scholarly journals Equatorial Superrotation and Barotropic Instability: Static Stability Variants

2006 ◽  
Vol 63 (5) ◽  
pp. 1548-1557 ◽  
Author(s):  
G. P. Williams
Keyword(s):  
Atmospheric Circulation ◽  
Baroclinic Instability ◽  
Static Stability ◽  
Equation Model ◽  
Primary Process ◽  
Barotropic Instability ◽  
Newtonian Heating ◽  
Low Latitude ◽  
Primitive Equation ◽  
Model Subject

Abstract Altering the tropospheric static stability changes the nature of the equatorial superrotation associated with unstable, low-latitude, westerly jets, according to calculations with a dry, global, multilevel, spectral, primitive equation model subject to a simple Newtonian heating function. For a low static stability, the superrotation fluxes with the simplest structure occur when the stratospheric extent and horizontal diffusion are minimal. Barotropic instability occurs on the jet's equatorward flank and baroclinic instability occurs on the jet's poleward flank. Systems with a high static stability inhibit the baroclinic instability and thereby reveal more clearly that the barotropic instability is the primary process driving the equatorial superrotation. Such systems produce a flatter equatorial jet and also take much longer to equilibrate than the standard atmospheric circulation.

Circulation Sensitivity to Tropopause Height

2006 ◽  
Vol 63 (7) ◽  
pp. 1954-1961 ◽  
Author(s):  
G. P. Williams
Keyword(s):  
Equation Model ◽  
Planetary Waves ◽  
Ice Age ◽  
Jet Stream ◽  
Tropopause Height ◽  
Newtonian Heating ◽  
Standard State ◽  
Primitive Equation ◽  
Stratospheric Temperature ◽  
Model Subject

Abstract The possibility that the tropopause could be lower during an ice-age cooling leads to an examination of the general sensitivity of global circulations to the tropopause height by altering a constant stratospheric temperature Ts in calculations with a dry, global, multilevel, spectral, primitive equation model subject to a simple Newtonian heating function. In general, lowering the tropopause by increasing the stratospheric temperature causes the jet stream to move to lower latitudes and the eddies to become smaller. Near the standard state with Ts = 200 K, the jets relocate themselves equatorward by 2° in latitude for every 5 K increase in the stratospheric temperature. A double-jet system, with centers at 30° and 60° latitude, occurs when the equatorial tropopause drops to 500 mb (for Ts = 250 K), with the high-latitude component extending throughout the stratosphere. The eddy momentum flux mainly traverses poleward across the standard jet at 40°, in keeping with the predominantly equatorward propagation of the planetary waves. But when the jet lies at 30° (for Ts = 225 K) the flux converges on the jet in keeping with planetary waves that propagate both equatorward and poleward. Two sets of such wave propagation occur in the double-jet system. As the troposphere becomes even shallower, the flux reverts to being primarily poleward across the jet (for Ts = 260 K) but then becomes uniquely primarily equatorward across the jet (for Ts = 275 K) before the circulation approaches extinction. Thus the existence of a predominantly poleward flux in the standard state appears to be parametrically fortuitous.

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.

Why Anticyclones Can Split

2003 ◽  
Vol 33 (8) ◽  
pp. 1579-1591 ◽  
Author(s):  
S. S. Drijfhout
Keyword(s):  
Deep Layer ◽  
Baroclinic Instability ◽  
Equation Model ◽  
Vertical Transport ◽  
Phase Lag ◽  
Primitive Equation ◽  
Baroclinic Energy Conversion ◽  
Break Up ◽  
Baroclinic Vortices ◽  
Surrounding Fluid

