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.

A Thickness-Weighted Average Perspective of Force Balance in an Idealized Circumpolar Current

2017 ◽  
Vol 47 (2) ◽  
pp. 285-302 ◽  
Author(s):  
Todd Ringler ◽  
Juan A. Saenz ◽  
Phillip J. Wolfram ◽  
Luke Van Roekel
Keyword(s):  
Surface Layer ◽  
Wind Stress ◽  
Potential Vorticity ◽  
Weighted Average ◽  
Ocean Surface ◽  
Force Balance ◽  
Mean Flow ◽  
Meridional Transport ◽  
Circumpolar Current ◽  
Meridional Advection

AbstractThe exact, three-dimensional, thickness-weighted averaged (TWA) Boussinesq equations are used to diagnose eddy–mean flow interaction in an idealized circumpolar current (ICC). The force exerted by mesoscale eddies on the TWA velocity is expressed as the divergence of the Eliassen–Palm flux tensor. Consistent with previous findings, the analysis indicates that the dynamically relevant definition of the ocean surface layer is composed of the set of buoyancy coordinates that ever reside at the ocean surface at a given horizontal position. The surface layer is found to be a physically distinct object with a diabatic and force balance that is largely isolated from the underlying adiabatic region in the interior. Within the ICC surface layer, the TWA meridional velocity is southward/northward in the top/bottom half and has a value near zero at the bottom. In the top half of the surface layer, the zonal forces due to wind stress and meridional advection of potential vorticity act to accelerate the TWA zonal velocity; equilibrium is obtained by eddies decelerating the zonal flow via a downward flux of eastward momentum that increases with depth. In the bottom half of the surface layer, the accelerating force of the wind stress is balanced by the eddy force and meridional advection of potential vorticity. The bottom of the surface layer coincides with the location where the zonal eddy force, meridional advection of potential vorticity, and zonal wind stress force are all zero. The net meridional transport Sf within the surface layer is a small residual of its southward and northward TWA meridional flows. The mean meridional gradient of the surface layer buoyancy is advected by Sf to balance the surface buoyancy flux.

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.

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.

Baroclinic Turbulence in the Ocean: Analysis with Primitive Equation and Quasigeostrophic Simulations

2011 ◽  
Vol 41 (9) ◽  
pp. 1605-1623 ◽  
Author(s):  
Antoine Venaille ◽  
Geoffrey K. Vallis ◽  
K. Shafer Smith
Keyword(s):  
Southern Ocean ◽  
Energy Levels ◽  
Baroclinic Instability ◽  
Primary Source ◽  
Equation Model ◽  
Ocean Modeling ◽  
Length Scale ◽  
Primitive Equation ◽  
Eddy Field ◽  
Quasigeostrophic Model

Abstract This paper examines the factors determining the distribution, length scale, magnitude, and structure of mesoscale oceanic eddies in an eddy-resolving primitive equation simulation of the Southern Ocean [Modeling Eddies in the Southern Ocean (MESO)]. In particular, the authors investigate the hypothesis that the primary source of mesoscale eddies is baroclinic instability acting locally on the mean state. Using local mean vertical profiles of shear and stratification from an eddying primitive equation simulation, the forced–dissipated quasigeostrophic equations are integrated in a doubly periodic domain at various locations. The scales, energy levels, and structure of the eddies found in the MESO simulation are compared to those predicted by linear stability analysis, as well as to the eddying structure of the quasigeostrophic simulations. This allows the authors to quantitatively estimate the role of local nonlinear effects and cascade phenomena in the generation of the eddy field. There is a modest transfer of energy (an “inverse cascade”) to larger scales in the horizontal, with the length scale of the resulting eddies typically comparable to or somewhat larger than the wavelength of the most unstable mode. The eddies are, however, manifestly nonlinear, and in many locations the turbulence is fairly well developed. Coherent structures also ubiquitously emerge during the nonlinear evolution of the eddy field. There is a near-universal tendency toward the production of grave vertical scales, with the barotropic and first baroclinic modes dominating almost everywhere, but there is a degree of surface intensification that is not captured by these modes. Although the results from the local quasigeostrophic model compare well with those of the primitive equation model in many locations, some profiles do not equilibrate in the quasigeostrophic model. In many cases, bottom friction plays an important quantitative role in determining the final scale and magnitude of eddies in the quasigeostrophic simulations.

