As a consequence of Kolmogorov's similarity hypotheses that are valid for locally homogeneous and isotropic turbulence
, the turbulent energy spectrum E(k) ([m.sup.3] [s.sup.-2]) of three-dimensional wind velocities in the inertial subrange is partitioned among the eddies in a universal form (Kolmogorov 1941; Sutton 1953; Pope 2000):
However, as in all RANS models, SST uses the Boussinesq hypothesis on turbulent viscosity , which is valid only in the case of isotropic turbulence
. For turbulent convection, the anisotropic properties of the flow have a significant effect; this is due to the complex nature of the flow and the presence of secondary currents.
To obtain the optimal value of [C.sub.ISAS], a recommended way is to calculate the simple decaying homogeneous isotropic turbulence
(DHIT), for example, the classical test case performed by Comte-Bellot and Corrsin , just as that did for most LES and hybrid models calibrations [19, 29, 32, 36].
Hence, the objective of the present work is to develop a theoretical analysis based on the aforementioned properties which leads to determining the statistics of the local finite scale Lyapunov exponent in fully developed homogeneous isotropic turbulence
for incompressible fluids.
The VLES method is validated interactively in the process of the model derivation by computing a series of generic flows, such as the natural decay of the homogeneous isotropic turbulence
, fully-developed flow in a plane channel and a separating flow over a periodic arrangement of smoothly-contoured 2-D hills in a Reynolds number range.
It is important to stress that (14) was derivate for conditions of continuous, homogenous, and isotropic turbulence
; and such conditions are not present in the very stable regime of the SBL.
Pirozzoli and Grasso  studied the influence of initial compressibility on flow topology in compressible isotropic turbulence
and found that the p.d.f.s of the Q-R diagram exhibited a universal teardrop shape as in the incompressible case.
Measured turbulence levels during this work is less than 9%, which Bruun (1995) showed that the problem of rectification is limited below the level considering homogeneous and isotropic turbulence
. Relative expanded uncertainty of velocity measurements by the single-sensor hot-wire probe in air is 4.23%.
The distributions of [[DELTA].sub.u], [[DELTA].sub.v], and [[DELTA].sub.w] are uniform, which corresponds to the initial grid-generated homogeneous isotropic turbulence
that decays downstream (see Figs 2 and 3).
RSM provides anisotropic turbulence to flows; when the hypothesis of turbulent viscosity is used, model gives isotropic turbulence
. In the first case, Reynolds stress transfer equations are being solved for separate stress components.
The closure assumptions of the k-[epsilon] model are only valid for high-intensity and nearly isotropic turbulence
. In this case there are the zones where the turbulence is intense (mixing zone) and the zones where the flow is almost laminar [13-14].
Chapters cover the motion of particles and heat exchange in homogeneous isotropic turbulence
and gradient turbulent flows; collisions of particles in a turbulent flow; and dispersion, collision, and clustering of monodispersed and bidispersed particles in homogeneous turbulence.