Journal articles: 'Quasigeostrophic formulation'

1

Holm, Darryl D. "Hamiltonian formulation of the baroclinic quasigeostrophic fluid equations." Physics of Fluids 29, no. 1 (1986): 7. http://dx.doi.org/10.1063/1.865956.

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Zurita-Gotor, Pablo, and Geoffrey K. Vallis. "Circulation Sensitivity to Heating in a Simple Model of Baroclinic Turbulence." Journal of the Atmospheric Sciences 67, no. 5 (May 1, 2010): 1543–58. http://dx.doi.org/10.1175/2009jas3314.1.

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Abstract This paper examines the sensitivity of the circulation of an idealized primitive equation two-level model on the form and strength of the heating, aiming to understand the qualitatively different sensitivity of the isentropic slope on differential heating reported by previous idealized studies when different model formulations are used. It is argued that this contrasting behavior might arise from differences in the internal determination of the heating. To test this contention, the two-level model is forced using two different heating formulations: a standard Newtonian cooling formulation and a highly simplified formulation in which the net lower-to-upper troposphere heat transport is prescribed by construction. The results are interpreted using quasigeostrophic turbulent closures, which have previously been shown to have predictive power for the model. It is found that the strength of the circulation, as measured by eddy length and velocity scales and by the strength of the energy cycle, scales with the vertical heating (the lower-to-upper troposphere heat transport), with a weak dependence. By contrast, the isentropic slope is only sensitive to the structure of the heating, as measured by the ratio between meridional versus vertical heating, and not to the actual strength of the heating. In general the heating is internally determined, and this ratio may either increase or decrease as the circulation strengthens. It is shown that the sign of the sensitivity depends on the steepness of the relation between vertical heating and stratification for the particular heating formulation used. The quasigeostrophic limit (fixed stratification) and the prescribed heating model constrain the possible range of behaviors and provide bounds of sensitivity for the model. These results may help explain the different sensitivity of the isentropic slope on differential heating for dry and moist models and for quasigeostrophic and primitive equation models.

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Kiss, A. E. "A modified quasigeostrophic formulation for weakly nonlinear barotropic flow with large-amplitude depth variations." Ocean Modelling 5, no. 2 (January 2003): 171–91. http://dx.doi.org/10.1016/s1463-5003(02)00038-0.

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Chavanne, Cédric P., and Patrice Klein. "Quasigeostrophic Diagnosis of Mixed Layer Dynamics Embedded in a Mesoscale Turbulent Field." Journal of Physical Oceanography 46, no. 1 (January 2016): 275–87. http://dx.doi.org/10.1175/jpo-d-14-0178.1.

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AbstractA quasigeostrophic model is developed to diagnose the three-dimensional circulation, including the vertical velocity, in the upper ocean from high-resolution observations of sea surface height and buoyancy. The formulation for the adiabatic component departs from the classical surface quasigeostrophic framework considered before since it takes into account the stratification within the surface mixed layer that is usually much weaker than that in the ocean interior. To achieve this, the model approximates the ocean with two constant stratification layers: a finite-thickness surface layer (or the mixed layer) and an infinitely deep interior layer. It is shown that the leading-order adiabatic circulation is entirely determined if both the surface streamfunction and buoyancy anomalies are considered. The surface layer further includes a diabatic dynamical contribution. Parameterization of diabatic vertical velocities is based on their restoring impacts of the thermal wind balance that is perturbed by turbulent vertical mixing of momentum and buoyancy. The model skill in reproducing the three-dimensional circulation in the upper ocean from surface data is checked against the output of a high-resolution primitive equation numerical simulation.

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Harnik, N., E. Heifetz, O. M. Umurhan, and F. Lott. "A Buoyancy–Vorticity Wave Interaction Approach to Stratified Shear Flow." Journal of the Atmospheric Sciences 65, no. 8 (August 1, 2008): 2615–30. http://dx.doi.org/10.1175/2007jas2610.1.

