Low Rossby Number Research Articles

Mathematical analysis of fluids in motion: from well-posedness to model reduction

This paper reviews some recent results on the Navier-Stokes-Fourier system governing the evolution of a general compressible, viscous, and heat conducting fluid. We discuss several concepts of weak solutions, in particular, using the implications of the Second law of thermodynamics. We introduce the concept of relative entropy and dissipative solution and show the principle of weak-strong uniqueness. The second part of the paper is devoted to problems of model reduction and the related singular limits. Several examples of singular limits are presented: The incompressible limit, the inviscid limit, the low Rossby number limit and their combinations.

What controls the magnetic geometry of M dwarfs?

Context: observations of rapidly rotating M dwarfs show a broad variety of large-scale magnetic fields encompassing dipole-dominated and multipolar geometries. In dynamo models, the relative importance of inertia in the force balance -- quantified by the local Rossby number -- is known to have a strong impact on the magnetic field geometry. Aims: we aim to assess the relevance of the local Rossby number in controlling the large-scale magnetic field geometry of M dwarfs. Methods: we explore the similarities between anelastic dynamo models in spherical shells and observations of active M-dwarfs, focusing on field geometries derived from spectropolarimetric studies. To do so, we construct observation-based quantities aimed to reflect the diagnostic parameters employed in numerical models. Results: the transition between dipole-dominated and multipolar large-scale fields in early to mid M dwarfs is tentatively attributed to a Rossby number threshold. We interpret late M dwarfs magnetism to result from a dynamo bistability occurring at low Rossby number. By analogy with numerical models, we expect different amplitudes of differential rotation on the two dynamo branches.

Statistical and physical balances in low Rossby number Rayleigh–Bénard convection

Rapidly rotating Rayleigh–Bénard convection is studied using an asymptotically reduced equation set valid in the limit of low Rossby numbers. Four distinct dynamical regimes are identified: a disordered cellular regime near threshold, a regime of weakly interacting convective Taylor columns at larger Rayleigh numbers, followed for yet larger Rayleigh numbers by a breakdown of the convective Taylor columns into a disordered plume regime characterized by reduced efficiency and finally by geostrophic turbulence. The transitions are quantified by examining the properties of the horizontally and temporally averaged temperature and thermal dissipation rate. The maximum of the thermal dissipation rate is used to define the width of the thermal boundary layer. In contrast to the non-rotating Rayleigh–Bénard convection, the temperature drop across this layer decreases monotonically with increasing Rayleigh number and does not saturate. The breakdown of the convective Taylor column regime is attributed to the onset of convective instability of the thermal boundary layer and confirmed using the explicit linear stability analysis. Horizontal spectra of the vorticity, vertical velocity and temperature fluctuations are computed and their evolution with time is elucidated. A large-scale barotropic mode evolves from random initial conditions on an extremely long time scale and leads to continued evolution of the nominally saturated Nusselt number and its variance over very long times. The results are used to provide insights into the dynamics of rapidly rotating convection outside the asymptotic regime described by the reduced equations.

Radiative instability of an anticyclonic vortex in a stratified rotating fluid

AbstractIn strongly stratified fluids, an axisymmetric vertical columnar vortex is unstable because of a spontaneous radiation of internal waves. The growth rate of this radiative instability is strongly reduced in the presence of a cyclonic background rotation $f/ 2$ and is smaller than the growth rate of the centrifugal instability for anticyclonic rotation, so it is generally expected to affect vortices in geophysical flows only if the Rossby number $Ro= 2\Omega / f$ is large (where $\Omega $ is the angular velocity of the vortex). However, we show here that an anticyclonic Rankine vortex with low Rossby number in the range $\ensuremath{-} 1\leq Ro\lt 0$, which is centrifugally stable, is unstable to the radiative instability when the azimuthal wavenumber $\vert m\vert $ is larger than 2. Its growth rate for $Ro= \ensuremath{-} 1$ is comparable to the values reported in non-rotating stratified fluids. In the case of continuous vortex profiles, this new radiative instability is shown to occur if the potential vorticity of the base flow has a sufficiently steep radial profile. The most unstable azimuthal wavenumber is inversely proportional to the steepness of the vorticity jump. The properties and mechanism of the instability are explained by asymptotic analyses for large wavenumbers.

