Eddy Amplitudes in Baroclinic Turbulence Driven by Nonzonal Mean Flow: Shear Dispersion of Potential Vorticity

2007 ◽  
Vol 37 (4) ◽  
pp. 1037-1050 ◽  
Author(s):  
K. Shafer Smith
Keyword(s):  
Potential Vorticity ◽  
Large Scale ◽  
Dispersion Model ◽  
Baroclinic Instability ◽  
Zonal Flow ◽  
Mean Flow ◽  
Jet Mixing ◽  
Zonal Jets ◽  
Shear Dispersion ◽  
The Cross

Abstract As in the midlatitude atmosphere, midocean eddies are primarily generated by baroclinically unstable mean currents. In contrast to the atmosphere, however, oceanic currents are significantly nonzonal. Even weak nonzonal currents are linearly unstable since β does not suppress growing meridional waves. Theories for the nonlinear equilibration of baroclinic instability, and hence theories for the amplitudes of midocean eddies, must therefore take into account the different dynamics of nonzonal flow. It is shown here that the amplitude of fully developed baroclinic turbulence due to nonzonal shears differs from that due to zonal shears primarily in the nature of the eddy generation. Since β will act to create large-scale zonal jet structures regardless of the generation source, the nature of eddy fluxes of potential vorticity (the source of eddy energy) in the zonal and meridional directions are fundamentally different. The cross-jet mixing has been shown previously to obey a mixing-length scaling, and this corresponds to the generation due to unstable zonal flow. The along-jet mixing, which corresponds to the generation due to the meridional shear, is shown here to be best described by a shear dispersion model. The resulting flux is orders of magnitude higher than in the cross-jet direction, and thus eddy energies driven by baroclinically unstable mean flows with a nonzero meridional component are much larger. This provides an explanation for recently reported results. Moreover, given recent observational and modeling studies showing the ubiquitous presence of zonal jets in the oceans, the results presented here indicate a powerful source of eddy energy.

Inertia–gravity waves in a liquid-filled, differentially heated, rotating annulus

2015 ◽  
Vol 782 ◽  
pp. 144-177 ◽  
Author(s):  
Anthony Randriamampianina ◽  
Emilia Crespo del Arco
Keyword(s):  
Prandtl Number ◽  
Gravity Waves ◽  
Large Scale ◽  
Baroclinic Instability ◽  
Zonal Flow ◽  
Small Scale ◽  
Mean Flow ◽  
Baroclinic Waves ◽  
Fluid Properties ◽  
Spatio Temporal

Direct numerical simulations based on high-resolution pseudospectral methods are carried out for detailed investigation into the instabilities arising in a differentially heated, rotating annulus, the baroclinic cavity. Following previous works using air (Randriamampianina et al., J. Fluid Mech., vol. 561, 2006, pp. 359–389), a liquid defined by Prandtl number $Pr=16$ is considered in order to better understand, via the Prandtl number, the effects of fluid properties on the onset of gravity waves. The computations are particularly aimed at identifying and characterizing the spontaneously emitted small-scale fluctuations occurring simultaneously with the baroclinic waves. These features have been observed as soon as the baroclinic instability sets in. A three-term decomposition is introduced to isolate the fluctuation field from the large-scale baroclinic waves and the time-averaged mean flow. Even though these fluctuations are found to propagate as packets, they remain attached to the background baroclinic waves, locally triggering spatio-temporal chaos, a behaviour not observed with the air-filled cavity. The properties of these features are analysed and discussed in the context of linear theory. Based on the Richardson number criterion, the characteristics of the generation mechanism are consistent with a localized instability of the shear zonal flow, invoking resonant over-reflection.

scholarly journals Jet Formation and Evolution in Baroclinic Turbulence with Simple Topography

2010 ◽  
Vol 40 (2) ◽  
pp. 257-278 ◽  
Author(s):  
Andrew F. Thompson
Keyword(s):  
Southern Ocean ◽  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Length Scale ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Jet Formation ◽  
Meridional Transport ◽  
Jet Behavior ◽  
Jet Variability

