Rhines Scale Research Articles

Comparative terrestrial atmospheric circulation regimes in simplified global circulation models. Part I: From cyclostrophic super‐rotation to geostrophic turbulence

The regimes of possible global atmospheric circulation patterns in an Earth‐like atmosphere are explored using a simplified Global Circulation Model (GCM) based on the University of Hamburg's Portable University Model for the Atmosphere (PUMA)—with simplified (linear) boundary‐layer friction, a Newtonian cooling scheme, and dry convective adjustment (designated here as PUMA‐S). A series of controlled experiments is conducted by varying planetary rotation rate and imposed equator‐to‐pole temperature difference. These defining parameters are combined further with each other into dimensionless forms to establish a parameter space in which the occurrences of different circulation regimes are mapped and classified. Clear, coherent trends are found when varying planetary rotation rate (thermal Rossby number) and frictional and thermal relaxation time‐scales. The sequence of circulation regimes as a function of parameters, such as the planetary rotation rate, strongly resembles that obtained in laboratory experiments on rotating, stratified flows, especially if a topographic β‐effect is included in those experiments to emulate the planetary vorticity gradients in an atmosphere induced by the spherical curvature of the planet. A regular baroclinic wave regime is also obtained at intermediate values of thermal Rossby number and its characteristics and dominant zonal wavenumber depend strongly on the strength of radiative and frictional damping. These regular waves exhibit some strong similarities to baroclinic storms observed on Mars under some conditions. Multiple jets are found at the highest rotation rates, when the Rossby deformation radius and other eddy‐related length‐scales are much smaller than the radius of the planet. These exhibit some similarity to the multiple zonal jets observed on gas giant planets. Jets form on a scale comparable to the most energetic eddies and the Rhines scale poleward of the supercritical latitude. The balance of heat transport varies strongly with Ω∗ between eddies and zonally symmetric flows, becoming weak with fast rotation.

Zonal Flows in Two-Dimensional Decaying Magnetohydrodynamic Turbulence on a β-Plane

A scale for two-dimensional β-plane magnetohydrodynamic turbulence is proposed that characterizes an upper bound of the energy containing interval similar to a classical Rhines scale for neutral fluid turbulence on a -plane. It is found that only unsteady zonal flows with complex temporal dynamics are formed in two-dimensional magnetohydrodynamic turbulence on the -plane. It is shown that flow nonstationarity is due to the appearance of isotropic magnetic islands caused by the Lorentz force in the system. The characteristic dimensions of a flow are in agreement with the proposed scale.

Inverse Cascades of Kinetic Energy as a Source of Intrinsic Variability: A Global OGCM Study

AbstractA seasonally forced 1/12° global ocean/sea ice simulation is used to characterize the spatiotemporal inverse cascade of kinetic energy (KE). Nonlinear scale interactions associated with relative vorticity advection are evaluated using cross-spectral analysis in the frequency–wavenumber domain from sea level anomaly (SLA) time series. This analysis is applied within four eddy-active midlatitude regions having large intrinsic variability spread over a wide range of scales. Over these four regions, mesoscale surface KE is shown to spontaneously cascade toward larger spatial scales—between the deformation scale and the Rhines scale—and longer time scales (possibly exceeding 10 years). Other nonlinear processes might have to be invoked to explain the longer time scales of intrinsic variability, which have a substantial surface imprint at midlatitudes. The analysis of a fully forced 1/12° hindcast shows that low-frequency and synoptic atmospheric forcing barely affects this inverse KE cascade. The inverse cascade is also at work in a 1/4° simulation, albeit with a weaker intensity, consistent with the weaker intrinsic variability found at this coarser resolution. In the midlatitude North Pacific, the spatiotemporal cascade transfers KE from high-frequency frontal Rossby waves (FRWs), probably generated by baroclinic instability, toward the lower-frequency, westward-propagating mesoscale eddy (WME) field. The WMEs provide local gradients of potential vorticity that support these short Doppler-shifted FRWs. FRWs have periods shorter than 2 months and might be subsampled by altimetric observations, perhaps explaining why the temporal inverse cascade deduced from high-resolution models and mapped altimeter products can be quite different. The nature of the nonlinear interactions between FRWs and WMEs remains unclear but might involve wave turbulence processes.