Helical Turbulence Prevails over Inertial Waves in Forced Rotating Flows at High Reynolds and Low Rossby Numbers

Abstract A study of spectral laws for helical turbulence in the presence of solid body rotation up to Reynolds numbers Re ~ 1 × 105 and down to Rossby numbers Ro ~ 3 × 10−3 is presented. The forcing function is a fully helical flow that can also be viewed as mimicking the effect of atmospheric convective motions. Variants of a model developed previously by Baerenzung et al. are tested in the helical case against direct numerical simulation (DNS), using data from a run on a grid of 15363 points; its efficiency is also contrasted against a spectral large-eddy simulation (LES) by Chollet and Lesieur, as well as an underresolved DNS. The model including the contribution of helicity to the spectral eddy dissipation and eddy noise behaves best, allowing the recovery of statistical features of the flow. Even if the model is based on isotropic assumptions, the authors demonstrated in a previous study that the small scales of flows at moderate Rossby number can be considered to be isotropic in the range of parameters considered here and that therefore their model is appropriate to treat this kind of flow. An exploration of parameter space is then performed beyond what is feasible today using DNS. At a fixed Reynolds number, lowering the Rossby number leads to a regime of wave-mediated inertial helicity cascades to small scales. However, at a fixed Rossby number, increasing the Reynolds number leads the system to be dominated by turbulent energy exchanges where the role of inertial waves is to weaken the direct cascade of energy while strengthening the large scales. It is found that a useful parameter for partitioning the data is , with Urms, ν, and Ω being the rms velocity, the viscosity, and the rotation rate, respectively. The parameter that determines how much the energy cascade is direct or inverse—in which case the cascade to small scales is predominantly that of helicity—is linked to Ro.

Global dynamo models from direct numerical simulations and their mean-field counterparts

Context. The recently developed test-field method permits to compute dynamo coefficients from global, direct numerical simulations. The subsequent use of these parameters in mean-field models enables us to compare self-consistent dynamo models with their mean-field counterparts. So far, this has been done for a simulation of rotating magnetoconvection and a simple benchmark dynamo, which are both (quasi-)stationary. Aims. It is shown that chaotically time-dependent dynamos in a low Rossby number regime may be appropriately described by corresponding mean-field results. Also, it is pointed out under which conditions mean-field models do not match direct numerical simulations. Methods. We solve the equations of magnetohydrodynamics (MHD) in a rotating, spherical shell in the Boussinesq approximation. Based on this, we compute mean-field coefficients for several models with the help of the previously developed test-field method. The parameterization of the mean electromotive force by these coefficients is tested against direct numerical simulations. In addition, we use the determined dynamo coefficients in mean-field models and compare the outcome with azimuthally averaged fields from direct numerical simulations. Results. The azimuthally and time-averaged electromotive force in fast rotating dynamos is sufficiently well parameterized by the set of determined mean-field coefficients. In comparison to the previously considered (quasi-)stationary dynamo, the chaotic time-dependence leads to an improved scale separation and thus to a better agreement between direct numerical simulations and mean-field results.

(A)geostrophic adjustment of dipolar perturbations, formation of coherent structures and their properties, as follows from high-resolution numerical simulations with rotating shallow water model

In the general context of the geostrophic adjustment, we study the formation of coherent structures in a rotating shallow water model on the f-plane starting from localized dipolar configurations. We perform direct numerical simulations with such initial conditions with the help of a well-balanced high-resolution finite-volume numerical scheme. Initializations with geostrophically balanced quasigeostrophic modons with high enough Rossby numbers lead to adjustment toward quasistationary coherent ageostrophic dipoles. Like in laboratory experiments, cyclonic potential vorticity is being detrained from the dipoles and their trajectories bend. Comparisons with recently found exact steady-moving localized dipolar solutions show similarities and differences at the same time. Initializations with unbalanced dipolar initial conditions lead to similar quasistationary configurations at high enough effective Rossby numbers. At low Rossby numbers the classical geostrophic adjustment is observed. Ageostrophic quasistationary dipoles emerging from the simulations are surprisingly robust. They undergo frontal collisions with an exchange of cyclonic partners, which are essentially elastic and do not change their structure. They also keep coherence when encountering a steep topography and ballistically transport passive tracers.