Abstract Satellite altimetry and high-resolution ocean models indicate that the Southern Ocean comprises an intricate web of narrow, meandering jets that undergo spontaneous formation, merger, and splitting events, as well as rapid latitude shifts over periods of weeks to months. The role of topography in controlling jet variability is explored using over 100 simulations from a doubly periodic, forced-dissipative, two-layer quasigeostrophic model. The system is forced by a baroclinically unstable, vertically sheared mean flow in a domain that is large enough to accommodate multiple jets. The dependence of (i) meridional jet spacing, (ii) jet variability, and (iii) domain-averaged meridional transport on changes in the length scale and steepness of simple sinusoidal topographical features is analyzed. The Rhines scale, ℓβ = 2πVe/β, where Ve is an eddy velocity scale and β is the barotropic potential vorticity gradient, measures the meridional extent of eddy mixing by a single jet. The ratio ℓβ /ℓT, where ℓT is the topographic length scale, governs jet behavior. Multiple, steady jets with fixed meridional spacing are observed when ℓβ ≫ ℓT or when ℓβ ≈ ℓT. When ℓβ < ℓT, a pattern of perpetual jet formation and jet merger dominates the time evolution of the system. Zonal ridges systematically reduce the domain-averaged meridional transport, while two-dimensional, sinusoidal bumps can increase transport by an order of magnitude or more. For certain parameters, bumpy topography gives rise to periodic oscillations in the jet structure between purely zonal and topographically steered states. In these cases, transport is dominated by bursts of mixing associated with the transition between the two regimes. Topography modifies local potential vorticity (PV) gradients and mean flows; this can generate asymmetric Reynolds stresses about the jet core and can feed back on the conversion of potential energy to kinetic energy through baroclinic instability. Both processes contribute to unsteady jet behavior. It is likely that these processes play a role in the dynamic nature of Southern Ocean jets.

scholarly journals Dynamics of Convectively Driven Banded Jets in the Laboratory

2007 ◽  
Vol 64 (11) ◽  
pp. 4031-4052 ◽  
Author(s):  
Peter L. Read ◽  
Yasuhiro H. Yamazaki ◽  
Stephen R. Lewis ◽  
Paul D. Williams ◽  
Robin Wordsworth ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flows ◽  
Large Scale ◽  
Zonal Flow ◽  
Inertial Range ◽  
Instability Criterion ◽  
Rossby Wave Breaking ◽  
Outer Planets ◽  
Zonal Jets ◽  
Geostrophic Turbulence

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

scholarly journals The Role of the Divergent Circulation for Large-Scale Eddy Momentum Transport in the Tropics. Part I: Observations

2019 ◽  
Vol 76 (4) ◽  
pp. 1125-1144 ◽  
Author(s):  
Pablo Zurita-Gotor
Keyword(s):  
Momentum Flux ◽  
Large Scale ◽  
Zonal Flow ◽  
Stationary Wave ◽  
Hadley Cell ◽  
Momentum Transport ◽  
Mean Flow ◽  
Meridional Transport ◽  
The Tropics

Abstract This work investigates the role played by the divergent circulation for meridional eddy momentum transport in the tropical atmosphere. It is shown that the eddy momentum flux in the deep tropics arises primarily from correlations between the divergent eddy meridional velocity and the rotational eddy zonal velocity. Consistent with previous studies, this transport is dominated by the stationary wave component, associated with correlations between the zonal structure of the Hadley cell (zonal anomalies in the meridional overturning) and the climatological-mean Rossby gyres. This eddy momentum flux decomposition implies a different mechanism of eddy momentum convergence from the extratropics, associated with upper-level mass convergence (divergence) over sectors with anomalous westerlies (easterlies). By itself, this meridional transport would only increase (decrease) isentropic thickness over regions with anomalous westerly (easterly) zonal flow. The actual momentum mixing is due to vertical (cross isentropic) advection, pointing to the key role of diabatic processes for eddy–mean flow interaction in the tropics.

