Symmetries of fluid dynamics with polytropic exponent

Horváthy, P. A.

doi:10.1016/s0375-9601(00)00834-3

Cited by 38 publications

(23 citation statements)

References 17 publications

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“…which generate the centre-free optical Lie algebra, i.e., the Galilei Lie algebra augmented with time dilations, found earlier as a symmetry of the Chaplygin gas with viscosity [36]. Finally, the vector fields (VII.13) preserving the Carroll space C viewed as the t = 0 slice of B, are of the form…”

Section: B Massless Systemsmentioning

confidence: 87%

Conformal Carroll groups

Duval¹,

Gibbons²,

Horváthy³

2014

J. Phys. A: Math. Theor.

185

197

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Conformal extensions of Lévy-Leblond's Carroll group, based on geometric properties analogous to those of Newton-Cartan space-time are proposed. The extensions are labeled by an integer k. This framework includes and extends our recent study of the Bondi-Metzner-Sachs (BMS) and Newman-Unti (NU) groups. The relation to Conformal Galilei groups is clarified. Conformal Carroll symmetry is illustrated by "Carrollian photons". Motion both in the Newton-Cartan and Carroll spaces may be related to that of strings in the Bargmann space.arXiv:1403.4213 [hep-th]

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Section: B Massless Systemsmentioning

confidence: 87%

Conformal Carroll groups

Duval¹,

Gibbons²,

Horváthy³

2014

J. Phys. A: Math. Theor.

185

197

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“…It states that the motion may be regarded as the projection of the motion of light rays moving in a fivedimensional extended spacetime and obtain for the first time Kepler For further details and applications of conformal symmetries for gravitational waves, see [15,16]. Other examples of Chrono-Projective transformations include the Schrödinger-Newton equations [17], hydrodynamics [18], Schrödinger operators [19] and projective dynamics [20]. where l the total angular momentum and n is the principal quantum number, respectively.…”

Section: Discussionmentioning

confidence: 99%

“Kepler Harmonies” and conformal symmetries

et al. 2019

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Kepler's rescaling becomes, when "Eisenhart-Duval lifted" to 5-dimensional "Bargmann" gravitational wave spacetime, an ordinary spacetime symmetry for motion along null geodesics, which are the lifts of Keplerian trajectories. The lifted rescaling generates a well-behaved conserved Noether charge upstairs, which takes an unconventional form when expressed in conventional terms. This conserved quantity seems to have escaped attention so far. Applications include the Virial Theorem and also Kepler's Third Law. The lifted Kepler rescaling is a Chrono-Projective transformation. The results extend to celestial mechanics and Newtonian Cosmology.

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“…We list the commutation relations of this algebra 4 , and the action of its generators on the velocity fields, in detail in the next section. The conformal symmetry algebra described above is just subset of the full infinte dimensonal symmetry algebra of the Navier Stokes equations [16] (see also [17][18][19] for other related work) . The additional generators of the full symmetry algebra are very easy to describe; they consist of boosts to a reference frame whose velocity is homogeneous in space but an arbitrary function of time.…”

Section: Introduction and Discussionmentioning

confidence: 99%

The incompressible non-relativistic Navier-Stokes equation from gravity

Bhattacharyya

Minwalla

Wadia

2009

J. High Energy Phys.

141

199

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We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid. We demonstrate that special conformal symmetries of the parent relativistic theory descend to 'accelerated boost' symmetries of the Navier-Stokes equations, uncovering a conformal symmetry structure of these equations. Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations. In the holographic context we also find a simple forced steady state shear solution to the Navier-Stokes equations, and demonstrate that this solution turns unstable at high enough Reynolds numbers, indicating a possible eventual transition to turbulence.

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Symmetries of fluid dynamics with polytropic exponent

Cited by 38 publications

References 17 publications

Conformal Carroll groups

Conformal Carroll groups

“Kepler Harmonies” and conformal symmetries

The incompressible non-relativistic Navier-Stokes equation from gravity

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