
Review of Short Phrases and Links 
This Review contains major "Vorticity" related terms, short phrases and links grouped together in the form of Encyclopedia article.
Definitions
 Vorticity is a property of the flow of air (or any other fluid, for that matter).
 Vorticity is a mathematical concept used in fluid dynamics.
 Vorticity is the curl of the velocity field.
 Vorticity is a vector, therefore, there are three components.
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 Vorticity is one of four quantities that are called the kinematic properties of fluid flow.
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 The vorticity equation is an important prognostic equation in the atmospheric sciences.
 The vorticity equation describes the evolution of the vorticity of a fluid element as it moves around.
 The properties of vorticity in 2 and 3 dimensions are treated in some depth in George Batchelor 's famous textbook (ch 5 & ch 7 et seq.).
 The first term on the RHS of the vorticity equation, , describes the stretching or tilting of vorticity due to the velocity gradients.
 The approximate form of the vorticity equation for the largescale flow will be presented.
Vorticity
 In the atmospheric sciences, vorticity is a property that characterizes largescale rotation of air masses.
 The absolute vorticity of an air mass will change if the air mass is stretched (or compressed) in the z direction.
 It has vorticity and usually has closed streamlines.
 If that tiny new solid particle would be rotating, rather than just translating, then there is vorticity in the flow.
 DENVER CYCLONE VORTICITY ZONE  A region of mesoscale low pressure created by the front range of the Rocky Mountains west of Denver, Colorado.
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 Couette Flow), the vorticity will be diffused throughout the flow field and it is probably simpler to look at the velocity field (i.e.
 In fluid dynamics vorticity is defined as the circulation per unit area at a point in the flow field.
 For a twodimensional flow, the vorticity vector is perpendicular to the plane.
 The total 3dimensional vorticity vector is the vector sum of these three.
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 Instead of computing the circulation on the closed contour C(t) we can compute the mean vorticity normal to A(t) and multiply that by the area within.
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 This can be seen by the diffusion term in the vorticity transport equation.
 In such a case you get the vorticity transport equation which is as follows in the case of incompressible (i.e.
 Incompressible viscous flows: vorticity transport equation, stream function equation, and boundary conditions.
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 The scalar vorticity is positive when the parcel has a counterclockwise rotation for the Northern Hemisphere.
 In the Northern Hemisphere, vorticity is positive for counterclockwise (i.e., cyclonic) rotation, and negative for clockwise (i.e, anticyclonic) rotation.
 Today, one can scarcely imagine an investigation in fluid mechanics that does not invoke the role of vorticity or vortices in some way.
 The Rossby number is a measure of the departure of the vorticity from that of solid body rotation.
 Baroclinic flows can be contrasted with barotropic flows in which density and pressure surfaces coincide and there is no baroclinic generation of vorticity.
 It is also of interest in the creation of vorticity by the passage of shocks through inhomogenous media, such as in the RichtmeyerMeshkov instability.
 Keywords: Shallow water model, Shallowwater instabilities, Unstable normalmodes, Potential vorticity fronts.
 Keywords: Shallow water model, Equatorial dynamics, Potential vorticity fronts, Kelvin waves.
 Continuously stratified dynamics: Inertiagravity waves, potential vorticity, quasigeostrophy.
 Nonlinear geostrophic adjustment, cycloneanticyclone asymmetry, and potential vorticity rearrangement.
 Shows that geostrophic balance is the minimum energy state for a given field of potential vorticity, in the linear approximation.
 In fluid dynamics, vorticity is the curl of the fluid velocity.
 They used a simplified form of atmospheric dynamics based on the barotropic_vorticity_equation.
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 Basic equations governing atmospheric motions and their elementary applications; circulation and vorticity; dynamics of midlatitude disturbances.
 The Vortex Dynamics Laboratory specializes in fluid dynamics research related to vorticity and particulate transport in incompressible fluids.
 Conservation of potential vorticity (PV) and Kelvin's circulation theorem express two of the fundamental concepts in ideal fluid dynamics.
 Thus, the more densely packed the vortex lines passing through some plane, the greater the vorticity.
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 In the same way that streamlines point in the direction of the wind flow, the vortex lines point in the direction of the vorticity vectors.
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 Series of "swirling motions" (spanwise vorticity) on lines at 1213 deg.
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 Typical analytical solutions apply to discrete distributions of vorticity, such as point vortices and vortex patches (e.g., Lamb 1932, Arts.
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 Fig. 3. An illustration of circular flow, showing the vorticity associated with this flow.
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 Where the streamlines have high curvature, the vorticity is high owing to the curvature contribution.
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 The horizontal part of the vorticity has two components, just like the horizontal wind has two components.
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 As shown in Mathematical Diversion  3, the horizontal vorticity vectors are dominated by the vertical wind shear of the horizontal wind.
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 A useful related quantity is potential vorticity.
 In general, the presence of viscosity causes a diffusion of vorticity away from these small regions (e.g.
 When the air converges, to maintain potential vorticity, the air speed increases, resulting in a stretched vortex.
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 Baroclinic instability requires the presence of a potential vorticity gradient along which waves amplify during cyclogenesis.
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 Viscous forces cause the diffusion of vorticity.
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 More precisely, a flow in solid body rotation has vorticity that is proportional to its angular velocity.
 From the numerical vorticity distribution, the position of the outer edge of the vortical region is determined as a function of the angular coordinate.
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 The Ekman pumping is a very small and the changes induced in the angular momentum (vorticity) are very weak.
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 In the atmospheric sciences, vorticity is the rotation of air around a vertical axis.
 Consider the following example of the vertical component of vorticity ( z), shown in Fig.
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 It is therefore common to use only the vertical component of the vorticity vector for meteorological applications.
 On the opposite side of the updraft, of course, an anticyclonically rotating vertical component of vorticity is found.
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 Lectures will continue with vertical structure, stratification effects and introduce vorticity and potential vorticity.
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 Suppose the flow is such that the lowlevel wind shear is producing only crosswise vorticity.
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 Real atmospheric vortices (in 2d flow) have a combination of shear and curvature vorticity (see below).
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 A vortex can be any circular or rotary flow that possesses vorticity.
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 An irrotational fluid is one whose vorticity=0.
 A vortex is concentrated vorticity.
 Introduced vorticity by analyzing a rotational vortex and an irrotational vortex.
 For an irrotational vortex, vorticity is zero everywhere except at the center of the vortex (where vorticity is infinite).
 In modern numerical weather forecasting models and GCMs, vorticity may be one of the prognostic variables.
 The mutual stretching of skewed vortex tubes, when they are close to each other, causes rapid growth of vorticity.
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 The next term, , describes stretching of vorticity due to flow compressibility.[2] Sometimes the negative sign is included in the term.
 Thus, it's possible for a vortex to be rotating cyclonically throughout, with a cyclonic vorticity core and a ring of anticyclonic vorticity surrounding it.
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 Therefore the baroclinic vector is nonzero, and the sense of the baroclinic vector is to create vorticity to make the interface level out.
 If the fingers curving in the sense of rotation force the thumb to point downward, the vorticity is negative.
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 The thin lines show the flow direction and the bold line indicates the sense of rotation associated with the vorticity.
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 The next three chapters deal with standard and introductory material on Kinematics, Conservation Laws, and Vorticity Dynamics.
 Keywords: Quasigeostrophic model, Potential vorticity fronts.
 Ertel's potential vorticity theorem in physical oceanography.
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 Rotunno, R., 1980: Vorticity dynamics of a convective swirling boundary layer.
 Flapping insect flight generates high mean lift by the interaction of the wings with the shed vorticity.
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