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Abstract Motivated by the success of potential vorticity (PV) thinking for Rossby waves and related shear flow phenomena, this work develops a buoyancy–vorticity formulation of gravity waves in stratified shear flow, for which the nonlocality enters in the same way as it does for barotropic/baroclinic shear flows. This formulation provides a time integration scheme that is analogous to the time integration of the quasigeostrophic equations with two, rather than one, prognostic equations, and a diagnostic equation for streamfunction through a vorticity inversion. The invertibility of vorticity allows the development of a gravity wave kernel view, which provides a mechanistic rationalization of many aspects of the linear dynamics of stratified shear flow. The resulting kernel formulation is similar to the Rossby-based one obtained for barotropic and baroclinic instability; however, since there are two independent variables—vorticity and buoyancy—there are also two independent kernels at each level. Though having two kernels complicates the picture, the kernels are constructed so that they do not interact with each other at a given level.

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6

Held, Isaac M. "100 Years of Progress in Understanding the General Circulation of the Atmosphere." Meteorological Monographs 59 (January 1, 2019): 6.1–6.23. http://dx.doi.org/10.1175/amsmonographs-d-18-0017.1.

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Abstract Some of the advances of the past century in our understanding of the general circulation of the atmosphere are described, starting with a brief summary of some of the key developments from the first half of the twentieth century, but with a primary focus on the period beginning with the midcentury breakthrough in baroclinic instability and quasigeostrophic dynamics. In addition to baroclinic instability, topics touched upon include the following: stationary wave theory, the role played by the two-layer model, scaling arguments for the eddy heat flux, the subtlety of large-scale eddy momentum fluxes, the Eliassen–Palm flux and the transformed Eulerian mean formulation, the structure of storm tracks, and the controls on the Hadley cell.

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Hutchinson, David K., Andrew Mc C. Hogg, and Jeffrey R. Blundell. "Southern Ocean Response to Relative Velocity Wind Stress Forcing." Journal of Physical Oceanography 40, no. 2 (February 1, 2010): 326–39. http://dx.doi.org/10.1175/2009jpo4240.1.

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Abstract An eddy-resolving quasigeostrophic model of the Southern Ocean coupled to a dynamic atmospheric mixed layer is used to compare the performance of two different wind stress parameterization schemes. The first is the standard quadratic drag law, based on atmospheric velocity alone, whereas the second (more exact) formulation is based on the difference between ocean and atmosphere velocities. The two different schemes give very similar magnitudes of mean stress; however, the relative velocity scheme has substantially lower power input, resulting in a weaker eddy field, and consequently, greater circumpolar transport. These results are explored in terms of the existing theories of the Antarctic Circumpolar Current (including eddy saturation and eddy damping) and the implications for modeling the Southern Ocean are discussed.

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Primeau, François, and David Newman. "Elongation and Contraction of the Western Boundary Current Extension in a Shallow-Water Model: A Bifurcation Analysis." Journal of Physical Oceanography 38, no. 7 (July 1, 2008): 1469–85. http://dx.doi.org/10.1175/2007jpo3658.1.

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Abstract The double-gyre circulation, formulated in terms of the quasigeostrophic equations, has a symmetry about the basin midlatitude (y → −y, ψ → −ψ), which is absent in a formulation based on the shallow-water equations. As a result, the shallow-water model does not have the pitchfork bifurcation structures that, in the case of the quasigeostrophic model, connect together multiple solution branches with elongated and contracted recirculation gyres. For the shallow-water model, solution branches with elongated recirculation gyres are disconnected, and a one-parameter bifurcation analysis is unable to detect their existence. The deeply penetrating jet solution branches do, however, continue to exist, and can be found using a bifurcation analysis couched in terms of two parameters. An effective pair of parameters is the viscosity and a parameter controlling the symmetry of the wind stress profile. A bifurcation analysis with these parameters reveals the existence of new solution branches that were not found in previous bifurcation analyses of the shallow-water model. The new solutions have a jet extension that penetrates farther eastward and that is more stable than the jet-up and jet-down solutions found in previous studies. Furthermore, the origin of the low-frequency variability at low viscosities is associated with a sequence of bifurcations originating from one of the new steady-state solution branches. In particular, the eigenmode analysis of the new branch reveals that a so-called gyre mode is at the origin of the model’s low-frequency variability at decadal time scales.