scholarly journals Comparison of the Effect of Parameterized Eddy Fluxes of Thickness and Potential Vorticity

2014 ◽  
Vol 44 (9) ◽  
pp. 2470-2484 ◽  
Author(s):  
V. O. Ivchenko ◽  
S. Danilov ◽  
J. Schröter
Keyword(s):  
Potential Vorticity ◽  
Velocity Profiles ◽  
Momentum Conservation ◽  
Ocean Dynamics ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Alternative Scheme ◽  
Zonal Velocity ◽  
Eddy Fluxes ◽  
The Impact

Abstract Parameterization of mesoscale eddies is an important problem of modern ocean dynamics and modeling. The most widely used scheme is the so-called Gent–McWilliams parameterization, which describes the eddy-induced transport of tracers, including temperature, density, and isopycnal thickness (TH). An alternative scheme, proposed by Green and Welander, deals with parameterizing eddy fluxes of potential vorticity (PV). Many recent studies propose using it, for it includes the effect of eddy Reynolds stresses that may influence mean flows. These two schemes are compared in the simplest configuration of two-layer quasigeostrophic channel flow, which enables analytical solutions for zonal-mean fields. It is shown how the parameterizations shape the zonally averaged zonal velocity profiles, with special attention paid to the role of the Reynolds stresses and momentum conservation. The zonally averaged zonal velocity profiles are sensitive to the amplitude and profiles of TH and PV diffusivities. For small enough diffusivities the TH parameterization may lead to solutions resembling those for the PV parameterization if it uses the diffusivity of the latter; that is, it may mimic the impact of the Reynolds stresses on the mean flow.

scholarly journals Jet–Topography Interactions Affect Energy Pathways to the Deep Southern Ocean

2017 ◽  
Vol 47 (7) ◽  
pp. 1799-1816 ◽  
Author(s):  
Alice Barthel ◽  
Andrew McC. Hogg ◽  
Stephanie Waterman ◽  
Shane Keating
Keyword(s):  
Southern Ocean ◽  
Ocean Circulation ◽  
Baroclinic Instability ◽  
Deep Ocean ◽  
Ocean Model ◽  
Shear Instability ◽  
Horizontal Shear ◽  
Mean Flow ◽  
Flat Bottom ◽  
Turbulent Dissipation

AbstractIn the Southern Ocean, strong eastward ocean jets interact with large topographic features, generating eddies that feed back onto the mean flow. Deep-reaching eddies interact with topography, where turbulent dissipation and generation of internal lee waves play an important role in the ocean’s energy budget. However, eddy effects in the deep ocean are difficult to observe and poorly characterized. This study investigates the energy contained in eddies at depth, when an ocean jet encounters topography. This study uses a two-layer ocean model in which an imposed unstable jet encounters a topographic obstacle (either a seamount or a meridional ridge) in a configuration relevant to an Antarctic Circumpolar Current frontal jet. The authors find that the presence of topography increases the eddy kinetic energy (EKE) at depth but that the dominant processes generating this deep EKE depend on the shape and height of the obstacle as well as on the baroclinicity of the jet before it encounters topography. In cases with high topography, horizontal shear instability is the dominant source of deep EKE, while a flat bottom or a strongly sheared inflow leads to deep EKE being generated primarily through baroclinic instability. These results suggest that the deep EKE is set by an interplay between the inflowing jet properties and topography and imply that the response of deep EKE to changes in the Southern Ocean circulation is likely to vary across locations depending on the topography characteristics.

scholarly journals The Kuroshio Extension Northern Recirculation Gyre: Profiling Float Measurements and Forcing Mechanism

2008 ◽  
Vol 38 (8) ◽  
pp. 1764-1779 ◽  
Author(s):  
Bo Qiu ◽  
Shuiming Chen ◽  
Peter Hacker ◽  
Nelson G. Hogg ◽  
Steven R. Jayne ◽  
...  
Keyword(s):  
Potential Vorticity ◽  
North Pacific Ocean ◽  
Kuroshio Extension ◽  
Japan Trench ◽  
Gradient Field ◽  
Momentum Balance ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Recirculation Gyre ◽  
The Kuroshio

