Convective Scale Research Articles

Inviscid evolution of a uniform vortex dipole in a strain field

Competing models employing anti-parallel vortex collision in search of a finite-time singularity of Euler's equation have arisen recently. Both the vortex sheet model proposed by Brenner et al. (Phys. Rev. Fluids, vol. 1, 2016, 084503) and the ‘tent’ model proposed by Moffatt & Kimura (J. Fluid Mech., vol. 861, 2019, pp. 930–967) consider a vortex monopole exposed to a strain flow to model the evolution of interacting anti-parallel vortices, a fundamental element in the turbulent cascade. Herein we employ contour dynamics to explore the inviscid evolution of a vortex dipole subjected to an external strain flow with and without axial stretching. We find that for any strain-to-vorticity ratio $\mathcal {E}$ , the constituent vortices compress indefinitely, with weaker strain flows causing flattening to occur more slowly. At low $\mathcal {E}$ , the vortex dipole forms the well-documented head–tail structure, whereas increasing $\mathcal {E}$ results in the dipole compressing into a pair of vortex sheets with no appreciable head structure. Axial stretching effectively lowers $\mathcal {E}$ dynamically throughout the evolution, thus delaying the transition from the head–tail regime to the vortex sheet regime to higher strain-to-vorticity ratios. Findings from this study offer a bridge between the two cascade models, with the particular mechanism arising depending on $\mathcal {E}$ . It also suggests limits for the ‘tent’ model for a finite-time singularity, wherein the curvature-induced strain flow must be very weak in comparison with the vorticity density-driven mutual attraction such that the convective time scale of the evolution exceeds the core flattening time scale.

Electron heat flux and propagating fronts in plasma thermal quench via ambipolar transport

The thermal collapse of a nearly collisionless plasma interacting with a cooling spot, in which the electron parallel heat flux plays an essential role, is both theoretically and numerically investigated. We show that such thermal collapse, which is known as thermal quench in tokamaks, comes about in the form of propagating fronts, originating from the cooling spot, along magnetic field lines. The slow fronts, propagating with local ion sound speed, limit the aggressive cooling of plasma, which is accompanied by a plasma cooling flow toward the cooling spot. The extraordinary physics underlying such a cooling flow is that the fundamental constraint of ambipolar transport along the field line limits the spatial gradient of electron thermal conduction flux to the much weaker convective scaling, as opposed to the free-streaming scaling, so that a large electron temperature and, hence, pressure gradient can be sustained. The last ion front for a radiative cooling spot is a shock front where cold but flowing ions meet hot ions.

Predicting Turbulent Vertical Velocity in the Ocean Surface Layer under Mixed Convective and Wind/Wave Forcing

Abstract Turbulence in the ocean surface layer is forced by a mixture of buoyancy, wind, and wave processes that evolves over time scales from the diurnal scale of buoyancy forcing, through storm time scales, to the annual cycle. This study seeks a predictor for root-mean-square w (rmsw), a time and surface layer average of turbulent vertical velocity w measured by bottom-mounted vertical-beam acoustic Doppler current profilers, in terms of concurrently measured surface forcing fields. Data used are from two coastal sites, one shallow (LEO, 15-m depth) and one deeper (R2, 26-m depth). The analysis demonstrates that it is possible to predict observed rmsw with a simple linear combination of two scale velocities, one the convective scale velocity familiar from the atmospheric literature, the other a scale velocity wS representing combined wind and wave effects. Three variants are considered for this latter scale velocity, the wind stress velocity alone and two forms using both and US, a Stokes velocity characteristic of the surface wave field. At both sites, the two-parameter fit using alone is least accurate, while fits using the other two variants are essentially indistinguishable. At both sites, the coefficient multiplying is the same, within error bounds, and within the range of previous observations. At the deeper site, the coefficient multiplying the wind/wave scale velocity wS is approximately half that at the shallow site, a difference here attributed to difference in wave character.