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9

Pietri, Alice, Xavier Capet, Francesco d’Ovidio, Marina Levy, Julien Le Sommer, Jean-Marc Molines, and Hervé Giordani. "Skills and Limitations of the Adiabatic Omega Equation: How Effective Is It to Retrieve Oceanic Vertical Circulation at Mesoscale and Submesoscale?" Journal of Physical Oceanography 51, no. 3 (March 2021): 931–54. http://dx.doi.org/10.1175/jpo-d-20-0052.1.

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AbstractThe quasigeostrophic and the generalized omega equations are the most widely used methods to reconstruct vertical velocity w from in situ data. As observational networks with much higher spatial and temporal resolutions are being designed, the question arises of identifying the approximations and scales at which an accurate estimation of w through the omega equation can be achieved and what critical scales and observables are needed. In this paper we test different adiabatic omega reconstructions of w over several regions representative of main oceanic regimes of the global ocean in a fully eddy-resolving numerical simulation with a 1/60° horizontal resolution. We find that the best reconstructions are observed in conditions characterized by energetic turbulence and/or weak stratification where near-surface frontal processes are felt deep into the ocean interior. The quasigeostrophic omega equation gives satisfactory results for scales larger than ~10 km horizontally while the improvements using a generalized formulation are substantial only in conditions where frontal turbulent processes are important (providing improvements with satisfactory reconstruction skill down to ~5 km in scale). The main sources of uncertainties that could be identified are related to processes responsible for ocean thermal wind imbalance (TWI), which is particularly difficult to account for (especially in observation-based studies) and to the deep flow that is generally improperly accounted for in omega reconstructions through the bottom boundary condition. Nevertheless, the reconstruction of mesoscale vertical velocities may be sufficient to estimate vertical fluxes of oceanic properties in many cases of practical interest.

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10

Takaya, Koutarou, and Hisashi Nakamura. "A Formulation of a Phase-Independent Wave-Activity Flux for Stationary and Migratory Quasigeostrophic Eddies on a Zonally Varying Basic Flow." Journal of the Atmospheric Sciences 58, no. 6 (March 2001): 608–27. http://dx.doi.org/10.1175/1520-0469(2001)058<0608:afoapi>2.0.co;2.

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11

Yano, Jun-Ichi, and Joseph J. Tribbia. "Tropical Atmospheric Madden–Julian Oscillation: A Strongly Nonlinear Free Solitary Rossby Wave?" Journal of the Atmospheric Sciences 74, no. 10 (October 1, 2017): 3473–89. http://dx.doi.org/10.1175/jas-d-16-0319.1.

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Abstract The Madden–Julian oscillation (MJO), a planetary-scale eastward-propagating coherent structure with periods of 30–60 days, is a prominent manifestation of intraseasonal variability in the tropical atmosphere. It is widely presumed that small-scale moist cumulus convection is a critical part of its dynamics. However, the recent results from high-resolution modeling as well as data analysis suggest that the MJO may be understood by dry dynamics to a leading-order approximation. Simple, further theoretical considerations presented herein suggest that if it is to be understood by dry dynamics, the MJO is most likely a strongly nonlinear solitary Rossby wave. Under a global quasigeostrophic equivalent-barotropic formulation, modon theory provides such analytic solutions. Stability and the longevity of the modon solutions are investigated with a global shallow-water model. The preferred modon solutions with the greatest longevities compare well overall with the observed MJO in scale and phase velocity within the factors.

