By Pierre Sagaut

This e-book summarizes the newest theoretical, computational and experimental effects facing homogeneous turbulence dynamics. a wide classification of flows is roofed: flows ruled by means of anisotropic construction mechanisms (e.g. shear flows) and flows with out construction yet ruled by way of waves (e.g. homogeneous rotating or stratified turbulence). Compressible turbulent flows also are thought of. In each one case, major traits are illustrated utilizing computational and experimental effects, whereas either linear and nonlinear theories and closures are mentioned. information about linear theories (e.g. quick Distortion thought and variations) and nonlinear closures (e.g. EDQNM) are supplied in devoted chapters, following a completely unified strategy. The emphasis is on homogeneous flows, together with a number of interactions (rotation, stratification, shear, surprise waves, acoustic waves, and extra) that are pertinent to many purposes fields - from aerospace engineering to astrophysics and Earth sciences.

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**Extra resources for Homogeneous Turbulence Dynamics**

**Example text**

This gap in the spectral description precludes the capture of the VSHF mode in physical space. To solve this problem, one can define an orthonormal frame of reference, which is nothing but the local reference frame of a polar-spherical system of coordinates for k (see Fig. 67) with k × n = 0. Local frame vectors e(1) , e(2) , e(3) may coincide with the fixed frame of reference, with e(3) = n for k n. The only price to pay for matching toroidal– poloidal modes to the VSHF one is to accept a nonuniform definition for k × n = 0 and k × n = 0, but this is well known using any polar-spherical coordinate system.

Navier had already distinguished two types of motion, “regulier” (mean) and “tumultueux” (turbulent), foreshadowing Osborne’s Reynolds decomposition. The idea that two length scales are present was also considered by Saint-Venant. 22:32 P1: irk/QPJ/RPW book-sagaut-cambon P2: irk/irp/KAA/SPO QC: irk/irp CUUS150-Sagaut 978 0 521 855488 14 April 22, 2008 Statistical Analysis of Homogeneous Turbulent Flows This Poisson-type equation displays how the pressure is connected to the terms that are not divergence free in the Navier–Stokes equations† : the acceleration term itself (contributing to the first term on the right-hand side) and possibly the bodyforce term (second term on the right-hand side).

Kassinos, Reynolds, and Rogers (KRR) (2001). In general, there is no direct link between Mi j pq and the RST, even if the identity Mi j pp = Ri j holds, and the problem of closure arises from the two-point structure in Eq. 51). In classical closures, the nondimensional tensor Mi j pq /(2K) is sought as a tensorial function of the nondimensional deviatoric tensor bi j defined in Eq. 43). Models range from linear (Launder, Reece, and Rodi, 1975) to cubic tensorial expansions. Similarly, the slow pressure–strain tensor is assumed to be an isotropic tensorial (s) function of bi j .