2009/11/30 by Stephen C. Anco, Amanullah Dar · 20 citations
Engineering · Mathematics · Physics and Astronomy · #Barotropic fluid #Conservation law #Conserved quantity #Enstrophy #Euler equations #Fluid dynamics #Fluid dynamics and aerodynamics studies #Inviscid flow #Navier-Stokes equation solutions #Noether's theorem #Nonlinear Waves and Solitons #Polytropic process #Vorticity #physics.flu-dyn
paper · pdf · doi:10.1098/rspa.2009.0579
published in Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences 466(2121), 2605-2632 (Royal Society) · 24 pages; minor corrections to eqns (5.9)& (5.1) in published version
openalex publication_date 2010/03/24 · arxiv created 2015/03/07 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Recent work giving a classification of kinematic and vorticity conservation laws of compressible fluid flow with barotropic equations of state (where pressure is a function only of the fluid density) in n >1 spatial dimensions is extended to general non-isentropic equations of state in which the pressure is also a function of the dynamical entropy (per unit mass) of the fluid. Two main results are obtained. First, we find that, apart from the familiar conserved integrals for mass, momentum, energy, angular momentum, Galilean momentum and volumetric entropy, additional kinematic conserved integrals arise only for non-isentropic equations of state given by a generalized form of the well-known polytropic equation of state with dimension-dependent exponent γ =1+2/ n , such that the proportionality coefficient is an arbitrary function of the entropy (per unit mass). Second, we show that the only vorticity conserved integrals consist of a circulatory entropy (which vanishes precisely when the fluid flow is irrotational) in all even dimensions. In particular, the vorticity integrals for helicity in odd dimensions and enstrophy in even dimensions are found to be no longer conserved for any non-isentropic equation of state.