STATISTICAL DECOUPLING OF A LAGRANGIAN FLUID PARCEL IN NEWTONIAN COSMOLOGY
The Lagrangian dynamics of a single fluid element within a selfgravitational matter field is intrinsically nonlocal due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the densityweighted probability density function (ρPDF). Consequently it is guaranteed that the onepoint ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, andmore »
 Authors:

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^{[1]}
 Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218 (United States)
 Publication Date:
 OSTI Identifier:
 22518574
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Astrophysical Journal; Journal Volume: 820; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; CONTINUITY EQUATIONS; COSMOLOGY; DECOUPLING; DENSITY; DIAGRAMS; FLUID MECHANICS; FLUIDS; LAGRANGIAN FUNCTION; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; NONLUMINOUS MATTER; PROBABILITY DENSITY FUNCTIONS; TENSORS; TRANSPORT THEORY; UNIVERSE