A contemporary look at Hermann Hankel’s 1861 pioneering work on Lagrangian fluid dynamics

Frisch, U.; Grimberg, Gerard; Villone, B.

doi:10.1140/epjh/e2017-80038-2

Cited by 6 publications

(4 citation statements)

References 41 publications

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“…This theorem is closely related to the circulation theorem which is usually attributed to Lord Kelvin. Using the Cauchy invariants and Stoke's theorem, we obtain the (combined) Kelvin-Helmholtz theo-rem that states that [41] Γ ≡…”

Section: B Invariants Associated With Vorticitymentioning

confidence: 99%

Semiclassical path to cosmic large-scale structure

et al. 2019

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We chart a path toward solving for the nonlinear gravitational dynamics of cold dark matter by relying on a semiclassical description using the propagator. The evolution of the propagator is given by a Schrödinger equation, where the small parameter acts as a softening scale that regulates singularities at shell-crossing. The leading-order propagator, called free propagator, is the semiclassical equivalent of the Zel'dovich approximation (ZA), that describes inertial particle motion along straight trajectories. At next-to-leading order, we solve for the propagator perturbatively and obtain, in the classical limit the displacement field from second-order Lagrangian perturbation theory (LPT). The associated velocity naturally includes an additional term that would be considered as third order in LPT. We show that this term is actually needed to preserve the underlying Hamiltonian structure, and ignoring it could lead to the spurious excitation of vorticity in certain implementations of second-order LPT. We show that for sufficiently small the corresponding propagator solutions closely resemble LPT, with the additions that spurious vorticity is avoided and the dynamics at shell-crossing is regularised. Our analytical results possess a symplectic structure that allows us to advance numerical schemes for the large-scale structure. For times shortly after shell-crossing, we explore the generation of vorticity, which in our method does not involve any explicit multi-stream averaging, but instead arises naturally as a conserved topological charge.

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Section: B Invariants Associated With Vorticitymentioning

confidence: 99%

Semiclassical path to cosmic large-scale structure

et al. 2019

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“…However, his law was generalized beyond this approximation by other authors. The validity of the theorem for a barotropic fluid was proved by Hankel (see[4,5] for an english translation of his work).…”

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confidence: 99%

The generation of vorticity in cosmological N-body simulations

Jelic-Cizmek

Lepori

Adamek

et al. 2018

J. Cosmol. Astropart. Phys.

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Clustering of a perfect fluid does not lead to the generation of vorticity. It is the collisionless nature of dark matter, inducing velocity dispersion and shell crossing, which is at the origin of cosmological vorticity generation. In this paper we investigate the generation of vorticity during the formation of cosmological large scale structure using the public relativistic N-body code gevolution. We test several methods to compute the vorticity power spectrum and we study its convergence with respect to the mass and grid resolution of our simulations. We determine the power spectrum, the spectral index on large-scales, the amplitude of the peak position and their time evolution. We also compare the vorticity extracted from our simulations with the vector perturbations of the metric. Our results are accompanied by resolution studies and compared with previous studies in the literature.

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“… 2 Augustin-Louis Cauchy presented a Lagrangian formulation of three-dimensional incompressible hydrodynamics in a seminal, albeit forgotten, work in 1815 (Frisch & Villone 2014); see also Frisch, Grimberg & Villone (2017). …”

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confidence: 99%

A class of three-dimensional gyroviscous magnetohydrodynamic models

2020

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A Hamiltonian and action principle formalism for deriving three-dimensional gyroviscous magnetohydrodynamic models is presented. The uniqueness of the approach in constructing the gyroviscous tensor from first principles and its ability to explain the origin of the gyromap and the gyroviscous terms are highlighted. The procedure allows for the specification of free functions, which can be used to generate a wide range of gyroviscous models. Through the process of reduction, the noncanonical Hamiltonian bracket is obtained and briefly analysed.

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A contemporary look at Hermann Hankel’s 1861 pioneering work on Lagrangian fluid dynamics

Cited by 6 publications

References 41 publications

Semiclassical path to cosmic large-scale structure

Semiclassical path to cosmic large-scale structure

The generation of vorticity in cosmological N-body simulations

A class of three-dimensional gyroviscous magnetohydrodynamic models

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