HIDA DISTRIBUTION CONSTRUCTION OF NON-GAUSSIAN REFLECTION POSITIVE GENERALIZED RANDOM FIELDS

Multiple stochastic integrals with respect to the Gaussian white noise indexed by Rd are used for the construction of reflection positive non-Gaussian [Formula: see text] valued random variables (random fields). This construction is then extended to a class of Hida distribution to consider several interesting examples. In particular, some new fields (without full Euclidean invariance but satisfying all other axioms, including space rotation invariance) are constructed through this probabilistic (and purely Euclidean) procedure.

On Euclidean invariance of algebraic Reynolds stress models in turbulence

This article shows how Euclidean invariance can be preserved in the so-called algebraic Reynolds stress model (ARSM) approximation. This approximation is used to reduce the transport equation for the Reynolds stresses to an explicit algebraic relation. A number of known models, which make use of this approximation, are not form-invariant under transformations to rotating coordinate systems. A simple extension is presented to show how this artifact can be removed.