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Wayne H. Schubert - One of the best experts on this subject based on the ideXlab platform.
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Potential Vorticity structure of simulated hurricanes
Journal of the Atmospheric Sciences, 2006Co-Authors: Scott A. Hausman, Katsuyuki V. Ooyama, Wayne H. SchubertAbstract:Abstract To better understand the processes involved in tropical cyclone development, the authors simulate an axisymmetric tropical-cyclone-like vortex using a two-dimensional model based on nonhydrostatic dynamics, equilibrium thermodynamics, and bulk microphysics. The Potential Vorticity principle for this nonhydrostatic, moist, precipitating atmosphere is derived. The appropriate generalization of the dry Potential Vorticity is found to be P = ρ−1 {(−∂υ/∂z) (∂θρ/∂r) + [ f + ∂(rυ)/r∂r] (∂θρ/∂z)}, where ρ is the total density, υ is the azimuthal component of velocity, and θρ is the virtual Potential temperature. It is shown that P carries all the essential dynamical information about the balanced wind and mass fields. In the fully developed, quasi-steady-state cyclone, the P field and the θρ field become locked together, with each field having an outward sloping region of peak values on the inside edge of the eyewall cloud. In this remarkable structure, the P field consists of a narrow, leaning tower in...
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Potential Vorticity in a Moist Atmosphere
Journal of the Atmospheric Sciences, 2001Co-Authors: Wayne H. Schubert, Scott A. Hausman, Matthew Garcia, Katsuyuki V. Ooyama, Hung-chi KuoAbstract:The Potential Vorticity principle for a nonhydrostatic, moist, precipitating atmosphere is derived. An appropriate generalization of the well-known (dry) Ertel Potential Vorticity is found to be P 5 r21(2 V1 = 3 u )· =ur, where r is the total density, consisting of the sum of the densities of dry air, airborne moisture (vapor and cloud condensate), and precipitation; u is the velocity of the dry air and airborne moisture; and ur 5 Tr is the virtual Potential R /c aP a (p /p) 0 temperature, with Tr 5 p/(rRa) the virtual temperature, p the total pressure (the sum of the partial pressures of dry air and water vapor), p0 the constant reference pressure, Ra the gas constant for dry air, and cPa the specific heat at constant pressure for dry air. Since ur is a function of total density and total pressure only, its use as the thermodynamic variable in P leads to the annihilation of the solenoidal term, that is, =ur ·( =r 3 =p) 5 0. In the special case of an absolutely dry atmosphere, P reduces to the usual (dry) Ertel Potential Vorticity. For balanced flows, there exists an invertibility principle that determines the balanced mass and wind fields from the spatial distribution of P. It is the existence of this invertibility principle that makes P such a fundamentally important dynamical variable. In other words, P (in conjunction with the boundary conditions associated with the invertibility principle) carries all the essential dynamical information about the slowly evolving balanced part of the flow.
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Potential Vorticity Anomalies Associated with Squall Lines
Monthly Weather Review, 1991Co-Authors: Rolf Hertenstein, Wayne H. SchubertAbstract:Abstract This study involves observations and model simulations of Potential Vorticity anomalies in the wake of midlatitude squall lines. Using data from the Oklahoma–Kansas PRE-STORM experiment, we analyze Potential Vorticity fields near two squall lines—one with and one without a trailing stratiform region. From this observational analysis we suggest that squall lines with trailing stratiform regions can leave large, positive, midtropospheric Potential Vorticity anomalies in their wake. To further interpret these observations we consider a two-dimensional version of semigeostrophic theory formulated in isentropic and geostrophic coordinates, which results in a simple Potential pseudodensity (inverse Potential Vorticity) equation. Using apparent heat source fields that model those computed diagnostically from PRE-STORM data, we find that theory does indeed predict large, midtropospheric Potential Vorticity anomalies for model squall lines with a trailing stratiform region but not for model squall lines t...