Chromospheric activity among fast-rotating M dwarfs in the open cluster NGC 2516

We report radial velocities (RVs), projected equatorial velocities (v sin i) and CaII triplet (CaT) chromospheric activity indices for 237 late-K to mid-M candidate members of the young open cluster NGC 2516. These stars have rotation periods between 0.1 and 15 days. Intermediate resolution spectra were obtained using the Giraffe spectrograph at the Very Large Telescope. Membership was confirmed on the basis of RVs for 210 targets. We see a marked increase in the fraction of rapidly rotators as we move to cooler spectral types. About 20 per cent of M0-M1 stars have v sin i >15km/s, increasing to 90 per cent of M4 stars. Activity indices derived from the first two lines of the CaT (8498A and 8542A) show differing dependencies on rotation period and mass for stars lying above and below the fully convective boundary. Higher mass stars, of spectral type K3-M2.5, show chromospheric activity which increases with decreasing Rossby number (the ratio of period to convective turnover time), saturating for Rossby numbers <0.1. For cooler stars, which are probably fully convective and almost all of which have Rossby numbers <0.1, there is a clear decrease in chromospheric activity as (V-I)_0 increases, amounting to a fall of about a factor of 2-3 between spectral types M2.5 and M4. This decrease in activity levels at low Rossby numbers is not seen in X-ray observations of the coronae of cluster M-dwarfs or of active field M-dwarfs. There is no evidence for supersaturation of chromospheric activity for stars of any spectral type at Rossby numbers <0.01. We suggest that the fall in the limiting level of chromospheric emission beyond spectral type M3 in NGC~2516 is, like the simultaneous increase in rotation rates in field stars, associated with a change in the global magnetic topology as stars approach the fully convective boundary and not due to any decrease in dynamo-generated magnetic flux.

Saturation and time dependence of geodynamo models

In this study we address the question under which conditions a saturated velocity field stemming from geodynamo simulations leads to an exponential growth of the magnetic field in a corresponding kinematic calculation. We perform global self-consistent geodynamo simulations and calculate the evolution of a kinematically advanced tracer field. The self-consistent velocity field enters the induction equation in each time step, but the tracer field does not contribute to the Lorentz force. This experiment has been performed by Cattaneo & Tobias (2009) and is closely related to the test field method by Schrinner et al. (2005, 2007). We find two dynamo regimes in which the tracer field either grows exponentially or approaches a state aligned with the actual self-consistent magnetic field after an initial transition period. Both regimes can be distinguished by the Rossby number and coincide with the dipolar and multipolar dynamo regimes identified by Christensen & Aubert (2006). Dipolar dynamos with low Rossby number are kinematically stable whereas the tracer field grows exponentially in the multipolar dynamo regime. This difference in the saturation process for dynamos in both regimes comes along with differences in their time variability. Within our sample of 20 models, solely kinematically unstable dynamos show dipole reversals and large excursions. The complicated time behaviour of these dynamos presumably relates to the alternating growth of several competing dynamo modes. On the other hand, dynamos in the low Rossby number regime exhibit a rather simple time dependence and their saturation merely results in a fluctuation of the fundamental dynamo mode about its critical state.

Rotating helical turbulence. I. Global evolution and spectral behavior

We present results from two 15363 direct numerical simulations of rotating turbulence where both energy and helicity are injected into the flow by an external forcing. The dual cascade of energy and helicity toward smaller scales observed in isotropic and homogeneous turbulence is broken in the presence of rotation, with the development of an inverse cascade of energy now coexisting with direct cascades of energy and helicity. In the direct cascade range, the flux of helicity dominates over that of energy at low Rossby number. These cascades have several consequences for the statistics of the flow. The evolution of global quantities and of the energy and helicity spectra is studied, and comparisons with simulations at different Reynolds and Rossby numbers at lower resolution are done to identify scaling laws.

On the stabilizing effect of the Coriolis force on the turbulent wake of a normal flat plate

The turbulent Karman vortex street behind a flat plate in a rotating fluid is explored by means of direct numerical simulations. The effect of the Coriolis force is often said to be stabilizing on the cyclonic side of the wake and destabilizing on the anticyclonic side. The present computer experiments reveal a more subtle influence of the system rotation. The turbulence is suppressed at the cyclonic side of the wake at Rossby numbers of about unity whereas the cyclonic Karman roller eddies persist. The anticyclonic vortex cells which are blurred by the enhanced turbulence level are scarcely visible. The Strouhal number of this asymmetric vortex shedding is slightly higher than in the absence of rotation. At even higher rotation rates, the three-dimensional turbulence is suppressed also along the anticyclonic side of the wake and a nearly symmetric vortex street is observed at Rossby number of 0.16 with the Strouhal number significantly lower than for the nonrotating wake. At this rotation rate, the anticyclonically shed cells appeared as high-pressure zones. At even lower Rossby numbers, not only the turbulence but also the periodic vortex shedding is suppressed, in accordance with the demarcation line in a Rossby–Ekman number flow regime map.

