About Vortex Physics and Vortex Losses

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  • Ashdin PublishingJournal of Vortex Science and TechnologyVol. 1 (2012), Article ID 235563, 10 pagesdoi:10.4303/jvst/235563

    ASHDINpublishing

    Research Article

    About Vortex Physics and Vortex Losses

    Konstantin Meyl

    1st TZS, Erikaweg 32, D-78048 Villingen-Schwenningen, GermanyAddress correspondence to Konstantin Meyl, prof@meyl.eu

    Received 16 March 2012; Accepted 15 June 2012

    Abstract As quantum physics nowadays tries to reframeand explain electric and magnetic field phenomena, we mustnot be mislead over the fact that quantum physics remainsa stepdaughter of field physics based solely on postulatesuntil eventually it will have found a way to calculate itsquanta. Furthermore, field physics is at least 25 times olderand can be traced back all the way to the early Greek naturalphilosophers. Vortex physics is another offspring of fieldphysics, however, it has been systematically rejected byquantum physics. Which in turn often times has a lot to dowith politics and not always with science. It could in factbe the case that vortex physics has been suppressed by itsown sister, ever since it also has produced distinguishedrepresentatives. A mathematical derivation shows that thecurrently known formulas and laws of electrodynamics areincomplete and insufficient in describing all its associatedphenomena. Via a new formulation and extension ofMaxwells equation it becomes possible to calculate apotential vortex, its effect on the dielectric medium can bemeasured and its existence made evident through observablenatural phenomena.

    Keywords vortex physics; potential vortex; duality; vortexlosses; capacitor losses

    1 Introduction

    In order for these preliminary statements not to contradictknown general conclusions, they have to include the follow-ing, vortices occurring in nature or technology as a matterof principal cannot be calculated or measured and in generalare not visible. They are there for out of reach of our pre-cise scientific methods, which seems to make it practicallyimpossible to prove their existence.

    Looking at this in depth we can thus conclude the fol-lowing.

    Calculating a vortex strictly speaking already stalls withthe attempt of forming a field equation that is able to deter-mine its dimensions in space and time. Even by taking intoconsideration all mathematical methods at hand, this fourdimensional field equation (a type of thermal conductionequation) is set to be unsolvable. Such an equation can there

    for only be resolved by applying simplified assumptions onthe vortexs dimensions in space and time [11].

    On trying to measure it we are faced with the samedilemma. Any kind of measuring probe we use woulddisrupt the vortex and cause it to swerve aside. We could atbest detect anomalies, which would in varying measuringattempts lose their repeatability.

    We are ultimately having to measure and calculate thevortex effects, e.g., its losses and compare those results [11].

    Negligence and measurement errors pose an additionaldifficulty on our way to finding proof of existence for vor-tices.

    We are there for relying less on measurements, in rela-tion to eddy currents, but much more on the existence of theestablished equations of Amperes law (1826) and the lawof induction (Faraday 1831), which J. C. Maxwell in 1873compiled and complemented.

    It would be hard to imagine the losses of eddy currentsnot to be identifiable and interpretable as such, without aset of equations. Rather a lack of uniformity, linearity andspecific material properties would in this case be acceptedas an explanation from a scientific point of view, then theactual causal, but not measurable eddy currents.

    This analogy ought to make us reconsider. It impliesthat neither the measuring of effects, nor the observation ofphenomena of a vortex would suffice as a scientific proof ofits existence. Only a mathematical description of the vortexthrough an appropriate field equation can be deemed satis-factory, from a precise scientific view point.

    2 Dual vortex phenomena in fluid mechanics

    In fluid engineering convincing and strong indications forthe correctness of the chosen approach can be found [8]. Itbenefits us that hydrodynamic vortices are visible, e.g., theinjection of smoke into a wind tunnel.

    Already Leonardo da Vinci had observed in liquids theexistence of two basic types of vortices in duality: one ofthese vortices moves slower at the center than it does at itsperimeter and the other moves faster at its center than it doesalong the perimeter.

  • 2 Journal of Vortex Science and Technology

    Figure 1: Velocity distribution v(R) for a vortex with rigidbody rotation.

