Lagrangian theory of gravitational instability of Friedman-Lemaitre cosmologies and the 'Zel'dovich approximation'

Details Lagrangian theory of gravitational instability of Friedman-Lemaitre cosmologies and the 'Zel'dovich approximation' Lagrangian theory of gravitational instability of Friedman-Lemaitre cosmologies and the 'Zel'dovich approximation'

Feb 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992mnras.254..729b&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 254, Feb. 15, 1992, p. 729-737. Research supported by D

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146

Astronomical Models, Cosmology, Gravitation Theory, Gravitational Effects, Computational Astrophysics, Euler-Lagrange Equation, Linearization, Potential Flow, Three Dimensional Models, Transport Theory, Vorticity

Scientific paper

The connection between the Zel'dovich approximation and perturbative solutions of the Euler Poisson system is clarified for the motion of a self-gravitating dust continuum, evaluated in the Lagrangian picture of fluid dynamics. Solutions of the Lagrangian equations, linearized at an isotropically expanding background, are derived. This approximation is investigated; it contains the Zel'dovich approximation as well as a generalized form of it as subclasses, and it allowed treatment of the nonlinear evolution of vortical perturbations consistently within the framework of self-gravitating motions. In contrast to the prediction of the standard linear approximation, vorticity is coupled to the density enhancement and is amplified in the present approximation. The transport equation for vorticity is examined and applied. Relations to the fully nonlinear equations are discussed in terms of the eigenvalues of the velocity gradient of the inhomogeneous deformation.

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