Rotational accelerations stabilize leading edge vortices on revolving fly wings

The aerodynamic performance of hovering insects is largely explained by the presence of a stably attached leading edge vortex (LEV) on top of their wings. Although LEVs have been visualized on real, physically modeled, and simulated insects, the physical mechanisms responsible for their stability are poorly understood. To gain fundamental insight into LEV stability on flapping fly wings we expressed the Navier-Stokes equations in a rotating frame of reference attached to the wing's surface. Using these equations we show that LEV dynamics on flapping wings are governed by three terms: angular, centripetal and Coriolis acceleration. Our analysis for hovering conditions shows that angular acceleration is proportional to the inverse of dimensionless stroke amplitude, whereas Coriolis and centripetal acceleration are proportional to the inverse of the Rossby number. Using a dynamically scaled robot model of a flapping fruit fly wing to systematically vary these dimensionless numbers, we determined which of the three accelerations mediate LEV stability. Our force measurements and flow visualizations indicate that the LEV is stabilized by the ;quasi-steady' centripetal and Coriolis accelerations that are present at low Rossby number and result from the propeller-like sweep of the wing. In contrast, the unsteady angular acceleration that results from the back and forth motion of a flapping wing does not appear to play a role in the stable attachment of the LEV. Angular acceleration is, however, critical for LEV integrity as we found it can mediate LEV spiral bursting, a high Reynolds number effect. Our analysis and experiments further suggest that the mechanism responsible for LEV stability is not dependent on Reynolds number, at least over the range most relevant for insect flight (100<Re<14,000). LEVs are stable and continue to augment force even when they burst. These and similar findings for propellers and wind turbines at much higher Reynolds numbers suggest that even large flying animals could potentially exploit LEV-based force augmentation during slow hovering flight, take-offs or landing. We calculated the Rossby number from single-wing aspect ratios of over 300 insects, birds, bats, autorotating seeds, and pectoral fins of fish. We found that, on average, wings and fins have a Rossby number close to that of flies (Ro=3). Theoretically, many of these animals should therefore be able to generate a stable LEV, a prediction that is supported by recent findings for several insects, one bat, one bird and one fish. This suggests that force augmentation through stably attached (leading edge) vortices could represent a convergent solution for the generation of high fluid forces over a quite large range in size.

Neutrally Stratified Turbulent Ekman Boundary Layer: Universal Similarity for a Transitional Rough Surface

The geostrophic Ekman boundary layer for large Rossby number (Ro) has been investigated by exploring the role played by the mesolayer (intermediate layer) lying between the traditional inner and outer layers. It is shown that the velocity and Reynolds shear stress components in the inner layer (including the overlap region) are universal relations, explicitly independent of surface roughness. This universality of predictions has been supported by observations from experiment, field and direct numerical simulation (DNS) data for fully smooth, transitionally rough and fully rough surfaces. The maxima of Reynolds shear stresses have been shown to be located in the mesolayer of the Ekman boundary layer, whose scale corresponds to the inverse square root of the friction Rossby number. The composite wall-wake universal relations for geostrophic velocity profiles have been proposed, and the two wake functions of the outer layer have been estimated by an eddy viscosity closure model. The geostrophic drag and cross-isobaric angle predictions yield universal relations, which are also supported by extensive field, laboratory and DNS data. The proposed predictions for the geostrophic drag and the cross-isobaric angle compare well with data for Rossby number Ro ≥ 105. The data show low Rossby number effects for Ro < 105 and higher-order effects due to the mesolayer compare well with the data for Ro ≥ 103.