Thermal analysis of radiative and electromagnetic flowing of hybridity nanofluid via Darcy–Forchheimer porous material with slippage constraints

The goal of this research is to address the electrical magnetohydrodynamic flow of hybridity nanoparticles through a stretched surface with the impact of the Darcy–Forchheimer permeable medium. By identifying appropriate similarity factors, the partial differential equation is converted into a set of ordinary differential equation with the help of R-K fourth-order approach based on shooting technique. The velocity, thermal, friction factor coefficient, and heat transport are investigated comprehensively for the influence of numerous blossoming parameters refer to in the present study by plots graphically. It is accomplished that due to the influence of the electric field associated with first- and second-order velocity slip impacts, the motion of liquid slows down. Moreover, the stream velocity grows for the boosting scales of mixed convection, which leads to eliminating sticking impact. The variation of important flowing variables on heat transport and the drag coefficient is also investigated. Here augmenting valuation of mixed convection parameter corresponds to boost up velocity curve. Furthermore, the influence of thermal field and heat transport are similar in view of the Biot number.

On the energetics of a tidally oscillating convective flow

ABSTRACT This paper examines the energetics of a convective flow subject to an oscillation with a period $t_{\rm osc}$ much smaller than the convective time-scale $t_{\rm conv}$, allowing for compressibility and uniform rotation. We show that the energy of the oscillation is exchanged with the kinetic energy of the convective flow at a rate $D_R$ that couples the Reynolds stress of the oscillation with the convective velocity gradient. For the equilibrium tide and inertial waves, this is the only energy exchange term, whereas for p modes there are also exchanges with the potential and internal energy of the convective flow. Locally, $\left| D_R \right| \sim u^{\prime 2} / t_{\rm conv}$, where $u^{\prime}$ is the oscillating velocity. If $t_{\rm conv} \ll t_{\rm osc}$ and assuming mixing length theory, $\left| D_R \right|$ is $\left( \lambda_{\rm conv} / \lambda_{\rm osc} \right)^2$ smaller, where $\lambda_{\rm conv}$ and $\lambda_{\rm osc}$ are the characteristic scales of convection and the oscillation. Assuming local dissipation, we show that the equilibrium tide lags behind the tidal potential by a phase $\delta(r) \sim r \omega_{\rm osc} / \left( g(r) t_{\rm conv}(r) \right)$, where g is the gravitational acceleration. The equilibrium tide can be described locally as a harmonic oscillator with natural frequency $\left( g/r \right)^{1/2}$ and subject to a damping force $-u^{\prime}/t_{\rm conv}$. Although $\delta(r)$ varies by orders of magnitude through the flow, it is possible to define an average phase shift $\overline{\delta }$ which is in good agreement with observations for Jupiter and some of the moons of Saturn. Finally, $1 / \overline{\delta }$ is shown to be equal to the standard tidal dissipation factor.

Tidal dissipation due to the elliptical instability and turbulent viscosity in convection zones in rotating giant planets and stars

ABSTRACT Tidal dissipation in star–planet systems can occur through various mechanisms, among which is the elliptical instability. This acts on elliptically deformed equilibrium tidal flows in rotating fluid planets and stars, and excites inertial waves in convective regions if the dimensionless tidal amplitude (ϵ) is sufficiently large. We study its interaction with turbulent convection, and attempt to constrain the contributions of both elliptical instability and convection to tidal dissipation. For this, we perform an extensive suite of Cartesian hydrodynamical simulations of rotating Rayleigh–Bénard convection in a small patch of a planet. We find that tidal dissipation resulting from the elliptical instability, when it operates, is consistent with ϵ3, as in prior simulations without convection. Convective motions also act as an effective viscosity on large-scale tidal flows, resulting in continuous tidal dissipation (scaling as ϵ2). We derive scaling laws for the effective viscosity using (rotating) mixing-length theory, and find that they predict the turbulent quantities found in our simulations very well. In addition, we examine the reduction of the effective viscosity for fast tides, which we observe to scale with tidal frequency (ω) as ω−2. We evaluate our scaling laws using interior models of Hot Jupiters computed with mesa. We conclude that rotation reduces convective length-scales, velocities, and effective viscosities (though not in the fast tides regime). We estimate that elliptical instability is efficient for the shortest period Hot Jupiters, and that effective viscosity of turbulent convection is negligible in giant planets compared with inertial waves.

