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Field theoretic formulation of fluid mechanics according to the geometric algebra.

Authors :
Sen, D
Source :
Pramana: Journal of Physics. Sep2023, Vol. 97 Issue 3, p1-12. 12p.
Publication Year :
2023

Abstract

A simple and coherent approach to fluid mechanics is presented using a proper formalism of geometric algebra. The analogy between the equations of electromagnetism and fluid mechanics provides reinterpretation of the equations for two constituent (vorticity and the Lamb vector) fields. Identifying certain quantities as the source fields, the guiding Navier–Stokes (NS) equations of fluid mechanics can be formulated as a set of four geometrically distinct field equations, resembling exactly the Maxwell equations for the constituent magnetic and electric fields. The same set of equations works for all the cases of compressible, incompressible, viscous and the inviscid fluid motions with appropriately modified source terms. The analogy is completed by defining the combined ‘fluidomechanic’ bivector field in space–time algebra and further extended to the fluidic analogue of the Poynting theorem, Poynting vector and Lorentz force. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
03044289
Volume :
97
Issue :
3
Database :
Academic Search Index
Journal :
Pramana: Journal of Physics
Publication Type :
Academic Journal
Accession number :
170072108
Full Text :
https://doi.org/10.1007/s12043-023-02617-x