Upwelling flow dynamics in long canyons at low Rossby number

Submarine canyons, topographic features incising the continental slope, vary in both shape and size. The dynamics of short canyons have been observed and described in the field, in the laboratory, and with numerical simulations. Flow within long canyons, such as Juan de Fuca canyon, located between Vancouver Island and Washington State in the Pacific Northwest, is less well understood. Physical models of both long and short canyons have been constructed to understand the upwelling dynamics in long canyons and how upwelling changes, as compared with the dynamics of short canyons, at low Rossby number. Stratification and rotation, both important parameters in determining the dynamics in canyons, can be controlled and scaled accordingly for replication of oceanic conditions. The physical model is spun up to an initial rotation rate, and the flow is forced by increasing the rotation rate over the equivalent of several days. Flow visualization is used to determine the strength and location of upwelling, the strength and mechanisms generating vorticity, as well as the differences between the flow within the long and short canyons. The pattern of upwelling between the two canyons is significantly different in the horizontal with upwelling occurring through the canyon head in the short canyon and upwelling occurring close to the mouth along the downstream rim in the long canyon. At high Rossby number, upwelling is similar in both the long and short canyon and is driven by advection. However, as Rossby number decreases, the flow in the long canyon is more strongly affected by the strong convergence of the isobaths near the canyon than by advection alone.

SURPRISINGLY WEAK MAGNETISM ON YOUNG ACCRETING BROWN DWARFS

We have measured the surface magnetic flux on four accreting young brown dwarfs and one non-accreting young very low-mass star utilizing high resolution spectra of absorption lines of the FeH molecule. A magnetic field of 1-2 kG had been proposed for one of the brown dwarfs, 2MASS J1207334$-$393254, because of its similarities to higher mass T Tauri stars as manifested in accretion and the presence of a jet. We do not find clear evidence for a kilo-Gauss field in any of our young brown dwarfs but do find a 2 kG field on the young VLM star. Our 3-$\sigma$ upper limit for the magnetic flux in 2MASS J1207334$-$393254 just reaches 1 kG. We estimate the magnetic field required for accretion in young brown dwarfs given the observed rotations, and find that fields of only a few hundred Gauss are sufficient for magnetospheric accretion. This predicted value is less than our observed upper limit. We conclude that magnetic fields in young brown dwarfs are a factor of five or more lower than in young stars of about one solar mass, and in older stars with spectral types similar to our young brown dwarfs. It is interesting that, during the first few million years, the fields scale down with mass in line with what is needed for magnetospheric accretion, yet no such scaling is observed at later ages within the same effective temperature range. This scaling is opposite to the trend in rotation, with shorter rotation periods for very young accreting brown dwarfs compared with accreting solar-mass objects (and very low Rossby numbers in all cases). We speculate that in young objects a deeper intrinsic connection may exist between magnetospheric accretion and magnetic field strength, or that magnetic field generation in brown dwarfs may be less efficient than in stars. Neither of these currently have an easy physical explanation.

Inner shelf circulation patterns and nearshore flow reversal under downwelling and stratified conditions off a curved coastline

The role of a curved coastline and associated bathymetry in the development of downwelling circulation in a stratified inner shelf is examined through a number of numerical experiments. Different scenarios include constant versus variable wind‐forcing and variations in bottom friction. The three‐dimensional response of the shelf within the domain (embayment enclosed by capes) is associated with the generation of a velocity/pycnocline disturbance at the upstream cape and its subsequent downstream advection. This disturbance is more pronounced under variable wind conditions. Its downstream advection through the bay exhibits different patterns depending on the competition between inertia and bottom friction near the cape. When inertia dominates, the disturbance separates from the cape and travels downwind with an enhanced downstream flow offshore and a countercurrent inshore. The separation occurs at a low Rossby number (Ro ∼ 0.15), which is attributed to the positive curvature of the coastline forming the cape. When friction dominates, the advection path is constrained along the coastline, resulting in an alongshore temperature gradient and a transient thermal front running almost perpendicular to the coast/isobaths. Simulations with spatially variable bottom friction, with higher friction toward the coast, result in the generation of eddy‐like features. The numerical results are in agreement with both observations and surface temperature imagery from Long Bay, South Carolina, an embayment enclosed by two capes, and emphasize the role that coastline and associated shelf morphology can play in enhancing cross‐shelf transport and exchange.

