Baroclinic instability and geostrophic turbulence

Salmon, Rick

doi:10.1080/03091928008241178

Cited by 238 publications

(253 citation statements)

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“…This does not contradict the well-known forward cascade of total baroclinic energy above the deformation scale (Charney 1971;Salmon 1998; also S. Danilov 2006, personal communication), because it turns out the forward potential energy cascade slightly overpowers the inverse kinetic energy (KE) cascade, leaving a small residual cascade of total energy converging toward the deformation scale. Because this baroclinic KE cascade dominates the surface layer cascade of the two-layer idealized quasigeostrophic (QG) model with surface-intensified stratification (thinner upper layer) used by SA07, it likely reflects the KE cascade observable with the altimeter data at least at scales larger than the deformation radius; at smaller scales, surface geostrophic turbulence effects become important (Lapeyre and Klein 2006).…”

Section: Introductionmentioning

confidence: 86%

“…A rich phenomenology has developed (Danilov and Gurarie 2000;Vallis 2006), with key features being a robust inverse cascade transferring total (kinetic plus potential) energy toward the deformation scale and toward lower baroclinic modes. The energy, after finally reaching the barotropic mode, is ultimately transferred toward larger scales via the classic barotropic inverse kinetic energy cascade (Charney 1971;Fu and Flierl 1980;Salmon 1980;Hua and Haidvogel 1986;Larichev and Held 1995;Salmon 1998;Smith and Vallis 2001). On a spherical planet the (meridional) planetary potential vorticity gradient ␤ may dominate, which tends to redirect the barotropic inverse cascade more into larger-scale zonally oriented flow at the expense of meridionally oriented flow (Rhines 1977;Vallis and Maltrud 1993;Galperin et al 2004;.…”

Section: Introductionmentioning

confidence: 99%

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Length Scales of Eddy Generation and Nonlinear Evolution of the Seasonally Modulated South Pacific Subtropical Countercurrent

Qiu

Scott

Chen

2008

Journal of Physical Oceanography

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The dynamical processes behind the seasonal modulation of the two-dimensional eddy kinetic energy (EKE) wavenumber spectrum in the Subtropical Countercurrent region of the South Pacific are investigated with 14 yr of satellite altimeter data and climatological hydrographic data. The authors find a seasonally modulated generation of EKE via baroclinic instability in modes with larger meridional length scales. Subsequent nonlinear eddy-eddy interactions redistribute the EKE to larger total horizontal length scales, and larger zonal scales in particular. This is confirmed by diagnosing the spectral transfer of EKE in the surface geostrophic flow, which is found to drive an anisotropic inverse cascade, being redirected in the sense consistent with the ␤ effect, as predicted by geostrophic turbulence theory on the ␤ plane. Because of the seasonal renewal of meridionally elongated anomalies by baroclinic instability and possibly because of the barotropization process, however, the net outcome for the formation of surface zonal flows is observed to be limited.

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Section: Introductionmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Length Scales of Eddy Generation and Nonlinear Evolution of the Seasonally Modulated South Pacific Subtropical Countercurrent

Qiu

Scott

Chen

2008

Journal of Physical Oceanography

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“…In his baroclinic adjustment theory, based on the two-layer quasi-geostrophic model (Phillips 1951), a rotating, stratified fluid may adjust the mean thermal structure to maintain a stably-stratified environment that is close to a marginally critical state for baroclinic instability (Stone 1978) with a criticality parameter,ξ, that equilibrates to ξ ≈ 1. ξ is a measure of the isentropic slope and defined as (Zurita-Gotor and Vallis 2010), with θ the mean potential temperature, f ≡ 2� sin φ (where φ is latitude) and β quantifies the (linearised) dependence of the coriolis force on latitude so that f ≃ f 0 + βy with f 0 a constant. Recent studies, however, have disputed this analysis, since numerical simulations have shown that the two-layer model does not necessarily equilibrate to a value of ξ ≈ 1 (e.g., Salmon 1978Salmon , 1980Vallis 1988). …”

Section: Introductionmentioning

confidence: 99%

A rotating annulus driven by localized convective forcing: a new atmosphere-like experiment

Scolan

Read

2017

Exp Fluids

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unstable flows which are qualitatively similar to those previously observed in the classical thermally driven annulus. However, in contrast to the classical configuration, they typically exhibit more spatio-temporal complexity. Thus, several regimes of flow demonstrate the equilibrated coexistence of, and interaction between, free convection and baroclinic wave modes. These new features were not previously observed in the classical annulus and validate the new setup as a tool for exploring fundamental atmosphere-like dynamics in a more realistic framework. Thermal structure in the fluid is investigated and found to be qualitatively consistent with previous numerical results, with nearly isothermal conditions, respectively, above and below the heat source and sink, and stably-stratified, sloping isotherms in the near-adiabatic interior.

