New conserved integrals and invariants of radial compressible flow in n > 1 dimensions. (26th April 2023)

• Record Type: Journal Article
• Authors: Anco, Stephen C.; Seifi, Sara; Dar, Amanullah
• Is Part Of: Proceedings. Volume 479:Number 2272(2023)
• Publication Date: 2023-04-26
• Subjects: compressible fluid -- radial flow -- conserved integral -- invariant -- advected scalar; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2022.0743
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : Conserved integrals and invariants (advected scalars) are studied for the equations of radial compressible fluid/gas flow in n > 1 dimensions. Apart from entropy, which is a well-known invariant, three additional invariants are found from an explicit determination of invariants up to first order. One holds for a general equation of state, and the two others hold only for entropic equations of state. A recursion operator on invariants is presented, which produces two hierarchies of higher-order invariants. Each invariant yields a corresponding integral invariant, describing an advected conserved integral on transported radial domains. In addition, a direct determination of kinematic conserved densities uncovers two 'hidden' non-advected conserved integrals: one describes enthalpy-flux, holding for barotropic equations of state; the other describes entropy-weighted energy, holding for entropic equations of state. A further explicit determination of a class of first-order conserved densities shows that the corresponding non-kinematic conserved integrals on transported radial domains are equivalent to integral invariants, modulo trivial densities.