Global-scale equatorial Rossby waves as an essential component of solar internal dynamics

The Sun's complex dynamics is controlled by buoyancy and rotation in the convection zone and by magnetic forces in the atmosphere and corona. While small-scale solar convection is well understood, the dynamics of large-scale flows in the solar convection zone is not explained by theory or simulations. Waves of vorticity due to the Coriolis force, known as Rossby waves, are expected to remove energy out of convection at the largest scales. Here we unambiguously detect and characterize retrograde-propagating vorticity waves in the shallow subsurface layers of the Sun at angular wavenumbers below fifteen, with the dispersion relation of textbook sectoral Rossby waves. The waves have lifetimes of several months, well-defined mode frequencies below 200 nHz in a co-rotating frame, and eigenfunctions of vorticity that peak at the equator. Rossby waves have nearly as much vorticity as the convection at the same scales, thus they are an essential component of solar dynamics. We find a transition from turbulence-like to wave-like dynamics around the Rhines scale of angular wavenumber of twenty; this might provide an explanation for the puzzling deficit of kinetic energy at the largest spatial scales.

Sphere-Filling Asymptotics of the Barotropic Potential Vorticity Staircase

Abstract For barotropic flow in spherical geometry, the ideal potential vorticity staircase with flat steps and vertical risers exhibits a relationship between prograde jet strength and spacing such that, for regular spacing, the distance between adjacent jets is given by a suitably defined “Rhines scale” multiplied by a positive constant equal to . This result was obtained previously by the author in the equatorial limit of spherical geometry and by others in periodic beta-plane geometry. An improved asymptotic method has been devised to explain the strength–spacing relationship in sphere-filling solutions. This analysis explains the approximate validity of the equatorial asymptotics and yields new insight on minimum energy states and staircase mode transitions simulated in the presence of random, persistent energy inputs at high horizontal wavenumber.

The Impact of Horizontal Resolution on Energy Transfers in Global Ocean Models

The ocean is a turbulent fluid with processes acting on a variety of spatio-temporal scales. The estimates of energy fluxes between length scales allows us to understand how the mean flow is maintained as well as how mesoscale eddies are formed and dissipated. Here, we quantify the kinetic energy budget in a suite of realistic global ocean models, with varying horizontal resolution and horizontal viscosity. We show that eddy-permitting ocean models have weaker kinetic energy cascades than eddy-resolving models due to discrepancies in the effect of wind forcing, horizontal viscosity, potential to kinetic energy conversion, and nonlinear interactions on the kinetic energy (KE) budget. However, the change in eddy kinetic energy between the eddy-permitting and the eddy-resolving model is not enough to noticeably change the scale where the inverse cascade arrests or the Rhines scale. In addition, we show that the mechanism by which baroclinic flows organise into barotropic flows is weaker at lower resolution, resulting in a more baroclinic flow. Hence, the horizontal resolution impacts the vertical structure of the simulated flow. Our results suggest that the effect of mesoscale eddies can be parameterised by enhancing the potential to kinetic energy conversion, i.e., the horizontal pressure gradients, or enhancing the inverse cascade of kinetic energy.

Impact of plasma parameter on self-organization of electron temperature gradient driven turbulence

Self-organization in the slab electron temperature gradient driven (ETG) turbulence is investigated based on gyrokinetic simulations and the Hasegawa-Mima (HM) equation. The scale and the anisotropy of self-organized turbulent structures vary depending on the Rhines scale and the characteristic scale given by the adiabatic response term in the HM equation. The former is determined by competition between the linear wave dispersion and the nonlinear turbulent cascade, while the latter is given as the scale, at which the turbulent cascade is impeded. These scales are controlled by plasma parameters such as the density and temperature gradient, and the temperature ratio of ion to electron. It is found that depending on the plasma parameters, the ETG turbulence shows either isotropic turbulence or zonal flows, which give significantly different transport levels. Although the modulational instability excites zonal modes regardless of the plasma parameters, the final turbulent structure is determined by the self-organization process.