The Internal Shear of Type Ia Supernova Progenitors During Accretion and Simmering

A white dwarf (WD) gains substantial angular momentum during the accretion process that grows it toward a Chandrasekhar mass. It is therefore expected to be quickly rotating when it ignites as a Type Ia supernova. The thermal and shearing profile are important for subsequent flame propagation. We highlight processes that could affect the WD shear, during accretion as well as during the ~1000 years of pre-explosive simmering. Baroclinic instabilities and/or the shear growth of small magnetic fields provide sufficient torque to bring the WD very close to solid body rotation during accretion. The lack of significant shear makes it difficult to grow a WD substantially past the typical Chandrasekhar mass. Once carbon ignites, a convective region spreads from the WD's center. This phase occurs regardless of progenitor scenario, and therefore it is of great interest for understanding how the WD interior is prepared before the explosive burning begins. We summarize some of the key properties of the convective region, which includes demonstrating that the mass enclosed by convection at any given time depends most sensitively on a single parameter that can be expressed as either the ratio of temperatures or densities at the top and bottom of the convection zone. At low Rossby numbers the redistribution of angular momentum by convection may result in significant shearing at the convective/non-convective boundary.

Stability of some exact solutions of the shallow‐water equations for testing numerical models in spherical geometry

AbstractFive families of exact axisymmetric solutions of the nonlinear shallow‐water equations in spherical geometry have recently been proposed as an aid to the development and testing of global numerical models. Sufficient conditions for the stability of these solutions are here derived to guide the choice of values for the family parameters. Thus it can be ensured that any significant time evolution occurring in a numerical model initialised with one of these exact solutions is of numerical origin, and does not reflect an inherent physical instability. With the caveat that only sufficient conditions for stability are examined, it appears that planetary rotation stabilises the solutions (as would be so if the flow were governed by barotropic vorticity dynamics), and that low Rossby and Froude numbers favour their stability. © Crown Copyright 2008. Reproduced with the permission of the Controller of HMSO. Published by John Wiley &amp; Sons, Ltd

Effect of Hydraulic Jump on Hydrodynamics and Heat Transfer in a Thin Liquid Film Flowing Over a Rotating Disk Analyzed by Integral Method

Flow and heat transfer in a liquid film flowing over the surface of a rotating disk was analyzed by integral technique. The integral analysis includes the prediction of the hydraulic jump and its effects on heat transfer. The results of this analysis are compared to the earlier results that did not include this effect. At low inlet Reynolds numbers and high Rossby numbers, corresponding to low film inertia and low rotation rates, respectively, a hydraulic jump appears on the disk surface. The location of the jump and the liquid film height at this location are predicted. A scaling analysis of the equations governing the film thickness provided a semi-empirical expression for these quantities that was found to be in very good agreement with numerical results. Heat transfer analysis shows that the Nusselt numbers for both constant disk surface temperature and constant disk surface heat flux boundary conditions are lowered in the vicinity of the hydraulic jump due to the thickened liquid film. This effect can be more pronounced for the constant heat flux case depending on the location of the hydraulic jump. The Nusselt number exhibits a turning point at the jump location and can have higher values downstream of the hydraulic jump compared to those obtained from the analysis that does not include the gravitational effects.

The theory of quasi-geostrophic von Kármán vortex streets in two-layer fluids on a beta-plane

In this study self-organized periodic coherent vortex structures arising in geophysical turbulent flows at low Rossby number are investigated by developing a conceptual model based on an analytical theory of von Kármán vortex streets affected by stratification and differential rotation. In the framework of a quasi-geostrophic (QG) two-layer beta-plane model vortex streets with three different types of vertical structures (barotropic, upper layer and hetonic) are analysed using the point vortex approximation. The streets are found to be exact solutions of the potential vorticity equation and to be characterized by four non-dimensional parameters. Von Kármán streets are semi-localized solutions which form a bridge between vortex pairs (limit of symmetric dilute streets) and two parallel vortex sheets (limit of dense streets). On the beta-plane QG von Kármán streets can only move to the east, i.e. with a speed outside the range of speeds of Rossby waves, so that a dynamical asymmetry in the zonal direction is introduced. A complete classification on a diagram of states shows that critical bounds exist in the parameter space, prescribing for example a maximum distance between vortex rows beyond which no QG vortex streets can be found. Typically a fast and a slow vortex street with different flow structures are found in the region of existence. As a function of distance between vortex rows baroclinic QG vortex streets show a characteristic non-monotonic speed behaviour at scales of the order of the baroclinic Rossby radius. A wide region of possible existence of QG von Kármán streets is found in atmospheric, oceanic and planetary conditions as well as in rotating tank experiments. The theory can be applied to describe the coherent part of turbulent baroclinic intermittent zonal jet-like and frontal flows and provides a scaling for such flows.