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Topic: Irrotational field

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	Conservative or Irrotational Fields
		field f must be the divergence of a scalar field w.
		We also saw that the circulation of a field with path independent tangent vector line integrals, must be 0.
		The field is the gradient of a scalar field.
	hemsidor.torget.se /users/m/mauritz/math/field/cons.htm (176 words)

	PlanetMath: irrotational field
		is a vector field with differentiable real (or possibly complex) valued component functions.
		irrotational vector field, curl free field, curl-free vector field
		This is version 6 of irrotational field, born on 2002-11-13, modified 2003-10-18.
	planetmath.org /encyclopedia/IrrotationalField.html (76 words)

	[No title]
		let (v',w') be c the irrotational component of (v,w) (i.e., (v',w') is generated c by assuming cr,ci are zero and synthesizing br,bi with vhsgs).
		c c note: for an irrotational vector field (v,w), subroutine igradgc c computes a scalar field whose gradient is (v,w).
		c c c nt nt is the number of scalar and vector fields.
	www.cisl.ucar.edu /css/software/spherepack/igradgc.txt (1022 words)

	Archive on Irrotational Motions of Viscous & Viscoelastic Fluids
		A viscous correction of the irrotational pressure is needed to resolve the discrepancy between the zero-shear-stress boundary condition at a free surface and the non-zero irrotational shear stress.
		We show that the irrotational viscous flow with pressure corrections gives rise to exactly the same dispersion relation as the dissipation method in which no pressure at all is required and the viscous effect is accounted for by evaluating the viscous dissipation using the irrotational flow.
		The stress fields on the surface of a tri-axial ellipsoid depend strongly on the ratios of principal axes and are such as to suggest the formation of gas bubble with a round flat nose and two-dimensional cusped trailing edge.
	www.aem.umn.edu /people/faculty/joseph/ViscousPotentialFlow/index-vpf.html (5623 words)

	[No title]
		It follows that the field due to a superposition of charges is the superposition of the fields associated with the individual charge components.
		The "fringing" field, i.e., the external field of the dipole layer, is finite and hence negligible in the evaluation of the internal field of the dipole layer.
		Thus, the composite field is normal to the symmetry plane, as illustrated in the figure.
	web.mit.edu /6.013_book/www/chapter4/4.html (10260 words)

	PlanetMath: irrotational field
		is a vector field with differentiable real (or possibly complex) valued component functions.
		irrotational vector field, curl free field, curl-free vector field
		This is version 6 of irrotational field, born on 2002-11-13, modified 2003-10-18.
	www.planetmath.org /encyclopedia/IrrotationalVectorField.html (76 words)

	PowerPedia:Scalar field theory - PESWiki
		Scalar field theory (SWT) is a set of theories in a abstract model which posits that there is a basic mechanism that produces the electric field and the magnetic field.
		A "scalar field" is a set of assigned observable magnitudes at every point in n-dimensional space (compare this with the the scalar field of the current academic definition; n is also 4 or greater).
		An "electric field" is composed of the spinning charged mass, in motion through a finite change in electrostatic scalar potential (as compareed with the electric field of current academic definition).
	www.peswiki.com /index.php/PowerPedia:Scalar_field_theory (4754 words)

	PowerPedia:Electrostatics - PESWiki
		Because of the electric field's relationship to and interaction with magnetism, electrostatics is a subfield of electromagnetism.
		Because the electric field is irrotational, it is possible to express the electric field as the gradient of a scalar function, called the electrostatic potential (also known as the voltage).
		The electric field (in units of volts per meter) is defined as the force (in newtons) per unit charge (in coulombs).
	peswiki.com /index.php/PowerPedia:Electrostatics (1502 words)

	chapt3
		Surface roughness effects on the flow field.- The effect of surface roughness of a body immersed in a flow field is that it causes the flow near the body to go from laminar to turbulent.
		The flow field ahead of the airfoil is only slightly modified and for all practical purposes the velocities and static pressures are the same as for the ideal fluid case.
		The flow field is disrupted because of viscosity to the extent that a pressure drag arises.
	history.nasa.gov /SP-367/chapt3.htm (7698 words)

	Glossary of Fluid Mechanics Terms
		An irrotational fluid flow is one whose streamlines never loop back on themselves.
		Of course, a uniform viscid fluid flow without boundaries is also irrotational, but this is a special (and boring!) case.
		A flow field that cannot be described with streamlines in the absolute sense.
	www.efunda.com /formulae/fluids/glossary.cfm (520 words)

	Vector calculus Summary
		At each point the value of the vector field is the vector whose tail is at that point, whose direction is given by the arrow and whose magnitude is the length of the arrow.
		Precisely, the curl of at a vector field F is equal to (∂K/∂y - ∂J/∂z, ∂I/∂z - ∂K/∂x, ∂J/∂x - ∂I/∂y).
		It states that the integral of the (normal component of the) curl of a vector field over a bounded surface is equal to the integral of the (tangential component of the) vector field along the boundary of the surface.
	www.bookrags.com /Vector_calculus (1351 words)

