrophic secondary circulation for a front is a single overturning cell with downwelling on the dense side, hence with a positive (restratifying) vertical buoyancy flux. For a dense filament the circulation is a double cell with central downwelling and again positive vertical buoyancy flux. The primary explanation for these secondary-circulation cells is a ‘turbulent thermal wind’ linear momentum balance. These circulation patterns, and their associated frontogenetic tendencies in both the velocity and buoyancy gradients, are qualitatively similar to those due to the ‘classical’ mechanism of strain-induced frontogenesis. For linear solutions, the secondary circulation and frontogenesis are essentially independent of wind direction, but in nonlinear solutions ageostrophic advection provides a strong intensification of the peak vertical velocity, while generally preserving the ageostrophic circulation pattern, when the Rossby number is order one and the wind orientation relative to the frontal axis is favourable. At large Rossby number the solution procedure fails to converge, with an implication of a failure of existence of wholly balanced circulations.

Enhanced azimuthal rotation of the large-scale flow through stochastic cessations in turbulent rotating convection with large Rossby numbers

We present measurements of the azimuthal orientation {\theta}(t) and thermal amplitude {\delta}(t) of the large-scale circulation (LSC) of turbulent rotating convection within an unprecedented large Rossby number range 1<Ro<314. Results of {\theta}(t) reveal persistent rotation of the LSC flow in the retrograde direction over the entire Ro range. The rotation speed ratio remains a constant of 0.13(${\pm}$0.01) for 10<Ro<70, but starts to increase with increasing Ro when Ro>70. We identify the mechanism through which the mean retrograde rotation speed can be enhanced by stochastic cessations in the presence of weak Coriolis force, and show that a low-dimensional, stochastic model provides predictions of the observed large-scale flow dynamics and interprets its retrograde rotation.