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The equations of motion for the nth order velocity differences raise the interest in correlation functions containing both large and small scales simultaneously. We consider the scaling of such objects and also their conditional average representation with emphasis on the question of whether they behave differently in the inertial or the viscous subranges. The turbulent flow data are obtained by Navier-Stokes solutions on a 60(3) grid with periodic boundary conditions and Re lambda = 70. Our results complement previous high Re data analysis based on measured data [A. L. Fairhall, V. S. L'vov, and I. Procaccia, Europhys. Lett 43, 277 (1998)] whose preference were the larger scales, and the analysis of both experimental and synthetic turbulence data by [R. Benzi and co-workers, Phys. Rev. Lett. 80, 3244 (1998); Phys. Fluids 11, 2215 (1999)]. The inertial range fusion rule is confirmed and insight is obtained for the conditional averages (the local dissipation rate conditioned on the velocity fluctuations).

It was shown recently that the anomalous scaling of simultaneous correlation functions in turbulence is intimately related to the breaking of temporal scale invariance, which is equivalent to the appearance of infinitely many times scales in the time dependence of time-correlation functions. In this paper we derive a continued fraction representation of turbulent time correlation functions which is exact and in which the multiplicity of time scales is explicit. We demonstrate that this form yields precisely the same scaling laws for time derivatives and time integrals as the "multi-fractal" representation that was used before. Truncating the continued fraction representation yields the "best" estimates of time correlation functions if the given information is limited to the scaling exponents of the simultaneous correlation functions up to a certain, finite order. It is worth noting that the derivation of a continued fraction representation obtained here for a time evolution operator which is not Hermitian or anti-Hermitian may be of independent interest.