Spherically Symmetric Fluid Cosmological Model with Anisotropic Stress Tensor in General Relativity

This paper deals with the cosmological models for the static spherically symmetric spacetime for perfect fluid with anisotropic stress energy tensor in general relativity by introducing the generating functions g(r) and w(r) and also discussing their physical and geometric properties.

ON THE INTERACTION BETWEEN THERMALIZED NEUTRINOS AND COSMOLOGICAL GRAVITATIONAL WAVES ABOVE THE ELECTROWEAK UNIFICATION SCALE

We investigate the interaction between the cosmological relic neutrinos, and primordial gravitational waves entering the horizon before the electroweak phase transition, corresponding to observable frequencies today ν0≳10-5 Hz . We give an analytic formula for the traceless transverse part of the anisotropic stress tensor, due to weakly interacting neutrinos, and derive an integro-differential equation describing the propagation of cosmological gravitational waves at these conditions. We find that this leads to a decrease of the wave intensity in the frequency region accessible to the LISA space interferometer, that is at the present the most promising way to obtain a direct detection of a cosmological gravitational wave. The absorbed intensity does not depend neither on the perturbation wavelength, nor on the details of neutrino interactions, and is affected only by the neutrino fraction fν. The transmitted intensity amounts to 88% for the standard value fν=0.40523. An approximate formula for non-standard values of fν is given.

Turbulent rotating flow calculations: An assessment of two-equation anisotropic and Reynolds stress models

The stress field in a rotating turbulent internal flow is highly anisotropic. This is true irrespective of whether the axis of rotation is aligned with or normal to the mean flow plane. Consequently, turbulent rotating flow is very difficult to model. This paper attempts to assess the relative merits of three different ways to account for stress anisotropies in a rotating flow. One is to assume an anisotropic stress tensor, another is to model the anisotropy of the dissipation rate tensor, while a third is to solve the stress transport equations directly. Two different near-wall two-equation models and one Reynolds stress closure are considered. All the models tested are asymptotically consistent near the wall. The predictions are compared with measurements and direct numerical simulation data. Calculations of turbulent flows with inlet swirl numbers up to 1.3, with and without a central recirculation, reveal that none of the anisotropic two-equation models tested is capable of replicating the mean velocity field at these swirl numbers. This investigation, therefore, indicates that neither the assumption of anisotropic stress tensor nor that of an anisotropic dissipation rate tensor is sufficient to model flows with medium to high rotation correctly. It is further found that, at very high rotation rates, even the Reynolds stress closure fails to predict accurately the extent of the central recirculation zone.