	Official website of Kishore Sundara Rajan (Site not responding. Last check: )
		The operation of fringing electric field sensors is governed by the electroquasistatic approximation to Maxwell's equations.
		When the material under test is present in the near vicinity of the sensor electrodes, the electric fields originating from the driving electrodes penetrate through the bulk of the material under test and then terminate on the sensing electrodes.
		In this approximation, the magnetic field energy stored in the system is much larger than the electric field energy, the system is inductive, and the time variations are sufficiently slow that the displacement current density on the right side of (4) is negligible.
	students.washington.edu /kishore/research.htm (2248 words)

	IRROTATIONAL FLOW OF AN INVISCID FLUID
		This lecture is devoted to the study of irrotational plane flows of an inviscid fluid.
		This apparent paradox can only be solved by dropping the hypothesis of irrotational (and inviscid) flow in a region close to the profile (boundary layer) where viscosity plays a fundamental role and the flow is rotational and viscous.
		Flow around a wing The irrotational flow around a wing is analysed in terms of flow and pressure fields.
	www.imaph.tu-bs.de /lehre/99/irro/lecture_e.html (440 words)

	Electrostatics Summary (Site not responding. Last check: )
		Because of the electric field's relationship to and interaction with magnetism, electrostatics is a subfield of electromagnetism.
		Because the electric field is irrotational, it is possible to express the electric field as the gradient of a scalar function, called the electrostatic potential (also known as the voltage).
		The electric field (in units of volts per meter) is defined as the force (in newtons) per unit charge (in coulombs).
	www.bookrags.com /Electrostatics (2929 words)

	Electric potential - ExampleProblems.com
		Technically, it is the potential φ (a scalar field) associated with the conservative electric field E (E = −∇φ) that occurs when the magnetic field is time invariant (so that ∇ × E = 0 from Faraday's law of induction).
		This force has the same direction as the electric field vector, and its magnitude is given by the size of the charge multiplied with the magnitude of the electric field.
		For certain forces, it is possible to define the "potential" of a field such that the potential energy of an object due to a field is dependent only on the position of the object with respect to the field.
	www.exampleproblems.com /wiki/index.php/Electric_potential (747 words)

	Navier-Stokes Equations: Potential Flows (Site not responding. Last check: )
		Thus, the full set of five field variables v, r, and T (or v, r, and s) reduce to the two variables f and r, where r, T, and s are the density, absolute temperature, and entropy, respectively.
		In the case of constant density flows, the four field variables v, p reduce to the two variables f and p, where p is the fluid pressure.
		For example, it could be argued that the discussion of the conditions required for irrotational flow in the Restrictions section is redundant.
	www.navier-stokes.net /nspfint.htm (328 words)

	FLOW AROUND AN AIRFOIL
		Using Kutta condition the circulation is not anymore a free variable and it is possible to evaluate the lift of an airfoil using the same techniques that were described for the cylinder.
		Note that the flow fields obtained for a fixed value of the circulation are all valid solutions of the flow around an airfoil.
		The flow field around the wing will then have zero circulation, with two stagnation points located one on the lower face of the wing, close to the leading edge, and one on the upper face, close to the trailing edge.
	www.av8n.com /irro/profilo_e.html (576 words)

	AMS Glossary
		Two equivalent properties of an irrotational field are that there is no circulation about any reducible curve within the fluid, and that a potential exists.
		An autobarotropic fluid is irrotational for all time if it is irrotational at any time.
		Meteorological motions of the smaller scales, for example, gravity waves, may be treated as irrotational, but when the scale is large enough to take the rotation of the earth into account, only rotational motions are of interest.
	amsglossary.allenpress.com /glossary/browse?p=39&s=I (423 words)

	Smooth and Quantal Properties of the Complex Wave.
		The four-space in which all these fields exist as wave functions is referred to as the Minkowski space to denote the way that one dimension, that associated with time, is treated differently from the other three "physical" space dimensions with their Euclidean geometric properties.
		For a bound multi-electron wave field it is possible to extract from the system differential operator a term in the second spatial derivative plus any and all of those terms that result from charge density and thereby associate with electric field divergence.
		The most simple and important cases of externally induced fields to be considered are those that are essentially of uniform stress in a single spatial direction throughout the model, and either constant in time or subject to an oscillatory modulation that may be described in terms of their frequency domain spectra.
	www.wavemodel.org /qed/smooth.html (15308 words)

	Model Gallery : Flow Duct
		The modeling of aircraft-engine noise is a central problem in the field of computational aeroacoustics.
		The acoustic field in a model of an axially symmetric aero-engine duct, generated by a noise source at the boundary, is computed and visualized.
		Results are presented for situations with as well as without a compressible irrotational background flow and for the cases of hard and lined duct walls.
	www.femlab.com /showroom/gallery/1371.php (64 words)

	Potential Flow and d'Alembert's Paradox
		The circulation of the vector field V around any simple closed path S is defined as the integral of the tangential component of V around that path (in the "right-handed" direction).
		This is important because we often imagine a large reservoir of essentially static or uniformly flowing (and therefore irrotational) fluid as the upstream boundary conditions of a problem, and we can therefore assume the flow is irrotational throughout the process.
		Consequently the velocity field is symmetrical on the upstream and downstream sides of the sphere.
	www.mathpages.com /home/kmath211/kmath211.htm (1579 words)