Verification of multiresolution model forecasts of heavy rainfall events from 23 to 26 August 2017 over Nigeria

AbstractThe study uses numerical weather prediction models to predict the occurrence of heavy convective rainfall associated with the passage of the African Easterly Wave (AEW) during the period 23–26 August 2017 over Nigeria. Fraction skill score (FSS) and method for object‐based diagnostic evaluation (MODE) verification techniques were applied to verify how well the models predict the high‐impact event and to demonstrate how these tools can support operational forecasting. Ensemble model forecasts at a convective scale from UK Met Office Unified Model (MetUM) and a one‐way nested weather research and forecasting (WRF) model were compared with the integrated multisatellite retrievals for global precipitation measurement (IMERG GPM). The purpose is to examine skills of improved model resolution and ensemble in reproducing rainfall forecasts on useful scales and how the skill varies with spatial scale. WRF 2 and 6 km model forecasts show comparable skill at smaller grid scales. The skill of MetUM improves dramatically when the verification statistics are applied to the ensemble mean of the binary fields of the individual member forecast. The object‐based analysis reveals a similar structure as observed, although displaced eastwards. Most improvement occurred for heavier rainfall events associated with the passage of the AEW. WRF 6 km compares reasonably well with WRF 2 km in terms of shape and structure of rainfall underscoring the ability of the model to reasonably represent convection at 6 km horizontal resolution. The ensemble members in MetUM explicitly reproduce convection at 4 km resolution but are displaced at about 166 km behind observed rainfall.

MJO in Different Orbital Regimes: Role of the Mean State in the MJO’s Amplitude during Boreal Winter

Abstract The Madden–Julian oscillation (MJO) exhibits pronounced seasonality, with one of the key unanswered questions being the following: what controls the maximum in MJO precipitation variance in the Southern Hemisphere during boreal winter? In this study, we examine a set of global climate model simulations in which the eccentricity and precession of Earth’s orbit are altered to change the boreal winter mean state in an attempt to reveal the processes that are responsible for the MJO’s amplitude in the boreal winter. In response to the forced insolation changes, the north–south asymmetry in sea surface temperature is amplified in boreal fall, which intensifies the Hadley circulation in boreal winter. The stronger Hadley circulation yields higher mean precipitation and stronger mean lower-tropospheric westerlies in the southern part of the Indo-Pacific warm pool. The MJO precipitation variability increases significantly where the mean precipitation and lower-tropospheric westerlies strengthen. In the column-integrated moisture budget of the simulated MJO, only surface latent heat flux feedback shows a trend that is consistent with the MJO’s amplitude, suggesting an important role for the surface latent heat flux feedback in the MJO’s amplitude during the boreal winter. An analysis of the moisture–precipitation relationship in the simulations shows that the increase in the mean precipitation lowers the convective moisture adjustment time scale, leading to the increase in precipitation variance. Our results suggest that the mean-state precipitation plays a critical role in the maintenance mechanism of the MJO.

The Departure from Mixed-Layer Similarity During the Afternoon Decay of Turbulence in the Free-Convective Boundary Layer: Results from Large-Eddy Simulations

This study analyses the departure of the velocity-variances profiles from their quasi-steady state described by the mixed-layer similarity, using large-eddy simulations with different prescribed shapes and time scales of the surface kinematic heat flux decay. Within the descriptive frames where the time is tracked solely by the forcing time scale (either constant or time-dependent) describing the surface heat flux decay, we find that the normalized velocity-variances profiles from different runs do not collapse while they depart from mixed-layer similarity. As the mixed-layer similarity relies on the assumption that the free-convective boundary layer is in a quasi-equilibrium, we consider the ratios of the forcing time scales to the convective eddy-turnover time scale. We find that the normalized velocity-variances profiles collapse in the only case where the ratio (widetilde{r}) of the time-dependent forcing time scale to the convective eddy-turnover time scale is used for tracking the time, supporting the independence of the departure from the characteristics of the surface heat flux decay. As a consequence of this result, the knowledge of widetilde{r} is sufficient to predict the departure of the velocity variances from their quasi-steady state, irrespective of the shape of the surface heat flux decay. This study highlights the importance of considering both the time-dependent forcing time scale and the convective eddy-turnover time scale for evaluating the response of the free-convective boundary layer to the surface heat flux decay.

