Planetary geostrophic Boussinesq dynamics: Barotropic flow, baroclinic instability and forced stationary waves

Motions on planetary spatial scales in the atmosphere are governed by the planetary geostrophic equations. However, not much attention has been paid to the interaction between the baroclinic and barotropic flow within the planetary geostrophic scaling. This is the focus of the present study by utilizing planetary geostrophic equations for a Boussinesq fluid supplemented by an asymptotically derived evolution equation for the barotropic flow. The latter is effected by meridional momentum flux due to baroclinic flow and drag by the surface wind. The barotropic wind on the other hand affects the baroclinic flow through buoyancy advection. By relaxing towards a prescribed buoyancy profile the model produces realistic major features of the zonally symmetric wind and temperature fields. We show that there is considerable cancelation between the barotropic and the baroclinic surface zonal mean zonal wind. The linear and nonlinear model response to steady diabatic zonally asymmetric forcing is investigated. The arising stationary waves are interpreted in terms of analytical solutions. We also study the problem of baroclinic instability on the sphere within the present model.Reference: Dolaptchiev, S. I., Achatz, U. and Th. Reitz, 2019: Planetary geostrophic Boussinesq dynamics: barotropic flow, baroclinic instability and forced stationary waves, Quart. J. Roy. Met. Soc., 145: 3751-3765.

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Equilibration of Baroclinic Turbulence in Primitive Equations and Quasigeostrophic Models

Journal of the Atmospheric Sciences ◽

10.1175/2008jas2848.1 ◽

2009 ◽

Vol 66 (4) ◽

pp. 837-863 ◽

Cited By ~ 19

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.

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Maintenance of the Stratospheric Structure in an Idealized General Circulation Model

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-12-0305.1 ◽

2013 ◽

Vol 70 (11) ◽

pp. 3341-3358 ◽

Cited By ~ 13

Author(s):

M. Jucker ◽

S. Fueglistaler ◽

G. K. Vallis

Keyword(s):

Temperature Field ◽

Seasonal Cycle ◽

General Circulation ◽

Lower Stratosphere ◽

Baroclinic Instability ◽

Circulation Model ◽

Basic Structure ◽

Wave Activity ◽

Temperature Structure ◽

Stationary Waves

Abstract This work explores the maintenance of the stratospheric structure in a primitive equation model that is forced by a Newtonian cooling with a prescribed radiative equilibrium temperature field. Models such as this are well suited to analyze and address questions regarding the nature of wave propagation and troposphere–stratosphere interactions. The focus lies on the lower to midstratosphere and the mean annual cycle, with its large interhemispheric variations in the radiative background state and forcing, is taken as a benchmark to be simulated with reasonable verisimilitude. A reasonably realistic basic stratospheric temperature structure is a necessary first step in understanding stratospheric dynamics. It is first shown that using a realistic radiative background temperature field based on radiative transfer calculations substantially improves the basic structure of the model stratosphere compared to previously used setups. Then, the physical processes that are needed to maintain the seasonal cycle of temperature in the lower stratosphere are explored. It is found that an improved stratosphere and seasonally varying topographically forced stationary waves are, in themselves, insufficient to produce a seasonal cycle of sufficient amplitude in the tropics, even if the topographic forcing is large. Upwelling associated with baroclinic wave activity is an important influence on the tropical lower stratosphere and the seasonal variation of tropospheric baroclinic activity contributes significantly to the seasonal cycle of the lower tropical stratosphere. Given a reasonably realistic basic stratospheric structure and a seasonal cycle in both stationary wave activity and tropospheric baroclinic instability, it is possible to obtain a seasonal cycle in the lower stratosphere of amplitude comparable to the observations.