	Smooth and Quantal Properties of the Complex Wave.
		The four-space in which all these fields exist as wave functions is referred to as the Minkowski space to denote the way that one dimension, that associated with time, is treated differently from the other three "physical" space dimensions with their Euclidean geometric properties.
		For a bound multi-electron wave field it is possible to extract from the system differential operator a term in the second spatial derivative plus any and all of those terms that result from charge density and thereby associate with electric field divergence.
		The most simple and important cases of externally induced fields to be considered are those that are essentially of uniform stress in a single spatial direction throughout the model, and either constant in time or subject to an oscillatory modulation that may be described in terms of their frequency domain spectra.
	wavemodel.org /qed/smooth.html (15308 words)

	Physics 47 (Advanced Electromagnetism) Home Page, Fall 2006
		Topics covered include: electrostatics, steady currents and static magnetic fields, time-dependent electric and magnetic fields, and the complete Maxwell theory, energy in the electromagnetic field, Poynting's theorem, electromagnetic waves, and radiation from time-dependent charge and current distributions.
		divergence of a vector field is a scalar.
		curl of a vector field is a vector field.
	www.amherst.edu /~waloinaz/Physics47_f06.html (2727 words)

	Math 252 Lecture 26 (Site not responding. Last check: )
		Irrotational Fields were defined [Transparancy 1] as fields which have a curl of zero everywhere.
		The proof involves assuming the vector field has a curl of zero, defining a scalar field, and showing that the vector field is the gradient of this scalar field.
		An example was considered [Transparancy 4], in which a vector field is irrotational (the curl of F is zero), and yet the field is not conservative.
	www.math.sfu.ca /~faculty/hebron/archive/1999-1/math252/lec_notes/lec26 (253 words)

	Session C2P - Poster Session: Turbulence Theory, Internal Transport Barriers, & Transport Modeling.
		The field line stochasticity arising around the current sheet exhibits some peculiarities due to the behaviour of the z-period of the unperturbed system: unlike the case of a double well potential, the period does not diverge on the separatrix, while its derivative diverges.
		Unfortunately, due to the memory bottle-neck represented by the grid arrays (the fields are computed on a spatial grid and then interpolated at each particle position), the physical-space resolution is limited by the RAM resources of the single processor, and its intrinsic scalability with the number of processors, typical of domain decomposition, is lost.
		The memory request related to the fields is thus drastically reduced and the scalability of the spatial resolution with the number of processors is recovered.
	flux.aps.org /meetings/YR98/BAPSDPP98/abs/S1200.html (5386 words)

	Active Contours, Deformable Models, and Gradient Vector Flow
		This field is computed as a spatial diffusion of the gradient of an edge map derived from the image.
		The GVF forces are used to drive the snake, modeled as a physical object having a resistance to both stretching and bending, towards the boundaries of the object.
		This is a gradient vector flow (GVF) field for a U-shaped object.
	iacl.ece.jhu.edu /projects/gvf (1914 words)

	4.2 Quantum models
		The field describing the beat fluctuations of this electromagnetic background can be shown to satisfy, once the dielectric medium is in motion, the same wave equation as that on a curved background.
		This is because that effect also requires the commutation relations of the field to generate the appropriate zero-point energy fluctuations (the vacuum structure) according to the Heisenberg uncertainty principle.
		This is not the case for the effective field describing the beat fluctuations of the system we have just described, which is equivalent to saying that it does not have a proper vacuum state (i.e., analogue to any physical field).
	relativity.livingreviews.org /Articles/lrr-2005-12/articlesu16.html (3709 words)

	1979: Journal of the Atmospheric Sciences, 36(10), 1844-1861
		These relationships are shown to exist because 1) the wind field responsible for the fluxes is quasi-geostrophic and 2) the instantaneous distributions of temperature, relative vorticity and potential vorticity tend to be rather similar to that of the geopotential field in the vicinity of the tropopause level.
		The distribution of transient eddy heat flux in the lower troposphere is primarily irrotational and directed down the local horizontal gradient of the time-averaged temperature field.
		The irrotational transient eddy flux of zonal momentum at the jet stream level is much smaller than the corresponding flux associated with momentum advection by the time-averaged flow and it is directed into regions of low zonal wind speed.
	www.gfdl.gov /reference/bibliography/1979/gl7901.html (608 words)

	FLOW AROUND A CYLINDER (Site not responding. Last check: )
		The irrotational solution cannot handle such phenomena and the resulting flow field does not resemble the real flow around a cylinder.
		First because it is a good example of an irrotational flow in a relatively complex geometry.
		If a wing profile is well oriented (small angle of attack) with respect to the uniform flow, boundary layer separation is negligible and the pressure field obtained by means of the irrotational flow solution can be considered as a good approximation of the actual pressure field.
	www.imaph.tu-bs.de /lehre/99/irro/cilindro_e.html (233 words)

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