Equatorial deep jets and their influence on the equatorial mean circulation in an idealised model forced by intraseasonal momentum flux convergence

2020 ◽  
Author(s):  
Swantje Bastin ◽  
Martin Claus ◽  
Peter Brandt ◽  
Richard J. Greatbatch
Keyword(s):  
Momentum Flux ◽  
Intraseasonal Variability ◽  
Zonal Flow ◽  
Wind Forcing ◽  
Vertical Resolution ◽  
Mean Flow ◽  
Geophysical Research ◽  
Zonal Jets ◽  
Total Magnitude ◽  
Idealised Model

<p>Equatorial deep jets (EDJ) are vertically stacked, downward propagating zonal jets that alternate in direction with depth. In the tropical Atlantic, they have been shown to influence both surface conditions and tracer variability. Despite their importance, the EDJ are absent in most ocean models, most likely due to a lack of vertical resolution. However, when the vertical resolution is sufficiently high, EDJ oscillating at a period of about 4.5 years are present in idealised model configurations driven by steady wind forcing. We have used such a model for a basin-wide reconstruction of the intraseasonal eddy momentum flux convergence, which has recently been shown to be a large contributor to the EDJ maintenance (Greatbatch et al., 2018). When we apply the diagnosed momentum flux convergence that is oscillating at the EDJ period as forcing in a model without wind forcing, EDJ develop, allowing us to verify the mechanism proposed in Greatbatch et al. (2018). Additionally, we can isolate the nonlinear effect that the EDJ have on the time mean zonal flow at intermediate depths. We can show that the EDJ drive time mean zonal flow that is similar in structure to the mean flow measured by Argo floats at 1000 m depth, contributing (in our idealised setup) about one fifth of the total magnitude of the observed flow, the rest likely resulting from direct forcing by downward propagating intraseasonal waves as shown before in other studies.</p><p> </p><p>References:</p><p>Greatbatch, R. J., M. Claus, P. Brandt, J.-D. Matthießen, F. P. Tuchen, F. Ascani, M. Dengler, J. Toole, C. Roth, J. T. Farrar, 2018: Evidence for the Maintenance of Slowly Varying Equatorial Currents by Intraseasonal Variability. <em>Geophysical Research Letters</em>, <strong>45</strong>, 1923-1929.</p>

scholarly journals A Framework for Parameterizing Eddy Potential Vorticity Fluxes

2012 ◽  
Vol 42 (4) ◽  
pp. 539-557 ◽  
Author(s):  
David P. Marshall ◽  
James R. Maddison ◽  
Pavel S. Berloff
Keyword(s):  
Stress Tensor ◽  
Potential Vorticity ◽  
Large Scale ◽  
Eddy Diffusivity ◽  
Linear Instability ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Conservation Of Energy ◽  
The Mean ◽  
Energy And Momentum

Abstract A framework for parameterizing eddy potential vorticity fluxes is developed that is consistent with conservation of energy and momentum while retaining the symmetries of the original eddy flux. The framework involves rewriting the residual-mean eddy force, or equivalently the eddy potential vorticity flux, as the divergence of an eddy stress tensor. A norm of this tensor is bounded by the eddy energy, allowing the components of the stress tensor to be rewritten in terms of the eddy energy and nondimensional parameters describing the mean shape and orientation of the eddies. If a prognostic equation is solved for the eddy energy, the remaining unknowns are nondimensional and bounded in magnitude by unity. Moreover, these nondimensional geometric parameters have strong connections with classical stability theory. When applied to the Eady problem, it is shown that the new framework preserves the functional form of the Eady growth rate for linear instability. Moreover, in the limit in which Reynolds stresses are neglected, the framework reduces to a Gent and McWilliams type of eddy closure where the eddy diffusivity can be interpreted as the form proposed by Visbeck et al. Simulations of three-layer wind-driven gyres are used to diagnose the eddy shape and orientations in fully developed geostrophic turbulence. These fields are found to have large-scale structure that appears related to the structure of the mean flow. The eddy energy sets the magnitude of the eddy stress tensor and hence the eddy potential vorticity fluxes. Possible extensions of the framework to ensure potential vorticity is mixed on average are discussed.

scholarly journals Rossby waves and two-dimensional turbulence in a large-scale zonal jet

