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For homogeneous flows the rapid pressure-strain correlation tensor can be written in terms of the mean velocity gradient and an integral of the two-point correlation tensor. In the present study the two-point correlation tensor is modeled and analytically integrated to obtain the pressure-strain model coefficients, which can then be expressed in terms of closed integrals of the two-point correlation model coefficients. Therefore, deficiencies of the pressure-strain models can be detected and resolved on the two-point correlation level. As an example for the new approach, direct numerical simulations results for a homogeneous shear flow are analyzed in detail and the resulting coefficients are compared to existing model coefficients for linear and nonlinear pressure-strain models.

The evolution of a symmetric pair of quasistreamwise vortical structures extracted from the two‐point correlation tensor of turbulent channel flow data by a linear stochastic estimation procedure is studied through direct numerical simulation. It is observed that an Ω‐shaped hairpin vortex is formed quickly from this initial structure. Sufficiently strong hairpin vortices are observed to generate a hierarchy of secondary hairpin vortices, and the mechanism of their creation closely resembles the formation of the primary hairpin vortex. New streamwise vortices are also generated, and this process provides a means for a few vortical disturbances of adequate strength to reproduce themselves and eventually populate the near‐wall layer.

A formalism for analyzing the complete set of field equations describing Macroscopic Gravity is presented. Using this formalism, a cosmological solution to the Macroscopic Gravity equations is determined. It is found that if a particular segment of the connection correlation tensor is zero and if the macroscopic geometry is described by a flat Robertson-Walker metric, then the effective correction to the averaged Einstein Field equations of General Relativity i.e., the backreaction, is equivalent to a positive spatial curvature term. This investigation completes the analysis of [Phys. Rev. Lett., vol. 95, 151102, (2005)] and the formalism developed provides a possible basis for future studies., Comment: 11 pages