arXiv subjects

Amanullah Dar

Publications and source records attributed to Amanullah Dar.

4 recordsLinked to original sources

arXiv2022

New conserved integrals and invariants of radial compressible flow in $n>1$ dimensions

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-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.

math-ph↗

arXiv2015

Conserved integrals for inviscid compressible fluid flow in Riemannian manifolds

An explicit determination of all local conservation laws of kinematic type on moving domains and moving surfaces is presented for the Euler equations of inviscid compressible fluid flow on curved Riemannian manifolds in n>1 dimensions. All corresponding kinematic constants of motion are also determined, along with all Hamiltonian kinematic symmetries and kinematic Casimirs which arise from the Hamiltonian structure of the inviscid compressible fluid equations.

math-ph↗

arXiv2015

Conservation laws of inviscid non-isentropic compressible fluid flow in n>1 spatial dimensions

Recent work giving a classification of kinematic and vorticity conservation laws of compressible fluid flow for 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 and 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.

physics.flu-dyn↗

arXiv2009

Classification of conservation laws of compressible isentropic fluid flow in n>1 spatial dimensions

For the Euler equations governing compressible isentropic fluid flow with a barotropic equation of state (where pressure is a function only of the density), local conservation laws in $n>1$ spatial dimensions are fully classified in two primary cases of physical and analytical interest: (1) kinematic conserved densities that depend only on the fluid density and velocity, in addition to the time and space coordinates; (2) vorticity conserved densities that have an essential dependence on the curl of the fluid velocity. A main result of the classification in the kinematic case is that the only equation of state found to be distinguished by admitting extra $n$-dimensional conserved integrals, apart from mass, momentum, energy, angular momentum and Galilean momentum (which are admitted for all equations of state), is the well-known polytropic equation of state with dimension-dependent exponent $γ=1+2/n$. In the vorticity case, no distinguished equations of state are found to arise, and here the main result of the classification is that, in all even dimensions $n\geq 2$, a generalized version of Kelvin's two-dimensional circulation theorem is obtained for a general equation of state.

physics.flu-dyn↗