Flow Development and Entrainment in Turbulent Particle‐Laden Jets

AbstractExplosive eruptions expel volcanic gases and particles at high pressures and velocities. Within this multiphase fluid, small ash particles affect the flow dynamics, impacting mixing, entrainment, turbulence, and aggregation. To examine the role of turbulent particle behavior, we conducted an analogue experiment using a particle‐laden jet. We used compressed air as the carrier fluid, considering turbulent conditions at Reynolds numbers from approximately 5,000 to 20,000. Two different particles were examined: 14‐μm diameter solid nickel spheres and 13‐μm diameter hollow glass spheres. These resulted in Stokes numbers between 1 and 35 based on the convective scale. The particle mass percentage in the mixture is varied from 0.3% to more than 20%. Based on a 1‐D volcanic plume model, these Stokes numbers and mass loadings corresponded to millimeter‐scale particle diameters at heights of 4–8 km above the vent during large, sustained eruptions. Through particle image velocimetry, we measured the mean flow behavior and the turbulence statistics in the near‐exit region, primarily focusing on the dispersed phase. We show that the flow behavior is dominated by the particle inertia, with high Stokes numbers reducing the entrainment by more than 40%. When applied to volcanic plumes, these results suggest that high‐density particles can greatly increase the probability of column collapse.

Rainy downdrafts in abyssal atmospheres

Context.Results from Juno’s Microwave Radiometer (MWR) indicate nonuniform mixing of ammonia vapor in Jupiter’s atmosphere down to tens of bars, far beneath the cloud level. Helioseismic observations suggest solar convection may require narrow, concentrated downdrafts called entropy rain to accommodate the Sun’s luminosity. Both observations suggest some mechanism of nonlocal convec-tive transport.Aims.We seek to predict the depth that a concentrated density anomaly can reach before efficiently mixing with its environment in bottomless atmospheres.Methods.We modified classic self-similar analytical models of entraining thermals to account for the compressibility of an abyssal atmosphere. We compared these models to the output of high-resolution three-dimensional fluid dynamical simulations to more accurately model the chaotic influence of turbulence.Results.We find that localized density anomalies propagate down to ~3−8 times their initial size without substantially mixing with their environment. Our analytic model accurately predicts the initial flow, but the self-similarity assumption breaks down after the flow becomes unstable at a characteristic penetration depth.Conclusions.In the context of Jupiter, our findings suggest that precipitation concentrated into localized downdrafts of size ~20 km can coherently penetrate to on the order of a hundred kilometers (tens of bars) beneath its initial vaporization level without mixing with its environment. This finding is consistent with expected convective storm length scales and Juno MWR measurements of ammonia depletion. In the context of the Sun, we find that turbulent downdrafts in abyssal atmospheres cannot maintain their coherence through the Sun’s convective layer, a potential challenge for the entropy rain hypothesis.

Strong surface winds in Storm Eunice. Part 1: storm overview and indications of sting jet activity from observations and model data

Strong surface winds in Storm <i>Eunice</i>. Part 1: storm overview and indications of sting jet activity from observations and model data

The influence of free stream turbulence on the development of a wind turbine wake

The wake of an isolated model-scale wind turbine is analysed in a set of inflow conditions having free stream turbulence intensity between 3 % and 12 %, and integral time scales in the range of 0.1–10 times the convective time scale based on the turbine diameter. It is observed that the wake generated by the turbine evolves more rapidly, with the onset of the wake evolution being closer to the turbine, for high turbulence intensity and low integral time scale flows, in accordance with literature, while flows at higher integral time scales result in a slow wake evolution, akin to that generated by low-turbulence inflow conditions despite the highly turbulent ambient condition. The delayed onset of the wake evolution is connected to the stability of the shear layer enveloping the near-wake, which is favoured for low-turbulence or high-integral time scale flows, and to the stability of the helical vortex set surrounding the wake, as this favours interaction events and prevents momentum exchange at the wake boundary which hinder wake evolution. The rate at which the velocity in the wake recovers to undisturbed conditions is instead analytically shown to be a function of the Reynolds shear stress at the wake centreline, an observation that is confirmed by measurements. The rate of production of Reynolds shear stress in the wake is then connected to the power harvested by the turbine to explain the differences between flows at equivalent turbulence intensity and different integral time scales. The wake recovery rate, and by extension the behaviour of the turbine wake in high-integral time scale flows, is seen to be a linear function of the free stream turbulence intensity for flows with Kolmogorov-like turbulence spectrum, in accordance with literature. This relation is seen not to hold for flows with different free stream turbulence spectral distribution; however, this trend is recovered if the contributions of low frequency velocity components to the turbulence intensity are ignored or filtered out from the computation.