On the energetics of a two-layer baroclinic flow

The formation, evolution and co-existence of jets and vortices in turbulent planetary atmospheres is examined using a two-layer quasi-geostrophic $\unicode[STIX]{x1D6FD}$-channel shallow-water model. The study in particular focuses on the vertical structure of jets. Following Panetta & Held (J. Atmos. Sci., vol. 45 (22), 1988, pp. 3354–3365), a vertical shear arising from latitudinal heating variations is imposed on the flow and maintained by thermal damping. Idealised convection between the upper and lower layers is implemented by adding cyclonic/anti-cyclonic pairs, called hetons, to the flow, though the qualitative flow evolution is evidently not sensitive to this or other small-scale stochastic forcing. A very wide range of simulations have been conducted. A characteristic simulation which exhibits alternation between two different phases, quiescent and turbulent, is examined in detail. We study the energy transfers between different components and modes, and find the classical picture of barotropic/baroclinic energy transfers to be too simplistic. We also discuss the dependence on thermal damping and on the imposed vertical shear. Both have a strong influence on the flow evolution. Thermal damping is a major factor affecting the stability of the flow while vertical shear controls the number of jets in the domain, qualitatively through the Rhines scale $L_{Rh}=\sqrt{U/\unicode[STIX]{x1D6FD}}$.

On the emergence of macroscopic transport barriers from staircase structures

This paper presents a theory for the formation and evolution of coupled density staircases and zonal shear profiles in a simple model of drift-wave turbulence. Density, vorticity, and fluctuation potential enstrophy are the fields evolved in this system. Formation of staircase structures is due to inhomogeneous mixing of generalized potential vorticity (PV), resulting in the sharpening of density and vorticity gradients in some regions, and weakening them in others. When the PV gradients steepen, the density staircase structure develops into a lattice of mesoscale “jumps,” and “steps,” which are, respectively, the regions of local gradient steepening and flattening. The jumps merge and migrate in radius, leading to the development of macroscale profile structures from mesoscale elements. The positive feedback process, which drives the staircase formation occurs via a Rhines scale dependent mixing length. We present extensive studies of bifurcation physics of the global state, including results on the global flux-gradient relations (flux landscapes) predicted by the model. Furthermore, we demonstrate that, depending on the sources and boundary conditions, either a region of enhanced confinement, or a region with strong turbulence can form at the edge. This suggests that the profile self-organization is a global process, though one which can be described by a local, but nonlinear model. This model is the first to demonstrate how the mesoscale condensation of staircases leads to global states of enhanced confinement.

Barotropic kinetic energy and enstrophy transfers in the atmosphere

AbstractThe midlatitude atmosphere is characterized by turbulent eddies that act to produce a depth‐independent (barotropic) mean flow. Using the NCEP (National Centers for Environmental Prediction) Reanalysis 2 data, the latitudinal dependence of barotropic kinetic energy and enstrophy are investigated. Most of the barotropization takes place in the extratropics with a maximum value at midlatitudes, due to the latitudinal variations of the static stability, tropopause height, and sphericity of the planet. Barotropic advection transfers the eddy kinetic energy to the zonal mean flow and thus maintains the barotropic component of the eddy‐driven jet. The classic description of geostrophic turbulence exists only at high latitudes, where the quasi‐geostrophic flow is supercritical to baroclinic instability; the eddy‐eddy interactions carry both the barotropization of eddy kinetic energy upscale to the Rhines scale and the barotropization of eddy potential enstrophy downscale.

A regime diagram for ocean geostrophic turbulence

A two‐dimensional regime diagram for geostrophic turbulence in the ocean is constructed by plotting observation‐based estimates of the non‐dimensional eddy length‐scale against a nonlinearity parameter equal to the ratio of the root‐mean‐square eddy velocity and baroclinic Rossby phase speed. Two estimates of the eddy length‐scale are compared: the equivalent eddy radius inferred from the area enclosed by contours of sea‐surface height, and the ‘unsuppressed’ mixing length, based on an estimate of the eddy diffusivity with mean flow effects removed. For weak nonlinearity, as found in the Tropics, the mixing length mostly corresponds to the stability threshold for baroclinic instability whereas the eddy radius corresponds to the Rhines scale; it is suggested that this mismatch is indicative of the inverse energy cascade that occurs at low latitudes in the ocean and the zonal elongation of eddies. At larger values of nonlinearity, as found at mid‐ and high latitudes, the eddy length‐scales are much shorter than the stability threshold, within a factor of 2.5 of the Rossby deformation radius.