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Potential Vorticity Modeling of the ITCZ and the Hadley Circulation
Journal of the Atmospheric Sciences, 1991Co-Authors: Wayne H. Schubert, Paul E. Ciesielski, Duane E. Stevens, Hung-chi KuoAbstract:Abstract A simple zonally symmetric balanced model of the Hadley circulation is presented. The model is based on Potential Vorticity arguments and consists of a predictive equation for the Potential pseudodensity and an invertibility principle to diagnose the associated balanced wind and mass fields. When the theory is formulated in the Potential latitude coordinate, the meridional advection is implicit in the coordinate transformation, which makes the prediction equation for Potential pseudodensity analytically solvable. For convective heating patterns that simulate the ITCZ, the model produces upper and lower tropospheric Potential Vorticity anomalies of opposite sign. The associated winds are easterly at low levels and westerly aloft, except between the equator and the ITCZ, where there are low-level westerlies and upper-level easterlies. Since the Potential Vorticity anomalies develop within a background state that has Potential Vorticity increasing to the north, reversed poleward gradients of potenti...
Alan J. Thorpe - One of the best experts on this subject based on the ideXlab platform.
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Superposing semi‐geostrophic Potential‐Vorticity anomalies
Quarterly Journal of the Royal Meteorological Society, 1997Co-Authors: H. R. Birkett, Alan J. ThorpeAbstract:A numerical method for inversion of the semi-geostrophic Potential-Vorticity equation is described. It is used to examine the validity of a strictly linear superposition principle when applied to this high-order balance model. These results are important when aiming to extend rigorously the value of recent ‘attribution’ ideas. Experiments conclude that the nonlinear components of the inversion have only a very short-range effect, with a magnitude which increases with the magnitude of the Potential-Vorticity anomalies. For balance of higher-order than quasi-geostrophic these results show that, whilst flow and temperature of an anomaly are nonlinear functions of Potential-Vorticity magnitude, spatially separated anomalies are quasi-linearly superposable.
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Potential Vorticity AND THE ELECTROSTATICS ANALOGY - ERTEL-ROSSBY FORMULATION
Quarterly Journal of the Royal Meteorological Society, 1995Co-Authors: Alan J. Thorpe, Craig H. BishopAbstract:The isomorphism between the theory of electrostatics and the quasi-geostrophic Potential Vorticity is extended to the Ertel-Rossby Potential Vorticity. Anomalies of mass-weighted Potential Vorticity are defined relative to an arbitrary zonal-mean or horizontal-average flow and given in terms of the divergence of a vector field. the vector is the sum of linear and non-linear contributions and can be written as a dielectric tensor acting on the geoPotential gradient. the linear components of the tensor differ from those for the quasi-geostrophic Potential Vorticity only if there exists a vertical variation of background Potential Vorticity, such as occurs at the tropopause, or if there is shear of the assumed background flow. the non-linear components are absent in the quasi-geostrophic case. The forms of free, bound and total charge are defined for accurate non-linear forms of the Potential Vorticity. the free-space Green's function for the operator defining the total charge is identical to that for quasi-geostrophic theory and provides a scheme whereby the field attributed to each Potential Vorticity element is an invariant quantity. One of the most important results arising from this formulation is that the non-linearities in the definition of Potential Vorticity can be neglected when considering the far-field effect of Potential Vorticity anomalies. an analytical example of these ideas is given for a uniform anomaly of semi-geostrophic Potential Vorticity embedded in an otherwise uniform background Potential Vorticity. the dielectric constant and bound charge are calculated and give a clear insight into the differences between this and the quasi-geostrophic solution.
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Potential Vorticity of Flow along the Alps
Journal of the Atmospheric Sciences, 1993Co-Authors: Alan J. Thorpe, Hans Volkert, Dietrich HeimannAbstract:Abstract Observations from the German Front Experiment are presented here that show the existence—in conditions with a dominant flow component parallel to the main Alpine chain—of a mesoscale region to the north of the Alps where the absolute and Potential Vorticity (PV) are substantially negative. These structures exist before the front arrives to the Alps and appear to be affected little by the passage of the front. A dynamical explanation for these and other mesoscale structures is sought by considering a simple unsheared airflow impinging on the Alps from the west. A linear frictionless model for the steady-state response is used as well as a full nonlinear numerical model with and without friction. A vastly simplified Alpine orography is considered as well as one that adequately describes its mesoscale detail. The results show that the frictionless linear dynamics lead to a zone north of the Alps with anticyclonic Vorticity but with uniform (positive) Potential Vorticity. With boundary-layer processe...
David P. Marshall - One of the best experts on this subject based on the ideXlab platform.
