Generalized sedeonic equations of hydrodynamics

We present a generalization of the equations of hydrodynamics based on the noncommutative algebra of space-time sedeons. It is shown that for vortex-less flow the system of Euler and continuity equations is represented as a single nonlinear sedeonic second-order wave equation for scalar and vector p...

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Bibliographic Details
Published inEuropean physical journal plus Vol. 135; no. 9; p. 708
Main Authors Mironov, V. L., Mironov, S. V.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2020
Springer Nature B.V
Subjects
Algebra
Applied and Technical Physics
Atomic
Complex Systems
Condensed Matter Physics
Continuity equation
Damping
Flow velocity
Fluid mechanics
Hydrodynamics
Mathematical analysis
Mathematical and Computational Physics
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Plane waves
Regular Article
Sound propagation
Sound waves
Spacetime
Theoretical
Vector potentials
Vortices
Wave equations
Wave propagation
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Summary:We present a generalization of the equations of hydrodynamics based on the noncommutative algebra of space-time sedeons. It is shown that for vortex-less flow the system of Euler and continuity equations is represented as a single nonlinear sedeonic second-order wave equation for scalar and vector potentials, which is naturally generalized on viscous and vortex flows. As a result we obtained the closed system of four equations describing the diffusion damping of translational and vortex motions. The main peculiarities of the obtained equations are illustrated on the basis of the plane wave solutions describing the propagation of sound waves.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-020-00700-5