New conserved integrals and invariants of radial compressible flow in dimensions
arXiv:2205.10950 · doi:10.1098/rspa.2022.0743
Abstract
Conserved integrals and invariants (advected scalars) are studied for the equations of radial compressible fluid/gas flow in dimensions. Apart from entropy, which is a well-know 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.
20 pages. Discussion of scaling properties and analysis applications of the new conserved integrals has been added