Beltrami vector fields hydrodynamics

As argued by Reed [4], the Beltrami vector field originated in hydrodynamics and is force-free. It is one of the three basic types of field solenoidal, complex lamellar, and Beltrami. These vector fields originated in hydrodynamics and describe the properties of the velocity field, flux or streamline, v, and the vorticity V x v. The Beltrami field is also a Magnus force free fluid flow and is expressed in hydrodynamics as... 

This vector field condition is sometimes referred to as Beltrami fluid flow, and was previously treated in a similar exposition by the author in 1995 [1], There it was indicated that Beltrami vector field flow is representative of a certain class of vector fields that are termed force-free. This type of field topology was first brought to prominence by Eugenio Beltrami in his 1889 paper Considerations on Hydrodynamics. [2], This type of morphology describes a regime of fluid... 

We remind our readers that vortical lines are curves whose points are tangential to the V A A field vectors at a any given instant. These curves will change in time. In the same spirit, the expressions current lines or field lines refer to the class of curves that are tangential in any of their points to the A field vectors at a given instant. Vortical lines usually differ from current lines. However, these lines sometimes match with each other and merge. This is the case when V A A = kA, where the A field defines the so-called Beltrami field, most often dealt with in hydrodynamics and in plasma physics. 

Although Beltrami fields have featured prominently in hydrodynamics for over a century, only until relatively recently have they received much attention in experimental and theoretical classical electrodynamics. The reason for the omission of this link in the standard development of electric/magnetic field theory can possibly be traced to a key related deficiency in the structure of vector... 

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See also in sourсe #XX -- [ , ]

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