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On the dynamical influence of ocean eddy Potential Vorticity fluxes
Ocean Modelling, 2015Co-Authors: James R. Maddison, David P. Marshall, Jemma ShiptonAbstract:Abstract The impact of eddy Potential Vorticity fluxes on the dynamical evolution of the flow is obscured by the presence of large and dynamically-inert rotational fluxes. However, the decomposition of eddy Potential Vorticity fluxes into rotational and divergent components is non-unique in a bounded domain and requires the imposition of an additional boundary condition. Here it is proposed to invoke a one-to-one correspondence between divergent eddy Potential Vorticity fluxes and non-divergent eddy momentum tendencies in the quasi-geostrophic residual-mean equations in order to select a unique divergent eddy Potential Vorticity flux. The divergent eddy Potential Vorticity flux satisfies a zero tangential component boundary condition. In a simply connected domain, the resulting divergent eddy Potential Vorticity flux satisfies a powerful optimality condition: it is the horizontally oriented divergent flux with minimum L2 norm. Hence there is a well-defined sense in which this approach removes as much of the dynamically inactive eddy Potential Vorticity flux as possible, and extracts an underlying dynamically active divergent eddy Potential Vorticity flux. It is shown that this approach leads to a divergent eddy Potential Vorticity flux which has an intuitive physical interpretation, via a direct relationship to the resulting forcing of the mean circulation.
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A Framework for Parameterizing Eddy Potential Vorticity Fluxes
Journal of Physical Oceanography, 2012Co-Authors: David P. Marshall, James R. Maddison, Pavel BerloffAbstract:A framework for parameterizing eddy Potential Vorticity fluxes is developed that is consistent with conservation of energy and momentum while retaining the symmetries of the original eddy flux. The framework involves rewriting the residual-mean eddy force, or equivalently the eddy Potential Vorticity flux, as the divergence of an eddy stress tensor. A norm of this tensor is bounded by the eddy energy, allowing the components of the stress tensor to be rewritten in terms of the eddy energy and nondimensional parameters describing the mean shape and orientation of the eddies. If a prognostic equation is solved for the eddy energy, the remaining unknowns are nondimensional and bounded in magnitude by unity. Moreover, these nondimensional geometric parameters have strong connections with classical stability theory. When applied to the Eady problem, it is shown that the new framework preserves the functional form of the Eady growth rate for linear instability. Moreover, in the limit in which Reynolds stresses are neglected, the framework reduces to a Gent and McWilliams type of eddy closure where the eddy diffusivity can be interpreted as the form proposed by Visbeck et al. Simulations of three-layer wind-driven gyres are used to diagnose the eddy shape and orientations in fully developed geostrophic turbulence. These fields are found to have large-scale structure that appears related to the structure of the mean flow. The eddy energy sets the magnitude of the eddy stress tensor and hence the eddy Potential Vorticity fluxes. Possible extensions of the framework to ensure Potential Vorticity is mixed on average are discussed.
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Vertical Fluxes of Potential Vorticity and the Structure of the Thermocline
Journal of Physical Oceanography, 2000Co-Authors: David P. MarshallAbstract:Abstract A new framework for understanding the vertical structure of ocean gyres is developed based on vertical fluxes of Potential Vorticity. The key ingredient is an integral constraint that in a steady state prohibits a net flux of Potential Vorticity through any closed contour of Bernoulli Potential or density. Applied to an ocean gyre, the vertical fluxes of Potential Vorticity associated with advection, friction, and buoyancy forcing must therefore balance in an integral sense. In an anticyclonic subtropical gyre, the advective and frictional Potential Vorticity fluxes are both directed downward, and buoyancy forcing is required to provide the compensating upward Potential Vorticity flux. Three regimes are identified: 1) a surface “ventilated thermocline” in which the upward Potential Vorticity flux is provided by buoyancy forcing within the surface mixed layer, 2) a region of weak stratification—“mode water”—in which all three components of the Potential Vorticity flux become vanishingly small, and...
Tapio Schneider - One of the best experts on this subject based on the ideXlab platform.
