Equilibration of Baroclinic Turbulence in Primitive Equations and Quasigeostrophic Models

2009 ◽  
Vol 66 (4) ◽  
pp. 837-863 ◽  
Author(s):  
Pablo Zurita-Gotor ◽  
Geoffrey K. Vallis
Keyword(s):  
Baroclinic Instability ◽  
Quantitative Agreement ◽  
Equation Model ◽  
Turbulence Theory ◽  
Mean Flow ◽  
Primitive Equation ◽  
Primitive Equation Model ◽  
Barotropic Flow ◽  
Quasigeostrophic Model ◽  
Parameter Ranges

Abstract This paper investigates the equilibration of baroclinic turbulence in an idealized, primitive equation, two-level model, focusing on the relation with the phenomenology of quasigeostrophic turbulence theory. Simulations with a comparable two-layer quasigeostrophic model are presented for comparison, with the deformation radius in the quasigeostrophic model being set using the stratification from the primitive equation model. Over a fairly broad parameter range, the primitive equation and quasigeostrophic results are in qualitative and, to some degree, quantitative agreement and are consistent with the phenomenology of geostrophic turbulence. The scale, amplitude, and baroclinicity of the eddies and the degree of baroclinic instability of the mean flow all vary fairly smoothly with the imposed parameters; both models are able, in some parameter ranges, to produce supercritical flows. The criticality in the primitive equation model, which does not have any convective parameterization scheme, is fairly sensitive to the external parameters, most notably the planet size (i.e., the f /β ratio), the forcing time scale, and the factors influencing the stratification. In some parameter settings of the models, although not those that are most realistic for the earth’s atmosphere, it is possible to produce eddies that are considerably larger than the deformation scales and an inverse cascade in the barotropic flow with a −5/3 spectrum. The vertical flux of heat is found to be related to the isentropic slope.

scholarly journals Dynamics of Midlatitude Tropopause Height in an Idealized Model

2011 ◽  
Vol 68 (4) ◽  
pp. 823-838 ◽  
Author(s):  
Pablo Zurita-Gotor ◽  
Geoffrey K. Vallis
Keyword(s):  
Baroclinic Instability ◽  
Equation Model ◽  
Tropopause Height ◽  
Mean Flow ◽  
Flow Properties ◽  
Primitive Equation ◽  
Conservation Of Energy ◽  
Primitive Equation Model ◽  
Eddy Transport ◽  
The Mean

Abstract This paper investigates the factors that determine the equilibrium state, and in particular the height and structure of the tropopause, in an idealized primitive equation model forced by Newtonian cooling in which the eddies can determine their own depth. Previous work has suggested that the midlatitude tropopause height may be understood as the intersection between a radiative and a dynamical constraint. The dynamical constraint relates to the lateral transfer of energy, which in midlatitudes is largely effected by baroclinic eddies, and its representation in terms of mean-flow properties. Various theories have been proposed and investigated for the representation of the eddy transport in terms of the mean flow, including a number of diffusive closures and the notion that the flow evolves to a state marginally supercritical to baroclinic instability. The radiative constraint expresses conservation of energy and so must be satisfied, although it need not necessarily be useful in providing a tight constraint on tropopause height. This paper explores whether and how the marginal criticality and radiative constraints work together to produce an equilibrated flow and a tropopause that is internal to the fluid. The paper investigates whether these two constraints are consistent with simulated variations in the tropopause height and in the mean state when the external parameters of an idealized primitive equation model are changed. It is found that when the vertical redistribution of heat is important, the radiative constraint tightly constrains the tropopause height and prevents an adjustment to marginal criticality. In contrast, when the stratification adjustment is small, the radiative constraint is only loosely satisfied and there is a tendency for the flow to adjust to marginal criticality. In those cases an alternative dynamical constraint would be needed in order to close the problem and determine the eddy transport and tropopause height in terms of forcing and mean flow.

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 Mean Circulation and Internal Variability in an Ocean Primitive Equation Model

1996 ◽  
Vol 26 (4) ◽  
pp. 559-580 ◽  
Author(s):  
Sybren Drijfhout ◽  
Christoph Heinze ◽  
Mojib Latif ◽  
Ernst Maier-Reimer
Keyword(s):  
Internal Variability ◽  
Equation Model ◽  
Primitive Equation ◽  
Primitive Equation Model ◽  
Mean Circulation

scholarly journals Ensemble Simulations and Pullback Attractors of a Periodically Forced Double-Gyre System

2014 ◽  
Vol 44 (12) ◽  
pp. 3245-3254 ◽  
Author(s):  
Stefano Pierini
Keyword(s):  
Initial Conditions ◽  
Kuroshio Extension ◽  
Ocean Model ◽  
Equation Model ◽  
Fundamental Aspect ◽  
Pullback Attractors ◽  
Primitive Equation ◽  
Ensemble Simulations ◽  
Primitive Equation Model ◽  
Double Gyre

Abstract A primitive equation ocean model has recently reproduced with reasonable realism the synchronization between the North Pacific Oscillation and the last two Kuroshio Extension decadal cycles observed from altimetry. However, the timing of the cycles is imperfect: could a different model initialization improve this fundamental aspect of the phenomenon? Ensemble simulations stemming from many initial conditions should be carried out to answer this question, but doing that with a primitive equation model is highly computationally expensive. A preliminary analysis is therefore performed here with a nonlinear low-order ocean model, which identifies a significant paradigm of intrinsic oceanic double-gyre low-frequency variability. The chaotic pullback attractors of the periodically forced model are first recognized to be periodic and cycloergodic. Two parameters are then introduced to analyze the topological structure of the pullback attractors as a function of the forcing period; their joint use allows one to identify four forms of sensitivity to initialization corresponding to different system behaviors. The model response under periodic forcing turns out to be, in most cases, very sensitive to initialization. Implications concerning the primitive equation model are finally discussed.

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