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The condition for validity of all results obtained in this paper is that jul (x; y)
1. We see that along the jet axis the results are valid for almost the whole initial part (x ¡ 8), whereas for y = 0:7 they are valid only for x ¡ 5. The change of j(x; y) as x increases is correlated with the change of the mean velocity (see below), but these changes are not fully identical. Let us trace the changes of the group wave velocity at St = Stm , as well as of the wave lengths in the longitudinal and transverse directions ( lon (Stm ; x) = 2 =K(Stm ; x) and tr (Stm ; x) = 2 = (Stm ; x), respectively), with increasing x.
In particular: (1) Our studies show that the shift of velocity pulsation power spectra to the low-frequency domain is caused mainly by the jet divergence, not pairing of vortices, so that it can therefore be calculated within the linear approximation. (2) The observed phenomenon of vortices pairing can be accounted for in terms of the increase in the longitudinal and transverse turbulent scales, which is caused by jet divergence and not by resonance relations. (3) The transformation of the mean velocity proÿle can be found without the use of the concept of turbulent viscosity.
S. L’vov, I. Procaccia, Exact resummation in the theory of hydrodynamic turbulence: on line resummed diagrammatic perturbation approach, in: F. David, P. Ginsparg, J. ), Les Houches Session LXII, 1994, Fluctuating Geometries in Statistical Mechanics and Field Theory, Elsevier, New York, 1995. S. L’vov, I. Procaccia, Anomalous scaling in turbulence: a ÿeld theoretic approach, in: E. Infeld, R. Zelazny, A. ), Nonlinear Dynamics, Chaotic and Complex Systems, Cambridge University Press, Cambridge, 1996.
Atomic Physics with Hard X-Rays from High-Brilliance Synch. Sources [wkshop procs]