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Zonal Momentum Balance, Potential Vorticity Dynamics, and Mass Fluxes on Near-Surface Isentropes
Journal of the Atmospheric Sciences, 2005Co-Authors: Tapio SchneiderAbstract:While it has been recognized for some time that isentropic coordinates provide a convenient framework for theories of the global circulation of the atmosphere, the role of boundary effects in the zonal momentum balance and in Potential Vorticity dynamics on isentropes that intersect the surface has remained unclear. Here, a balance equation is derived that describes the temporal and zonal mean balance of zonal momentum and of Potential Vorticity on isentropes, including the near-surface isentropes that sometimes intersect the surface. Integrated vertically, the mean zonal momentum or Potential Vorticity balance leads to a balance condition that relates the mean meridional mass flux along isentropes to eddy fluxes of Potential Vorticity and surface Potential temperature. The isentropic-coordinate balance condition formally resembles balance conditions well known in quasigeostrophic theory, but on near-surface isentropes it generally differs from the quasigeostrophic balance conditions. Not taking the intersection of isentropes with the surface into account, quasigeostrophic theory does not adequately represent the Potential Vorticity dynamics and mass fluxes on near-surface isentropes—a shortcoming that calls into question the relevance of quasigeostrophic theories for the macroturbulence and global circulation of the atmosphere.
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Boundary Effects in Potential Vorticity Dynamics
Journal of the Atmospheric Sciences, 2003Co-Authors: Tapio Schneider, Isaac M. Held, Stephen T. GarnerAbstract:Many aspects of geophysical flows can be described compactly in terms of Potential Vorticity dynamics. Since Potential temperature can fluctuate at boundaries, however, the boundary conditions for Potential Vorticity dynamics are inhomogeneous, which complicates considerations of Potential Vorticity dynamics when boundary effects are dynamically significant. A formulation of Potential Vorticity dynamics is presented that encompasses boundary effects. It is shown that, for arbitrary flows, the generalization of the Potential Vorticity concept to a sum of the conventional interior Potential Vorticity and a singular surface Potential Vorticity allows one to replace the inhomogeneous boundary conditions for Potential Vorticity dynamics by simpler homogeneous boundary conditions (of constant Potential temperature). Functional forms of the surface Potential Vorticity are derived from field equations in which the Potential Vorticity and a Potential Vorticity flux appear as sources of flow quantities in the same way in which an electric charge and an electric current appear as sources of fields in electrodynamics. For the generalized Potential Vorticity of flows that need be neither balanced nor hydrostatic and that can be influenced by diabatic processes and friction, a conservation law holds that is similar to the conservation law for the conventional interior Potential Vorticity. The conservation law for generalized Potential Vorticity contains, in the quasigeostrophic limit, the well-known dual relationship between fluctuations of Potential temperature at boundaries and fluctuations of Potential Vorticity in the interior of quasigeostrophic flows. A nongeostrophic effect described by the conservation law is the induction of generalized Potential Vorticity by baroclinicity at boundaries, an effect that plays a role, for example, in mesoscale flows past topographic obstacles. Based on the generalized Potential Vorticity concept, a theory is outlined of how a wake with lee vortices can form in weakly dissipative flows past a mountain. Theoretical considerations and an analysis of a simulation show that a wake with lee vortices can form by separation of a generalized Potential Vorticity sheet from the mountain surface, similar to the separation of a friction-induced Vorticity sheet from an obstacle, except that the generalized Potential Vorticity sheet can be induced by baroclinicity at the surface.
Jón Egill Kristjánsson - One of the best experts on this subject based on the ideXlab platform.
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The Usefulness of Piecewise Potential Vorticity Inversion
Journal of the Atmospheric Sciences, 2012Co-Authors: Bjørn Røsting, Jón Egill KristjánssonAbstract:AbstractIt is today widely accepted that Potential Vorticity (PV) thinking is a highly useful approach for understanding important aspects of dynamic meteorology and for validation of output from state-of-the-art numerical weather prediction (NWP) models. Egger recently presented a critical view on piecewise Potential Vorticity inversion (PPVI). This was done by defining a PV anomaly by retaining the observed PV field in a specific region, while changing the observed PV fields to zero elsewhere. Inversion of such a modified PV field yields a flow vastly different from the observed. On the basis of this result it was argued that PPVI is useless for understanding the dynamics of the flow.The present paper argues that the results presented by Egger are incomplete in the context of PPVI, since the complementary cases were not considered and that the results also depend on the idealized model formulations. The complementary case is defined by changing the observed PV to zero in the specific region, while retai...