Neural network models for the anisotropic Reynolds stress tensor in turbulent channel flow

A Review of Reynolds Stress Models for Turbulent Shear Flows

A detailed review of recent developments in Reynolds stress modeling for incompressible turbulent shear ows is provided. The mathematical foundations of both two-equation models and full second-order closures are explored in depth. It is shown how these models can be systematically derived for two-dimensional mean turbulent ows that are close to equilibrium. A variety of examples are provided t...

Asymptotic behaviour of commutation errors and the divergence of the Reynolds stress tensor near the wall in the turbulent channel flow

The derivation of the space averaged Navier–Stokes equations for the large eddy simulation (LES) of turbulent incompressible ows introduces two groups of terms which do not depend only on the space averaged ow eld variables: the divergence of the Reynolds stress tensor and commutation errors. Whereas the former is studied intensively in the literature, the latter terms are usually neglected. Th...

Turbulent pipe flow at extreme Reynolds numbers.

Both the inherent intractability and complex beauty of turbulence reside in its large range of physical and temporal scales. This range of scales is captured by the Reynolds number, which in nature and in many engineering applications can be as large as 10(5)-10(6). Here, we report turbulence measurements over an unprecedented range of Reynolds numbers using a unique combination of a high-press...

Direct solution for the anisotropy tensor in explicit algebraic Reynolds stress models

(cnL + cn−1L + · · ·+ c0I)(x) = 0, for all x ∈ V , cn = 1, cn−1 = −tr (L), · · · c0 = (−1) det(L), c−1 = 0, where I is the identity operator and all ck depend only on L. However, a special form of φ may imply that x also has a specific structure and on this contracted set an m power of L(x) can be expressed through a sum of lower powers with m < n. Consequently, computing the powers of the firs...

Effect of Reynolds Number in the Turbulent-flow Range