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“…Dubovikov (2003, D3) and Canuto and Dubovikov (2005, CD5) argued that mesoscale eddy energy (EKE) does cascade upscale, a process that is now commonly recognized (Ferrari and Wunsch, 2009;Bruggemann and Eden, 2015;Jansen et al, 2015) and confirmed by sea surface height (SSH) data (Scott and Wang, 2005;Scott and Arbic, 2007). It is worth noticing that the mentioned energy cascade is rather different than that in the two-level geostrophic model (Salmon, 1978(Salmon, ,1980(Salmon, , 1998 within which at scales larger than the Rossby deformation radius d r there are the down-scale baroclinic energy cascade and the upscale barotropic one while at scales less than d r both cascades are directed down-scale. It is clear that such a flow contains no "conundrum".…”

Section: Introductionmentioning

confidence: 99%

Mesoscale cascades and the conundrum of energy transfer from large to dissipation scales in an adiabatic ocean

Dubovikov

2017

Preprint

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A well-known "conundrum" in ocean dynamics has been expressed as follows: "How does the energy of the general circulation cascade from the large climate scales, where most of it is generated, to the small scales, where all of it is dissipated? In particular, how is the dynamical transition made from an anisotropic, 2D-like, geostrophic cascade at large scales-with its strong inhibition of down-scale energy flux-to 3D-like, down-scale cascades at small scales." (Muller, McWilliams and Molemaker, 2002). To study this as yet unsolved problem, we introduce in the analysis a dynamical consideration based on the mesoscale model developed by Dubovikov (2003) and Canuto and Dubovikov (2005) within which in a quasi-adiabatic ocean interior the large scale baroclinic instability generates mesoscale eddy potential energy (EPE) at scales of the Rossby deformation radius~d r . Since at those scales the mesoscale Rossby number is small, the generated EPE cannot convert into eddy kinetic energy (EKE) and cascades to smaller scales at which the spectral Rossby number increases until at some horizontal scales it reaches . Under this condition, EPE converts into EKE and thus the cascade of the former terminates while the inverse EKE cascade begins. At scales ~d r the inverse EKE cascade terminates and reinforces the EPE cascade produced by the large scale baroclinic instability thus closing the mesoscale energy cycle. If the flow were exactly adiabatic, i.e. eddy energy were not dissipated, the latter would increase unlimitedly at the expense of the permanent production of the total eddy energy (TEE) by the mean flow. However, at the same scales where the EPE cascade terminates and the inverse EKE cascade begins, the vertical eddy shear reaches the value of the buoyancy frequency N that gives rise to the Kelvin-Helmholtz instability. The latter generates the stratified turbulence which finally dissipates EKE. A steady state regime sets in when the dissipation balances the TEE production by the mean flow.() Ro k( 1/ )~1 RoÕ cean Sci. Discuss., doi:10.5194/os-2017Discuss., doi:10.5194/os- -23, 2017 Manuscript under review for journal Ocean Sci. 1.IntroductionFor a long time it is recognized that one of the most enigmatic conundrums of ocean general circulation is: "how and where does the energy of the general circulation cascade from the large climatic scales, where most of it is generated, to the small scales, where all of it is dissipated?" "In particular, how is the dynamical transition made from a 2-D like geostrophic cascade at large scales-with its strong inhibition of down-scale energy flux-to the more isotropic, 3D-like, downscale cascades at small scales" (Muller et al., 2002; Mc Williams, 2003). In fact, interior ocean flows in the adiabatic approximation are sets of 2D ones within isopycnal surfaces between which non-linear interactions vanish. As discussed by Kraichnan (1965Kraichnan ( , 1967, in 2D flows only inversed (upscale) energy cascades are possible. Dubovikov (2003, D3) and Canuto and Dubovikov (2005...

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Baroclinic instability and geostrophic turbulence

Cited by 238 publications

References 22 publications

Length Scales of Eddy Generation and Nonlinear Evolution of the Seasonally Modulated South Pacific Subtropical Countercurrent

Length Scales of Eddy Generation and Nonlinear Evolution of the Seasonally Modulated South Pacific Subtropical Countercurrent

A rotating annulus driven by localized convective forcing: a new atmosphere-like experiment

Mesoscale cascades and the conundrum of energy transfer from large to dissipation scales in an adiabatic ocean

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