Abstract Middepth, time-mean circulation in the western North Pacific Ocean (28°–45°N, 140°–165°E) is investigated using drift information from the profiling floats deployed in the Kuroshio Extension System Study (KESS) and the International Argo programs. A well-defined, cyclonic recirculation gyre (RG) is found to exist north of the Kuroshio Extension jet, confined zonally between the Japan Trench (∼145°E) and the Shatsky Rise (∼156°E), and bordered to the north by the subarctic boundary along ∼40°N. This northern RG, which is simulated favorably in the eddy-resolving OGCM for the Earth Simulator (OFES) hindcast run model, has a maximum volume transport at 26.4 Sv across 159°E and its presence persists on the interannual and longer time scales. An examination of the time-mean x-momentum balance from the OFES hindcast run output reveals that horizontal convergence of Reynolds stresses works to accelerate both the eastward-flowing Kuroshio Extension jet and a westward mean flow north of the meandering jet. The fact that the northern RG is eddy driven is further confirmed by examining the turbulent Sverdrup balance, in which convergent eddy potential vorticity fluxes are found to induce the cyclonic RG across the background potential vorticity gradient field. For the strength of the simulated northern RG, the authors find the eddy dissipation effect to be important as well.

Gravity Wave–Induced Anomalous Potential Vorticity Gradient Generating Planetary Waves in the Winter Mesosphere

2015 ◽  
Vol 72 (9) ◽  
pp. 3609-3624 ◽  
Author(s):  
Kaoru Sato ◽  
Masahiro Nomoto
Keyword(s):  
Gravity Wave ◽  
Potential Vorticity ◽  
General Circulation ◽  
Baroclinic Instability ◽  
Circulation Model ◽  
Planetary Waves ◽  
Mean Flow ◽  
Flux Divergence ◽  
Characteristic Structure ◽  
Simultaneous Generation

Abstract This study shows that gravity wave (GW) forcing (GWF) plays a crucial role in the barotropic/baroclinic instability that is frequently observed in the mesosphere and considered an origin of planetary waves (PWs) such as quasi-2-day and quasi-4-day waves. Simulation data from a GW-resolving general circulation model were analyzed, focusing on the winter Northern Hemisphere where PWs are active. The unstable field is characterized by a significant potential vorticity (PV) maximum with an anomalous latitudinal gradient at higher latitudes that suddenly appears in the midlatitudes of the upper mesosphere. This PV maximum is attributed to an enhanced static stability that develops through the following two processes: 1) strong PWs from the troposphere break in the middle stratosphere, causing a poleward and downward shift of the westerly jet to higher latitudes, and 2) strong GWF located above the jet simultaneously shifts and forms an upwelling in the midlatitudes, causing a significant increase in . An interesting feature is that the PV maximum is not zonally uniform but is observed only at longitudes with strong GWF. This longitudinally dependent GWF can be explained by selective filtering in the stratospheric mean flow modified by strong PWs. In the upper mesosphere, the Eliassen–Palm flux divergence by PWs has a characteristic structure, which is positive poleward and negative equatorward of the enhanced PV maximum, attributable to eastward- and westward-propagating PWs, respectively. This fact suggests that the barotropic/baroclinic instability is eliminated by simultaneous generation of eastward and westward PWs causing PV flux divergence.

Study of the Standard k-ε Model for Tip Leakage Flow in an Axial Compressor Rotor

2016 ◽  
Vol 33 (4) ◽  
Author(s):  
Yanfei Gao ◽  
Yangwei Liu ◽  
Luyang Zhong ◽  
Jiexuan Hou ◽  
Lipeng Lu
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Turbulent Viscosity ◽  
Axial Compressor ◽  
Leakage Flow ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Tip Leakage Flow ◽  
Tip Leakage ◽  
Compressor Rotor

AbstractThe standard k-ε model (SKE) and the Reynolds stress model (RSM) are employed to predict the tip leakage flow (TLF) in a low-speed large-scale axial compressor rotor. Then, a new research method is adopted to “freeze” the turbulent kinetic energy and dissipation rate of the flow field derived from the RSM, and obtain the turbulent viscosity using the Boussinesq hypothesis. The Reynolds stresses and mean flow field computed on the basis of the frozen viscosity are compared with the results of the SKE and the RSM. The flow field in the tip region based on the frozen viscosity is more similar to the results of the RSM than those of the SKE, although certain differences can be observed. This finding indicates that the non-equilibrium turbulence transport nature plays an important role in predicting the TLF, as well as the turbulence anisotropy.

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