Abstract The question of whether anticyclones can split and break up is readdressed using a numerical, multilayer, primitive equation model. Applying the conservation of integrated angular momentum (IAM) to barotropic and baroclinic vortices, it has been argued that anticyclones can never split, no matter what their structure is. When an anticyclone splits, the IAM has to increase as the newly formed eddies are pushed away from their original center. Conservation of IAM prohibits such an increase. Several numerical simulations, however, have shown anticyclonic splitting. In a multilayer model, a vertical transport of IAM is possible. For counterrotating eddies (an anticyclone on top of a cyclone) it is easy to see that a vertical exchange of IAM allows the eddy to break up. For a compensated or weakly corotating eddy, breakup is only possible when, in addition to a vertical transport of IAM, in the deep layer(s) IAM is exchanged between the core of the vortex and the surrounding fluid. In the presence of a tilting interface, the pressure gradient associated with the sea surface height (SSH) anomaly, in particular its non-equivalent-barotropic part, drives the required exchanges. The non-equivalent-barotropic SSH anomaly is associated with the vertical phase lag of the most unstable eigenmode (m = 2), which develops when this mode gains energy by baroclinic energy conversion. The previous conclusion that anticyclones cannot split on their own should be revised to the following: anticyclones cannot split by barotropic processes alone—baroclinic instability is a necessary ingredient for splitting to occur.

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 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.

Study of the Mechanisms of Vortex Variability in the Lofoten Basin Based on the Energy Analysis

2021 ◽  
Vol 37 (3) ◽  
Author(s):  
V. S. Travkin ◽  
◽  
T. V. Belonenko ◽  
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Baroclinic Instability ◽  
Positive Trend ◽  
Barotropic Instability ◽  
Available Potential Energy ◽  
Conversion Rates ◽  
Order Of Magnitude ◽  
The Mean ◽  
Mean Kinetic Energy

Purpose. The Lofoten Basin is one of the most energetic zones of the World Ocean characterized by high activity of mesoscale eddies. The study is aimed at analyzing different components of general energy in the basin, namely the mean kinetic and vortex kinetic energy calculated using the integral of the volume of available potential and kinetic energy of the Lofoten Vortex, as well as variability of these characteristics. Methods and Results. GLORYS12V1 reanalysis data for the period 2010–2018 were used. The mean kinetic energy and the eddy kinetic one were analyzed; and as for the Lofoten Vortex, its volume available potential and kinetic energy were studied. The mesoscale activity of eddies in winter is higher than in summer. Evolution of the available potential energy and kinetic energy of the Lofoten Vortex up to the 1000 m horizon was studied. It is shown that the vortex available potential energy exceeds the kinetic one by an order of magnitude, and there is a positive trend with the coefficient 0,23⋅1015 J/year. It was found that in the Lofoten Basin, the intermediate layer from 600 to 900 m made the largest contribution to the potential energy, whereas the 0–400 m layer – to kinetic energy. The conversion rates of the mean kinetic energy into the vortex kinetic one and the mean available potential energy into the vortex available potential one (barotropic and baroclinic instability) were analyzed. It is shown that the first type of transformation dominates in summer, while the second one is characterized by its increase in winter. Conclusions. The vertical profile shows that the kinetic energy of eddies in winter is higher than in summer. The available potential energy of a vortex is by an order of magnitude greater than the kinetic energy. An increase in the available potential energy is confirmed by a significant positive trend and by a decrease in the vortex Burger number. The graphs of the barotropic instability conversion rate demonstrate the multidirectional flows in the vortex zone with the dipole structure observed in a winter period, and the tripole one – in summer. The barotropic instability highest intensity is observed in summer. The baroclinic instability is characterized by intensification of the regime in winter that is associated with weakening of stratification in this period owing to winter convection.

scholarly journals Changes in the Low Latitude Atmospheric Circulation at the End of the 21stCentury Simulated by CMIP5 Models under Global Warming

Atmosphere ◽  
2013 ◽  
Vol 23 (4) ◽  
pp. 377-387 ◽  
Author(s):  
Yoo-Rim Jung ◽  
Da-Hee Choi ◽  
Hee-Jeong Baek ◽  
Chunho Cho
Keyword(s):  
Global Warming ◽  
Atmospheric Circulation ◽  
Cmip5 Models ◽  
Low Latitude
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