The Effect of Eddy–Eddy Interactions on Jet Formation and Macroturbulent Scales

Abstract The effect of eddy–eddy interactions on zonal and meridional macroturbulent scales is investigated over a wide range of eddy scales, using high-resolution idealized GCM simulations with and without eddy–eddy interactions. The wide range of eddy scales is achieved through systematic variation of the planetary rotation rate and thus multiple-jet planets. It is found that not only are eddy–eddy interactions not essential for the formation of jets, but the existence of eddy–eddy interactions decreases the number of eddy-driven jets in the atmosphere. The eddy–eddy interactions have little effect on the jet scale, which in both types of simulations coincides with the Rhines scale through all latitudes. The decrease in the number of jets in the presence of eddy–eddy interactions occurs because of the narrowing of the latitudinal region where zonal jets appear. This narrowing occurs because eddy–eddy interactions are mostly important at latitudes poleward of where the Rhines scale is equal to the Rossby deformation radius. Thus, once eddy–eddy interactions are removed, the conversion from baroclinic to barotropic eddy kinetic energy increases, and eddy–mean flow interactions intrude into these latitudes and maintain additional jets there. The eddy–eddy interactions are found to increase the energy-containing zonal scale so it coincides with the jets’ scale and thus make the flow more isotropic. While the conversion scale coincides with the most unstable scale, the Rossby deformation radius does not provide a good indication to these scales in both types of simulations.

The Latitudinal Dependence of Atmospheric Jet Scales and Macroturbulent Energy Cascades

Abstract The latitudinal width of atmospheric eddy-driven jets and scales of macroturbulence are examined latitude by latitude over a wide range of rotation rates using a high-resolution idealized GCM. It is found that for each latitude, through all rotation rates, the jet spacing scales with the Rhines scale. These simulations show the presence of a “supercriticality latitude” within the baroclinic zone, where poleward (equatorward) of this latitude, the Rhines scale is larger (smaller) than the Rossby deformation radius. Poleward of this latitude, a classic geostrophic turbulence picture appears with a − spectral slope of inverse cascade from the deformation radius up to the Rhines scale. A shallower slope than the −3 slope of enstrophy cascade is found from the deformation radius down to the viscosity scale as a result of the broad input of baroclinic eddy kinetic energy. At these latitudes, eddy–eddy interactions transfer barotropic eddy kinetic energy from the input scales of baroclinic eddy kinetic energy up to the jet scale and down to smaller scales. For the Earth case, this latitude is outside the baroclinic zone and therefore an inverse cascade does not appear. Equatorward of the supercriticality latitude, the − slope of inverse cascade vanishes, eddy–mean flow interactions play an important role in the balance, and the spectrum follows a −3 slope from the Rhines scale down to smaller scales, similar to what is observed on Earth. Moreover, the length scale of the energy-containing zonal wavenumber is equal to (larger than) the jet scale poleward (equatorward) of the supercriticality latitude.

Zonal jets in equilibrating baroclinic instability on the polar beta‐plane: Experiments with altimetry

AbstractResults from the laboratory experiments on the evolution of baroclinically unstable flows generated in a rotating tank with topographic β‐effect are presented. We study zonal jets of alternating direction which occur in these flows. The primary system we model includes lighter fluid in the South and heavier fluid in the North with resulting slow meridional circulation and fast mean zonal motion. In a two‐layer system, the velocity shear between the layers results in baroclinic instability which equilibrates with time and, due to interaction with β‐effect generates zonal jets. This system is archetypal for various geophysical systems including the general circulation and jet streams in the Earth's atmosphere, the Antarctic Circumpolar Current, or the areas in the vicinity of western boundary currents where baroclinic instability and multiple zonal jets are observed. The gradient of the surface elevation and the thickness of the upper layer are measured in the experiments using the Altimetric Imaging Velocimetry and the Optical Thickness Velocimetry techniques, respectively. Barotropic and baroclinic velocity fields are then derived from the measured quantities. The results demonstrate that the zonal jets are driven by “eddy forcing” due to continuously created baroclinic perturbations. The flow is baroclinic to a significant degree and the jets are “surface intensified.” The meridional wavelength of the jets varies linearly with the baroclinic radius of deformation and is also in a good agreement with a modified Rhines scale. This suggests a linear dependence of the perturbation velocity in the equilibrated baroclinically unstable flow on the β‐parameter.

