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We present a numerical study of the statistical properties ofthree-dimensional dissipative turbulent flows at scales larger than the forcingscale. Our results indicate that the large scale flow can be described to alarge degree by the truncated Euler equations with the predictions of the zeroflux solutions given by absolute equilibrium theory, both for helical andnon-helical flows. Thus, the functional shape of the large scale spectra can bepredicted provided that scales sufficiently larger than the forcing lengthscale but also sufficiently smaller than the box size are examined. Deviationsfrom the predictions of absolute equilibrium are discussed.

Statistical equilibria of large scales in dissipative hydrodynamic turbulence