Journal ArticleDOI
Eigenfunctions of the Curl Operator, Rotationally Invariant Helmholtz Theorem, and Applications to Electromagnetic Theory and Fluid Mechanics
TLDR
In this article, the authors introduced eigenfunctions of the curl operator, which can be used to handle the divergence and divergence operators, and solved the initial value problem of electromagnetic theory with given time and space-dependent sources and currents.Abstract:
In the present paper we introduce eigenfunctions of the curl operator. The expansion of vector fields in terms of these eigenfunctions leads to a decomposition of such fields into three modes, one of which corresponds to an irrotational vector field and two of which correspond to rotational circularly polarized vector fields of opposite signs of polarization. Under a rotation of coordinates, the three modes which are introduced in this fashion remain invariant. Hence we have introduced the Helmholtz decomposition of vector fields in an irreducible, rotationally invariant form.These expansions enable one to handle the curl and divergence operators simply. As illustrations of the use of the curl eigenfunctions, we solve four problems. The first problem that is solved is the initial value problem of electromagnetic theory with given time- and space-dependent sources and currents and we show that the radiation and longitudinal modes uncouple in a very simple way. In the second problem we show how fluid motion...read more
Citations
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Journal ArticleDOI
Physical and Dynamical Meteorolgy. By D. Brunt. Second edition. Pp. xxiv, 428. 25s. 1939. (Cambridge)
TL;DR: In this article, a sketch of the surface distribution of the meteorological elements over the globe is presented, along with some statistical and thermal relationships, and the transformations of energy in the atmosphere.
Journal ArticleDOI
The joint cascade of energy and helicity in three-dimensional turbulence
TL;DR: In this paper, it is shown that the transfer of energy to small scales produces a tremendous growth of helicity separately in the + and − helical modes at high wave numbers, diverging in the limi...
Journal ArticleDOI
Linked and knotted beams of light
TL;DR: In this article, the Chandrasekhar-Kendall curl eigenstate and Hopf fibration have been used to derive a new class of knotted beams of light and approximate knots of light may be generated using tightly focused circularly polarized laser beams.
Book ChapterDOI
Vorticity Dynamics on Boundaries
TL;DR: In this article, a unified general theory of the vorticity dynamics on various boundaries for viscous compressible flows and then reviews its applications to specific problems mainly confined to incompressible flows is presented.
Journal ArticleDOI
Polarized vorticity dynamics on a vortex column
Mogens V. Melander,Fazle Hussain +1 more
TL;DR: In this paper, it is shown that vortex core dynamics results from the interaction of two slowly deforming, but overlapping, helical vortex structures, which are obtained by a generalized Helmholtz decomposition of the vorticity field.
References
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Angular Momentum in Quantum Mechanics
TL;DR: In this paper, the angular momentum, one of the most fundamental quantities in all of quantum mechanics, is introduced and a concise introduction to its application in atomic, molecular, and nuclear physics is provided.
Book
Angular Momentum in Quantum Mechanics
TL;DR: In this article, the angular momentum, one of the most fundamental quantities in all of quantum mechanics, is introduced and a concise introduction to its application in atomic, molecular, and nuclear physics is provided.
Book
Theoretical Nuclear Physics
TL;DR: A semi-empirical basis is used to describe and correlate the known nuclear properties including the theoretical concepts, methods, and considerations which have been devised in order to interpret the experimentsl material and to advance the ability to predict and control nuclear phenomena.
Book
Physical and Dynamical Meteorology
TL;DR: In this article, a sketch of the surface distribution of the meteorological elements over the globe is presented, along with some statistical and thermal relationships, and the transformations of energy in the atmosphere.
Journal ArticleDOI
Physical and Dynamical Meteorolgy. By D. Brunt. Second edition. Pp. xxiv, 428. 25s. 1939. (Cambridge)
TL;DR: In this article, a sketch of the surface distribution of the meteorological elements over the globe is presented, along with some statistical and thermal relationships, and the transformations of energy in the atmosphere.