    A vortex of the first type, also called vortex with rigid-body rotation, is formed, for instance, by a liquid in acentrifuge, that due to its inertia of mass is pressed againstthe outer wall because there the largest velocity exists. Inan analogous way the electromagnetic vortex in electricallyconductive material shows the well-known skin effect(Figure 1).

    To explain the other vortex, Newton describes an exper-iment in which a rod is dipped into a liquid as viscous aspossible and then turned. In this potential vortex the velocityof the particle increases the closer to the rod it is (Figure 2).

    The duality of both vortex phenomena becomes obviousby bringing to mind that in the experiment with the cen-trifuge the more liquid presses towards the outside the lessviscous the medium is. And that on the other hand the poten-tial vortex forms the stronger the more viscous the mediumis.

    As conclusion we read in text books that the viscosity ofthe liquid decides whether a vortex with rigid-body rotationor a potential vortex is formed.

    When we, in a third experiment, immerse the centrifugefilled with water into a dense medium and rotate the cen-trifuge, then inside the centrifuge a vortex with rigid-bodyrotation forms and outside the centrifuge a potential vortex(Figure 3).

    It is obvious that either vortex always causes the othervortex with opposite properties and so the existence of onecauses that of the other. So in the first case, that of the vor-tex with rigid-body rotation, outside the centrifuge potentialvortices will form in the surrounding air, whereas in thesecond case, that of the potential vortex, the turning roditself can be interpreted as a special case of a vortex withrigid-body rotation.

    Hence in all conceivable experiments the conditionalways is fulfilled that in the center of the vortex the samestate of peace, which we can term zero, prevails as aninfinity.

    Figure 2: Velocity distribution v(R) in a potential vortex[8].

    Figure 3: Combination of a vortex with rigid-body rotationand a potential vortex [8].

    When we take a tornado as an example, thus a whirl-wind. In the eye of the cyclone theres no wind at all. Butif I was to leave the center, I would be blown to the outside.One could really feel this vortex with rigid-body rotationon the inside. If, however, one was to stand on the outside,the potential vortex would try to pull you towards its center.This potential vortex is responsible for the structure and inthe end also for the size of the tornado (Figure 4).

    At the radius of the vortex, the place with the highestwind speeds, an equilibrium prevails. The vortex withrigid-body rotation and the potential vortex at this point areequally powerful. Their power again is determined by theirviscosity, which in turn sets the radius of the vortex.

    Therefore meteorologists pursue with interest whethera tornado forms over land or over water. Over the oceanfor instance it sucks itself full with water. In that way, thepotential vortex increases in power, the radius of the vortexgets smaller and the energy density increases dangerously.

    3 Dual vortex phenomena in electrical engineering

    If the knowledge from hydrodynamics is transferred overto the area of electromagnetics, then the role of viscosity is

  • Journal of Vortex Science and Technology 3

    Figure 4: Tornado, composed of expanding vortex frominside and counter vortex contracting from outside.

    taken on by the electric conductivity. The well-known cur-rent vortex occurs in the conductor, whereas its counterpart,the potential vortex, forms in the poor-conducting medium,with preference in the dielectric.

    The duality of both vortices is expressed by the fact thatthe electric conductivity of the medium decides whethereddy currents or potential vortices can form and howfast they decay, i.e., convert their energy into heat. Figure 3shows that vortex and anti-vortex mutually cause each other.

    In high tension transmission lines we find a strikingexample for the combination of current vortex and potentialvortex.

    Within the conductor eddy currents are formed. Thus thecurrent density increases towards the surface of the conduc-tor (skin effect).

    Outside the conductor, in the air, the alternating fieldsfind a very poorly conducting medium. If one follows thetext book opinion, then the field outside the conductorshould be a non-rotational gradient field. But this statementcauses unsolvable problems.

    When vortices occur inside the conductor, because of adetachment of the vortices without jumps at the interface tothe dielectric, the fields in the air surrounding the conductormust also have the form and the properties of vortices. Noth-ing would be more obvious as to mathematically describeand interpret these so-called gradient fields as vortex fieldsas well. On closer inspection this argument is even manda-tory.

    Figure 5: Kirlian photograph of a leave.

    The laws of field refraction known as boundary condi-tions [6] in addition demand steadiness at the interface ofthe conductor to the dielectric and do not leave us any otherchoice. If there is a vortex field on