Parameterization of eddy fluxes based on a mesoscale energy budget

It has recently been proposed to formulate eddy diffusivities in ocean models based on a mesoscale eddy kinetic energy (EKE) budget. Given an appropriate length scale, the mesoscale EKE can be used to estimate an eddy diffusivity based on mixing length theory. This paper discusses some of the open questions associated with the formulation of an EKE budget and mixing length, and proposes an improved energy budget-based parameterization for the mesoscale eddy diffusivity. A series of numerical simulations is performed, using an idealized flat-bottomed β-plane channel configuration with quadratic bottom drag. The results stress the importance of the mixing length formulation, as well as the formulation for the bottom signature of the mesoscale EKE, which is important in determining the rate of EKE dissipation. In the limit of vanishing planetary vorticity gradient, the mixing length is ultimately controlled by bottom drag, though the frictional arrest scale predicted by barotropic turbulence theory needs to be modified to account for the effects of baroclinicity. Any significant planetary vorticity gradient, β, is shown to suppress mixing, and limit the effective mixing length to the Rhines scale. While the EKE remains moderated by bottom friction, the bottom signature of EKE is shown to decrease as the appropriately non-dimensionalized friction increases, which considerably weakens the impact of changes in the bottom friction compared to barotropic turbulence. For moderate changes in the bottom-friction, eddy fluxes are thus reasonably well approximated by the scaling relation proposed by Held and Larichev (1996), which ignores the effect of bottom friction.

Nonperturbative mean-field theory for minimum enstrophy relaxation.

The dual cascade of enstrophy and energy in quasi-two-dimensional turbulence strongly suggests that a viscous but otherwise potential vorticity (PV) conserving system decays selectively toward a state of minimum potential enstrophy. We derive a nonperturbative mean field theory for the dynamics of minimum enstrophy relaxation by constructing an expression for PV flux during the relaxation process. The theory is used to elucidate the structure of anisotropic flows emerging from the selective decay process. This structural analysis of PV flux is based on the requirements that the mean flux of PV dissipates total potential enstrophy but conserves total fluid kinetic energy. Our results show that the structure of PV flux has the form of a sum of a positive definite hyperviscous and a negative or positive viscous transport of PV. Transport parameters depend on zonal flow and turbulence intensity. Turbulence spreading is shown to be related to PV mixing via the link of turbulence energy flux to PV flux. In the relaxed state, the ratio of the PV gradient to zonal flow velocity is homogenized. This homogenized quantity sets a constraint on the amplitudes of PV and zonal flow in the relaxed state. A characteristic scale is defined by the homogenized quantity and is related to a variant of the Rhines scale. This relaxation model predicts a relaxed state with a structure which is consistent with PV staircases, namely, the proportionality between mean PV gradient and zonal flow strength.