Confronting the Convective Gray Zone in the Global Configuration of the Met Office Unified Model

AbstractIn atmospheric models with kilometer‐scale grids the resolution approaches the scale of convection. As a consequence the most energetic eddies in the atmosphere are partially resolved and partially unresolved. The modeling challenge to represent convection partially explicitly and partially as a subgrid process is called the convective gray zone problem. The gray zone issue has previously been discussed in the context of regional models, but the evolution in regional models is constrained by the lateral boundary conditions. Here we explore the convective gray zone starting from a defined global configuration of the Met Office Unified Model using initialized forecasts and comparing different model formulations to observations. The focus is on convection and turbulence, but some aspects of the model dynamics are also considered. The global model is run at nominal 5 km resolution and thus contributions from both resolved and subgrid turbulent and convective fluxes are non‐negligible. The main conclusion is that in the present assessment, the configurations which include scale‐aware turbulence and a carefully reduced and simplified mass‐flux convection scheme outperform both the configuration with fully parameterized convection as well as a configuration in which the subgrid convection parameterization is switched off completely. The results are more conclusive with regard to convective organization and tropical variability than extratropical predictability. The present study thus endorses the strategy to further develop scale‐aware physics schemes and to pursue an operational implementation of the global 5 km‐resolution model to be used alongside other ensemble forecasts to allow researchers and forecasters to further assess these simulations.

Dependency of vertical velocity variance on meteorological conditions in the convective boundary layer

Abstract. Measurements of vertical velocity from vertically pointing Doppler lidars are used to derive the profiles of normalized vertical velocity variance. Observations were taken during the FESSTVaL (Field Experiment on Submesoscale Spatio-Temporal Variability in Lindenberg) campaign during the warm seasons of 2020 and 2021. Normalized by the square of the convective velocity scale, the average vertical velocity variance profile follows the universal profile of Lenschow et al. (1980). However, daily profiles still show a high day-to-day variability. We found that moisture transport and the content of moisture in the boundary layer could explain the remaining variability of the normalized vertical velocity variance. The magnitude of the normalized vertical velocity variance is highest on clear-sky days and decreases as the absolute humidity increases and surface latent heat flux decreases on cloud-topped days. This suggests that moisture content and moisture transport are limiting factors for the intensity of turbulence in the convective boundary layer. We also found that the intensity of turbulence decreases with an increase in the boundary layer cloud fraction during FESSTVaL, while the latent heating in the cloud layer was not a relevant source of turbulence in this case. We conclude that a new vertical velocity scale has to be defined that would take into account the moist processes in the convective boundary layer.

Scaling of convection in high-pressure ice layers of large icy moons and implications for habitability

The existence of a high-pressure (HP) ice layer between the silicate core and the liquid ocean in large icy moons and ocean worlds is usually seen as a barrier to habitability, preventing a direct contact and therefore transfer of nutrients from the core to the liquid ocean. More recently, several studies challenged that hypothesis and showed that exchanges were possible under specific conditions, allowing transport of salts toward the ocean. In our study, we consider an effect not taken into account in the previous works, which is the dynamical implications of the phase equilibrium at the ice–ocean interface allowing a non-zero vertical velocity at the surface of the HP ice layer. This effect, which can be modeled as a phase change boundary condition for the ice layer, has a significant impact on the flow dynamics and enables exchanges with the ocean by fusion and crystallization at the top interface of the HP ice layer, even without partial melting in the bulk of the ice layer. For the same conditions as standard convective systems, it also leads to faster mass transfer in the bulk. These exchanges are directly linked to the melting capacity of the ice at the interface between the HP ice layer and the core, depending on the efficiency of convection in the liquid ocean. This is controlled by a dimensionless parameter noted Φ. Considering this boundary condition at the interface between the HP ice layer and the liquid ocean, we propose a scaling of the bottom temperature and the top vertical velocity as function of the Rayleigh number, in the case of a fixed heat flux from the core, a rigid or free-slip bottom boundary and various values of Φ.