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12

Durland, Theodore S., Michael A. Spall, and Joseph Pedlosky. "Response to a Steady Poleward Outflow. Part II: Oscillations and Eddies." Journal of Physical Oceanography 39, no. 7 (July 1, 2009): 1551–73. http://dx.doi.org/10.1175/2008jpo4152.1.

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Abstract A conceptually simple model is presented for predicting the amplitude and periodicity of eddies generated by a steady poleward outflow in a 1½-layer β-plane formulation. The prediction model is rooted in linear quasigeostrophic dynamics but is capable of predicting the amplitude of the β plume generated by outflows in the nonlinear range. Oscillations in the plume amplitude are seen to represent a near-zero group velocity response to an adjustment process that can be traced back to linear dynamics. When the plume-amplitude oscillations become large enough so that the coherent β plume is replaced by a robust eddy field, the eddy amplitude is still constrained by the plume-amplitude prediction model. The eddy periodicity remains close to that of the predictable, near-zero group-velocity linear oscillations. Striking similarities between the patterns of variability in the model and observations south of Indonesia’s Lombok Strait suggest that the processes investigated in this study may play an important role in the generation of the observed eddy field of the Indo-Australian Basin.

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13

Kinoshita, Takenari, and Kaoru Sato. "A Formulation of Three-Dimensional Residual Mean Flow Applicable Both to Inertia–Gravity Waves and to Rossby Waves." Journal of the Atmospheric Sciences 70, no. 6 (May 29, 2013): 1577–602. http://dx.doi.org/10.1175/jas-d-12-0137.1.

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Abstract The three-dimensional (3D) residual mean flow is expressed as the sum of the Eulerian-mean flow and the Stokes drift. The present study derives formulas that are approximately equal to the 3D Stokes drift for the primitive equation (PRSD) and for the quasigeostrophic equation (QGSD) using small-amplitude theory for a slowly varying time-mean flow. The PRSD has a broad utility that is applicable to both Rossby waves and inertia–gravity waves. The 3D wave activity flux whose divergence corresponds to the wave forcing is also derived using PRSD. The PRSD agrees with QGSD under the small-Rossby-number assumption, and it agrees with the 3D Stokes drift derived by S. Miyahara and by T. Kinoshita et al. for inertia–gravity waves under the constant-Coriolis-parameter assumption. Moreover, a phase-independent 3D Stokes drift is derived under the QG approximation. The 3D residual mean flow in the upper troposphere in April is investigated by applying the new formulas to the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Re-Analysis (ERA-Interim) data. It is observed that the PRSD is strongly poleward (weakly equatorward) upstream (downstream) of the storm track. A case study was also made for dominant gravity waves around the southern Andes in the simulation by a gravity wave–resolving general circulation model. The 3D residual mean flow associated with the gravity waves is poleward (equatorward) in the western (eastern) region of the southern Andes. This flow is due to the horizontal structure of the variance in the zonal component of the mountain waves, which do not change much while they propagate upward.

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14

de Vries, Hylke, John Methven, Thomas H. A. Frame, and Brian J. Hoskins. "Baroclinic Waves with Parameterized Effects of Moisture Interpreted Using Rossby Wave Components." Journal of the Atmospheric Sciences 67, no. 9 (September 1, 2010): 2766–84. http://dx.doi.org/10.1175/2010jas3410.1.