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Baroclinic Stationary Waves in Aquaplanet Models

Journal of the Atmospheric Sciences ◽

10.1175/2011jas3573.1 ◽

2011 ◽

Vol 68 (5) ◽

pp. 1023-1040 ◽

Cited By ~ 6

Author(s):

Giuseppe Zappa ◽

Valerio Lucarini ◽

Antonio Navarra

Keyword(s):

Dispersion Relation ◽

Baroclinic Instability ◽

Surface Wind ◽

Low Frequency ◽

Phase Speed ◽

Stationary Wave ◽

Instability Wave ◽

Stationary Waves ◽

Frequency Wave ◽

Inverse Energy Cascade

Abstract An aquaplanet model is used to study the nature of the highly persistent low-frequency waves that have been observed in models forced by zonally symmetric boundary conditions. Using the Hayashi spectral analysis of the extratropical waves, the authors find that a quasi-stationary wave 5 belongs to a wave packet obeying a well-defined dispersion relation with eastward group velocity. The components of the dispersion relation with k ≥ 5 baroclinically convert eddy available potential energy into eddy kinetic energy, whereas those with k < 5 are baroclinically neutral. In agreement with Green’s model of baroclinic instability, wave 5 is weakly unstable, and the inverse energy cascade, which had been previously proposed as a main forcing for this type of wave, only acts as a positive feedback on its predominantly baroclinic energetics. The quasi-stationary wave is reinforced by a phase lock to an analogous pattern in the tropical convection, which provides further amplification to the wave. It is also found that the Pedlosky bounds on the phase speed of unstable waves provide guidance in explaining the latitudinal structure of the energy conversion, which is shown to be more enhanced where the zonal westerly surface wind is weaker. The wave’s energy is then trapped in the waveguide created by the upper tropospheric jet stream. In agreement with Green’s theory, as the equator-to-pole SST difference is reduced, the stationary marginally stable component shifts toward higher wavenumbers, while wave 5 becomes neutral and westward propagating. Some properties of the aquaplanet quasi-stationary waves are found to be in interesting agreement with a low frequency wave observed by Salby during December–February in the Southern Hemisphere so that this perspective on low frequency variability, apart from its value in terms of basic geophysical fluid dynamics, might be of specific interest for studying the earth’s atmosphere.

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Baroclinic instability of axially symmetric flow over sloping bathymetry

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.376 ◽

2016 ◽

Vol 799 ◽

pp. 265-296 ◽

Cited By ~ 8

Author(s):

Aviv Solodoch ◽

Andrew L. Stewart ◽

James C. McWilliams

Keyword(s):

Channel Flow ◽

Baroclinic Instability ◽

Azimuthal Velocity ◽

Straight Channel ◽

Body Rotation ◽

Mean Flow ◽

Boundary Currents ◽

Solid Body Rotation ◽

Barotropic Flow ◽

The Mean

Observations and models of deep ocean boundary currents show that they exhibit complex variability, instabilities and eddy shedding, particularly over continental slopes that curve horizontally, for example around coastal peninsulas. In this article the authors investigate the source of this variability by characterizing the properties of baroclinic instability in mean flows over horizontally curved bottom slopes. The classical two-layer quasi-geostrophic solution for linear baroclinic instability over sloping bottom topography is extended to the case of azimuthal mean flow in an annular channel. To facilitate comparison with the classical straight channel instability problem of uniform mean flow, the authors focus on comparatively simple flows in an annulus, namely uniform azimuthal velocity and solid-body rotation. Baroclinic instability in solid-body rotation flow is analytically analogous to the instability in uniform straight channel flow due to several identical properties of the mean flow, including vanishing strain rate and vorticity gradient. The instability of uniform azimuthal flow is numerically similar to straight channel flow instability as long as the mean barotropic azimuthal velocity is zero. Non-zero barotropic flow generally suppresses the instability via horizontal curvature-induced strain and Reynolds stress work. An exception occurs when the ratio of the bathymetric to isopycnal slopes is close to (positive) one, as is often observed in the ocean, in which case the instability is enhanced. A non-vanishing mean barotropic flow component also results in a larger number of growing eigenmodes and in increased non-normal growth. The implications of these findings for variability in deep western boundary currents are discussed.

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