Large-Scale Convection during Gravitational Collapse with Neutrino Transport in 2D and 3D Models on Fine Grids

The problem of the gravitational collapse of the core of a massive star is considered, taking into account the neutrino transport in the flux-limited diffusion approximation. To reduce the computational domain of a multidimensional problem on a fixed computational grid, the core of a star, which is already at the stage of collapse, is considered. Since the collapse stage is delayed in time compared to the gas-dynamic time scale for an emerging proto-neutron star, we consider the mathematical problem for the initial configuration in equilibrium and neglected the initial radial velocity. Pressure for a long time at the collapse stage is provided by relativistic degenerate electrons, so the relationship between pressure and density in the initial configuration is described by a polytropic equation with the polytropic index n=3. The purpose of this paper is to test the hypothesis that large-scale convection is independent of the 2D and 3D geometry of the mathematical problem and computational grid parameters, as well as the choice of the initial stage of gravitational collapse. The scale of convection is determined by the size of the region of decreasing entropy with neutrino losses, i.e., nonequilibrium neutronization, and the presence of a weak initial rotation.

A Turbulence Survey in the Gulf of Naples, Mediterranean Sea, during the Seasonal Destratification

The seasonality of the vertical mixing at coastal sites is not well characterized yet. Here, a time series of the dissipation rate of turbulent kinetic energy (ε) was obtained from weekly morning microstructure observations covering the destratification period (July 2015, February 2016) at a coastal site in the western Mediterranean Sea, influenced by freshwater runoffs. Estimated with bulk parameters from the public re-analyzed dataset ERA5, the Ekman layer, and the convective penetration depth scale with the mixed layer depth (MLD) with a good agreement. Below the MLD, peaks of ε are observed in the baroclinic layers that progressively overlap with the bottom layer, where repeated near-bottom turbidity peaks provide evidence of sediment resuspension, suggesting energetic processes within the bottom boundary layer. In the subsurface, moderate values (10−9 to 10−8 W kg−1) are observed, following a Burr type XII distribution. Significant correlation with ε at MLD is obtained with a model combining the effects of wind, wind–wave, and convection, highlighting a calm sea bias in our data, plus a sunrise bias when morning buoyancy fluxes are stabilizing. Another correlation, obtained from a pure-wind estimation 18 h before, suggests the role of wind in generating internal waves in the stratified layers, thus, impacting mixing intensity.

Cooling flow regime of a plasma thermal quench

A large class of Laboratory, Space, and Astrophysical plasmas is nearly collisionless. When a localized energy or particle sink, for example, in the form of a radiative cooling spot or a black hole, is introduced into such a plasma, it can trigger a plasma thermal collapse, also known as a thermal quench in tokamak fusion. Here we show that the electron thermal conduction in such a nearly collisionless plasma follows the convective energy transport scaling in itself or in its spatial gradient, due to the constraint of ambipolar transport. As a result, a robust cooling flow aggregates mass toward the cooling spot and the thermal collapse of the surrounding plasma takes the form of four propagating fronts that originate from the radiative cooling spot, along the magnetic field line in a magnetized plasma. The slowest one, which is responsible for deep cooling, is a shock front.

Direct driving of simulated planetary jets by upscale energy transfer

Context. The precise mechanism that forms jets and large-scale vortices on the giant planets is unknown. An inverse cascade has been suggested by several studies. Alternatively, energy may be directly injected by small-scale convection. Aims. Our aim is to clarify whether an inverse cascade feeds zonal jets and large-scale eddies in a system of rapidly rotating, deep, geostrophic spherical-shell convection. Methods. We analyze the nonlinear scale-to-scale transfer of kinetic energy in such simulations as a function of the azimuthal wave number, m. Results. We find that the main driving of the jets is associated with upscale transfer directly from the small convective scales to the jets. This transfer is very nonlocal in spectral space, bypassing large-scale structures. The jet formation is thus not driven by an inverse cascade. Instead, it is due to a direct driving by Reynolds stresses, statistical correlations of velocity components of the small-scale convective flows. Initial correlations are caused by the effect of uniform background rotation and shell geometry on the flows and provide a seed for the jets. While the jet growth suppresses convection, it increases the correlation of the convective flows, which further amplifies the jet growth until it is balanced by viscous dissipation. To a much smaller extent, energy is transferred upscale to large-scale vortices directly from the convective scales, mostly outside the tangent cylinder. There, large-scale vortices are not driven by an inverse cascade either. Inside the tangent cylinder, the transfer to large-scale vortices is even weaker, but more local in spectral space, leaving open the possibility of an inverse cascade as a driver of large-scale vortices. In addition, large-scale vortices receive kinetic energy from the jets via forward transfer. We therefore suggest a jet instability as an alternative formation mechanism of large-scale vortices. Finally, we find that the jet kinetic energy scales approximatively as ℓ−5, the same as for the so-called zonostrophic regime.