By Alfredo Soldati, Rosesella Monti
Controlling turbulence is a vital factor for a couple of technological purposes. numerous how to modulate turbulence are at the moment being investigated. them all are according to the creation of a few type of perturbation into the circulation box which impact turbulence coherent constructions answerable for turbulence move mechanisms. The scope of the e-book is to explain a number of points of turbulence constitution and modulation and to provide an explanation for and speak about the main promising concepts in detail.
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Extra resources for Turbulence Structure and Modulation
Sample text
Another useful quantity is the spectrum of the helicity variance: I(k) = k2 I d(k/k)dk' < H(k)H(k') > ; I = I dkl(k). (142) (143) (144) We note that I(k) differs from the usual definition of a spectrum since I is not a local quantity. For the periodic box turbulence, the integration should be substituted by summation everywhere. A rigorous mathematical inequality relates E(k) and H(k) in the following way (Moffatt, 1975): I H(k) 1::; 2kE(k). (145) The mathematical upper bound for the helicity spectrum is constrained by the energy spectrum.
But to calculate uv , as in the general case, one has either to formulate a closure for the equation for a higher order correlator function, or to make a phenomenological assumption in many respects equivalent to a closure. As it is, Eq. 111 is subject to qualitative analysis. We notice that the total stress, that is the sum of the Reynolds stress uv, and the tangential viscous stress at the walls, or the friction force To, by virtue of Eq. 111 is: T dU = - _UV + V dY = To ( 1 - Y) D · There are three constants entering Eq.
The model simulations of turbulence which have prevailed so far were based, crudely 7 It should be remarked that the number of harmonics involving the energy containing and subviscous scales is negligible by comparison with Equation 80. 28 E. Levich speaking, on the assumption that the large wavenumber modes in the intertail range, predominantly contributing to the total number of modes, can be substituted by a macroscopic eddy, or turbulent viscosity. The eddy viscosity can be introduced as follows.