The Dynamics of Baroclinic Zonal Jets*

Abstract Multiple alternating zonal jets are a ubiquitous feature of planetary atmospheres and oceans. However, most studies to date have focused on the special case of barotropic jets. Here, the dynamics of freely evolving baroclinic jets are investigated using a two-layer quasigeostrophic annulus model with sloping topography. In a suite of 15 numerical simulations, the baroclinic Rossby radius and baroclinic Rhines scale are sampled by varying the stratification and root-mean-square eddy velocity, respectively. Small-scale eddies in the initial state evolve through geostrophic turbulence and accelerate zonally as they grow in horizontal scale, first isotropically and then anisotropically. This process leads ultimately to the formation of jets, which take about 2500 rotation periods to equilibrate. The kinetic energy spectrum of the equilibrated baroclinic zonal flow steepens from a −3 power law at small scales to a −5 power law near the jet scale. The conditions most favorable for producing multiple alternating baroclinic jets are large baroclinic Rossby radius (i.e., strong stratification) and small baroclinic Rhines scale (i.e., weak root-mean-square eddy velocity). The baroclinic jet width is diagnosed objectively and found to be 2.2–2.8 times larger than the baroclinic Rhines scale, with a best estimate of 2.5 times larger. This finding suggests that Rossby wave motions must be moving at speeds of approximately 6 times the turbulent eddy velocity in order to be capable of arresting the isotropic inverse energy cascade.

Scaling of Off-Equatorial Jets in Giant Planet Atmospheres

Abstract In the off-equatorial region of Jupiter’s and Saturn’s atmospheres, baroclinic eddies transport angular momentum out of retrograde and into prograde jets. In a statistically steady state, this angular momentum transfer by eddies must be balanced by dissipation, likely produced by magnetohydrodynamic (MHD) drag in the planetary interior. This paper examines systematically how an idealized representation of this drag in a general circulation model (GCM) of the upper atmosphere of giant planets modifies jet characteristics, the angular momentum budget, and the energy budget. In the GCM, Rayleigh drag at an artificial lower boundary (with mean pressure of 3 bar) is used as a simple representation of the MHD drag that the flow on giant planets experiences at depth. As the drag coefficient decreases, the eddy length scale and eddy kinetic energy increase, as they do in studies of two-dimensional turbulence. Off-equatorial jets become wider and stronger, with increased interjet spacing. Coherent vortices also become more prevalent. Generally, the jet width scales with the Rhines scale, which is of similar magnitude as the Rossby radius in the simulations. The jet strength increases primarily through strengthening of the barotropic component, which increases as the drag coefficient decreases because the overall kinetic energy dissipation remains roughly constant. The overall kinetic energy dissipation remains roughly constant presumably because it is controlled by baroclinic conversion of potential to kinetic energy in the upper troposphere, which is mainly determined by the differential solar radiation and is only weakly dependent on bottom drag and barotropic flow variations. For Jupiter and Saturn, these results suggest that the wider and stronger jets on Saturn may arise because the MHD drag on Saturn is weaker than on Jupiter, while the thermodynamic efficiencies of the atmospheres are not sensitive to the drag parameters.

Low frequency modulation of jets in quasigeostrophic turbulence

Quasigeostrophic turbulence on a β-plane with a finite deformation radius is studied numerically, with particular emphasis on frequency and combined wavenumber-frequency domain analyses. Under suitable conditions, simulations with small-scale random forcing and large-scale drag exhibit a spontaneous formation of multiple zonal jets. The first hint of wave-like features is seen in the distribution of kinetic energy as a function of frequency; specifically, for progressively larger deformation scales, there are systematic departures in the form of isolated peaks (at progressively higher frequencies) from a power-law scaling. Concomitantly, there is an inverse flux of kinetic energy in frequency space which extends to lower frequencies for smaller deformation scales. The identification of these peaks as Rossby waves is made possible by examining the energy spectrum in frequency-zonal wavenumber and frequency-meridional wavenumber diagrams. In fact, the modified Rhines scale turns out to be a useful measure of the dominant meridional wavenumber of the modulating Rossby waves; once this is fixed, apart from a spectral peak at the origin (the steady jet), almost all the energy is contained in westward propagating disturbances that follow the theoretical Rossby dispersion relation. Quite consistently, noting that the zonal scale of the modulating waves is restricted to the first few wavenumbers, the energy spectrum is almost entirely contained within the corresponding Rossby dispersion curves on a frequency-meridional wavenumber diagram. Cases when jets do not form are also considered; once again, there is a hint of Rossby wave activity, though the spectral peaks are quite muted. Further, the kinetic energy scaling in frequency domain follows a −5/3 power-law and is distributed much more broadly in frequency-wavenumber diagrams.

Multiple Zonal Jets in a Differentially Heated Rotating Annulus

AbstractA 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.