1987 ◽  
Vol 183 ◽  
pp. 467-509 ◽  
Author(s):  
Theodore G. Shepherd
Keyword(s):  
Large Scale ◽  
Zonal Flow ◽  
Order Effect ◽  
Spatial Inhomogeneity ◽  
Mean Flow ◽  
Scale Separation ◽  
Zonal Flows ◽  
Beta Plane ◽  
Zonal Wavenumber ◽  
Scale Shear

The theory of homogeneous barotropic beta-plane turbulence is here extended to include effects arising from spatial inhomogeneity in the form of a zonal shear flow. Attention is restricted to the geophysically important case of zonal flows that are barotropically stable and are of larger scale than the resulting transient eddy field.Because of the presumed scale separation, the disturbance enstrophy is approximately conserved in a fully nonlinear sense, and the (nonlinear) wave-mean-flow interaction may be characterized as a shear-induced spectral transfer of disturbance enstrophy along lines of constant zonal wavenumber k. In this transfer the disturbance energy is generally not conserved. The nonlinear interactions between different disturbance components are turbulent for scales smaller than the inverse of Rhines's cascade-arrest scale κβ≡ (β0/2urms)½ and in this regime their leading-order effect may be characterized as a tendency to spread the enstrophy (and energy) along contours of constant total wavenumber κ ≡ (k2 + l2)½. Insofar as this process of turbulent isotropization involves spectral transfer of disturbance enstrophy across lines of constant zonal wavenumber k, it can be readily distinguished from the shear-induced transfer which proceeds along them. However, an analysis in terms of total wavenumber K alone, which would be justified if the flow were homogeneous, would tend to mask the differences.The foregoing theoretical ideas are tested by performing direct numerical simulation experiments. It is found that the picture of classical beta-plane turbulence is altered, through the effect of the large-scale zonal flow, in the following ways: (i) while the turbulence is still confined to KKβ, the disturbance field penetrates to the largest scales of motion; (ii) the larger disturbance scales K < Kβ exhibit a tendency to meridional rather than zonal anisotropy, namely towards v2 > u2 rather than vice versa; (iii) the initial spectral transfer rate away from an isotropic intermediate-scale source is significantly enhanced by the shear-induced transfer associated with straining by the zonal flow. This last effect occurs even when the large-scale shear appears weak to the energy-containing eddies, in the sense that dU/dy [Lt ] κ for typical eddy length and velocity scales.

Laboratory and numerical studies of baroclinic waves in an internally heated rotating fluid annulus: a case of wave/vortex duality?

1997 ◽  
Vol 337 ◽  
pp. 155-191 ◽  
Author(s):  
P. L. READ ◽  
S. R. LEWIS ◽  
R. HIDE
Keyword(s):  
Numerical Simulations ◽  
Potential Vorticity ◽  
Axisymmetric Flow ◽  
Zonal Flow ◽  
Chaotic Advection ◽  
Rotating Fluid ◽  
Mean Flow ◽  
Baroclinic Waves ◽  
Vortex Merging ◽  
Flow Components

The structure, transport properties and regimes of flow exhibited in a rotating fluid annulus, subject to internal heating and sidewall cooling, are studied both in the laboratory and in numerical simulations. The performance of the numerical model is verified quantitatively to within a few per cent in several cases by direct comparison with measurements in the laboratory of temperature and horizontal velocity fields in the axisymmetric and regular wave regimes. The basic azimuthal mean flow produced by this distribution of heat sources and sinks leads to strips of potential vorticity in which the radial gradient of potential vorticity changes sign in both the vertical and horizontal directions. From diagnosis of the energy budget of numerical simulations, the principal instability of the flow is shown to be predominantly baroclinic in nature, though with a non-negligible contribution towards the maintenance of the non-axisymmetric flow components from the barotropic wave–zonal flow interaction. The structure of the regime diagram for the internally heated baroclinic waves is shown to have some aspects in common with conventional wall-heated annulus waves, but the former shows no evidence for time-dependence in the form of ‘amplitude vacillation’. Internally heated flows instead evidently prefer to make transitions between wavenumbers in the regular regime via a form of vortex merging and/or splitting, indicating a mixed vortex/wave character to the non-axisymmetric flows in this system. The transition towards irregular flow occurs via a form of wavenumber vacillation, also involving vortex splitting and merging events. Baroclinic eddies are shown to develop from an initial axisymmetric flow via a mixed sinuous/varicose instability, leading to the formation of detached vortices of the same sign as the ambient axisymmetric potential vorticity at that level, in a manner which resembles recent simulations of atmospheric baroclinic frontal instability and varicose barotropic instabilities. Dye tracer experiments confirm the mixed wave/vortex character of the equilibrated instabilities, and exhibit chaotic advection in time-dependent flows.

