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We compute solutions of the Lagrangian-Averaged Navier-Stokes alpha-model(LANS) for significantly higher Reynolds numbers (up to Re 8300) than havepreviously been accomplished. This allows sufficient separation of scales toobserve a Navier-Stokes (NS) inertial range followed by a 2nd LANS inertialrange. The analysis of the third-order structure function scaling supports thepredicted l^3 scaling; it corresponds to a k^(-1) scaling of the energyspectrum. The energy spectrum itself shows a different scaling which goes ask^1. This latter spectrum is consistent with the absence of stretching in thesub-filter scales due to the Taylor frozen-in hypothesis employed as a closurein the derivation of LANS. These two scalings are conjectured to coexist indifferent spatial portions of the flow. The l^3 (E(k) k^(-1)) scaling issubdominant to k^1 in the energy spectrum, but the l^3 scaling is responsiblefor the direct energy cascade, as no cascade can result from motions with nointernal degrees of freedom. We verify the prediction for the size of the LANSattractor resulting from this scaling. From this, we give a methodology eitherfor arriving at grid-independent solutions for LANS, or for obtaining aformulation of a LES optimal in the context of the alpha models. The fullyconverged grid-independent LANS may not be the best approximation to a directnumerical simulation of the NS equations since the minimum error is a balancebetween truncation errors and the approximation error due to using LANS insteadof the primitive equations. Furthermore, the small-scale behavior of LANScontributes to a reduction of flux at constant energy, leading to a shallowerenergy spectrum for large alpha. These small-scale features, do not precludeLANS to reproduce correctly the intermittency properties of high Re flow.

Highly turbulent solutions of LANS-alpha and their LES potential