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Abstract A theoretical framework is developed for the evolution of baroclinic waves with latent heat release parameterized in terms of vertical velocity. Both wave–conditional instability of the second kind (CISK) and large-scale rain approaches are included. The new quasigeostrophic framework covers evolution from general initial conditions on zonal flows with vertical shear, planetary vorticity gradient, a lower boundary, and a tropopause. The formulation is given completely in terms of potential vorticity, enabling the partition of perturbations into Rossby wave components, just as for the dry problem. Both modal and nonmodal development can be understood to a good approximation in terms of propagation and interaction between these components alone. The key change with moisture is that growing normal modes are described in terms of four counterpropagating Rossby wave (CRW) components rather than two. Moist CRWs exist above and below the maximum in latent heating, in addition to the upper- and lower-level CRWs of dry theory. Four classifications of baroclinic development are defined by quantifying the strength of interaction between the four components and identifying the dominant pairs, which range from essentially dry instability to instability in the limit of strong heating far from boundaries, with type-C cyclogenesis and diabatic Rossby waves being intermediate types. General initial conditions must also include passively advected residual PV, as in the dry problem.

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15

Cai, Ming, and Bohua Huang. "A Dissection of Energetics of the Geostrophic Flow: Reconciliation of Rossby Wave Energy Flux and Group Velocity." Journal of the Atmospheric Sciences 70, no. 7 (July 1, 2013): 2179–96. http://dx.doi.org/10.1175/jas-d-12-0249.1.

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Abstract It is shown in this paper that there is no ambiguity in the final form of the governing equations of a quasigeostrophic (QG) model after partitioning the total flow into the geostrophic, balanced ageostrophic, and unbalanced ageostrophic components. The uniqueness of the QG model formulation ensures that the energetics of a QG model is the same as that derived from the QG potential vorticity equation. Particularly, the well-known but somewhat mysterious “missing term” in the energetics of Rossby waves, identified in the literature as the difference between the pressure work and the energy flux transported at the group velocity, can be easily recovered. The missing term is the pressure work on the convergence of the balanced ageostrophic flow, representing a “hidden” conversion between kinetic and potential energy of the geostrophic flow that excites the unbalanced flow. This energy conversion equals the convergence of a one-directional energy flux that always transports energy westward at the zonal phase speed of Rossby waves. The pressure work on the divergence of the unbalanced flow does the actual conversion between kinetic and potential energy of the geostrophic flow and the pressure work on the unbalanced flow causes energy propagation in other directions. Therefore, it is the pressure work on the unbalanced flow that causes Rossby waves to be dispersive, leading to the downstream development. The sum of the energy transported at the zonal phase speed of Rossby waves and the pressure work on the unbalanced flow exactly equals the energy transported at the group velocity of Rossby waves.

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16

Davies, Huw C. "The Quasigeostrophic Omega Equation: Reappraisal, Refinements, and Relevance." Monthly Weather Review 143, no. 1 (January 1, 2015): 3–25. http://dx.doi.org/10.1175/mwr-d-14-00098.1.

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Abstract A two-component study is undertaken of the classical quasigeostrophic (QG) omega equation. First, a reappraisal is undertaken of extant formulations of the equation’s so-called forcing function. It pinpoints shortcomings of various formulations and prompts consideration of alternative forms. Particular consideration is given to the contribution of flow deformation to the forcing function, and to the role of the advection of the geostrophic flow by the thermal wind (the R vector). The latter is closely related to the Q vector, the horizontal component of the ageostrophic vorticity, and the forcing function itself. The reexamination promotes further examination of the physical interpretation and diagnostic use of the omega equation particularly for assessing richly structured subsynoptic flow features. Second, consideration is given to the dynamics associated with the equation and its more general utility. It is shown that the R vector is intrinsic to a quasigeostrophic cascade to finer-scaled flow, and that a fundamental feature of the QG omega equation—the in-phase relationship between cloud-diabatic heating and the attendant vertical velocity—has important potential ramifications for the assimilation of data in numerical weather prediction (NWP) models. Finally, it is shown that, in the context of considering NWP model output, mild generalizations of the quasigeostrophic R vector retain interpretative value for flow settings beyond geostrophy and warrant consideration when addressing some contemporary NWP challenges.

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Journal articles on the topic 'Quasigeostrophic formulation'

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