scholarly journals Characteristics and Dynamics of Density Fronts over the Inner to Mid-shelf under Weak Wind Conditions

2020 ◽  
Author(s):  
Xiaodong Wu ◽  
Falk Feddersen ◽  
Sarah N. Giddings
Keyword(s):  
Large Scale ◽  
Gravity Current ◽  
Vertical Mixing ◽  
Detection Algorithm ◽  
Mean Flow ◽  
Resolution Model ◽  
High Resolution Model ◽  
The Cross ◽  
Weak Winds ◽  
Light Side

AbstractHere, we explore the kinematics and dynamics of coastal density fronts (within 10 km from shore and < 30 m depth), identified using an edge detection algorithm, in a realistic high resolution model of the San Diego Bight with relatively weak winds and small freshwater input. The density fronts have lengths spanning 4 − 10 km and surface density gradients spanning 2 − 20 × 10−4 kg m−4. Cross-shore oriented fronts are more likely with northward subtidal flow and are 1/3 as numerous as alongshore oriented fronts which are more likely with onshore surface baroclinic diurnal flow. Using a subset of the cross-shore fronts, decomposed into cross-front mean and perturbation components, an ensemble front is created. The ensemble cross-front mean flow is largely geostrophic in the cross- and along-front directions. The ensemble cross-shore front extends several kilometers from shore, with a distinct linear front axis and downwelling (upwelling) on the dense (light) side of the front, convergent perturbation cross-front flow within the upper 5 m, strengthening the ensemble front. Vertical mixing of momentum is weak, counter to the turbulent thermal wind mechanism. The ensemble cross-shore front resembles a gravity current and is generated by a convergent strain field acting on the large scale density field. The ensemble front is bounded by the shoreline and is alongfront geostropic and cross-front ageostrophic. This contrasts with the cross-front geostrophic and along-front ageostrophic balances of classic deformation frontogenesis, but is consistent with semi-geostrophic coastal circulation.

scholarly journals Zonal Flow Regime Changes in a GCM and in a Simple Quasigeostrophic Model: The Role of Stratospheric Dynamics

2009 ◽  
Vol 66 (5) ◽  
pp. 1366-1383 ◽  
Author(s):  
Isabella Bordi ◽  
Klaus Fraedrich ◽  
Michael Ghil ◽  
Alfonso Sutera
Keyword(s):  
General Circulation ◽  
Baroclinic Instability ◽  
Three Dimensional ◽  
Vertical Wind Shear ◽  
Circulation Model ◽  
Zonal Flow ◽  
Heat Fluxes ◽  
Mean Flow ◽  
Single Wave

Abstract The atmospheric general circulation is characterized by both single- and double-jet patterns. The double-jet structure of the zonal mean zonal wind is analyzed in Southern Hemisphere observations for the two calendar months of November and April. The observed features are studied further in an idealized quasigeostrophic and a simplified general circulation model (GCM). Results suggest that capturing the bimodality of the zonal mean flow requires the parameterization of momentum and heat fluxes associated with baroclinic instability of the three-dimensional fields. The role of eddy heat fluxes in generating the observed double-jet pattern is ascertained by using an analytical Eady model with stratospheric easterlies, in which a single wave disturbance interacts with the mean flow. In this model, the dual jets are generated by the zonal mean flow correction. Sensitivity of the results to the tropospheric vertical wind shear (or, equivalently, the meridional temperature gradient in the basic state’s troposphere) is also studied in the Eady model and compared to related experiments using the simplified GCM.

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