Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes α model and their large-eddy-simulation potential (original) (raw)

We compute solutions of the Lagrangian-Averaged Navier-Stokes α−model (LANS−α) for significantly higher Reynolds numbers (up to Re ≈ 8300) than have previously been accomplished. This allows sufficient separation of scales to observe a Navier-Stokes inertial range followed by a second inertial range specific to LANS−α. Both fully helical and non-helical flows are examined, up to Reynolds numbers of ∼ 1300. The analysis of the third-order structure function scaling supports the predicted l 3 scaling; it corresponds to a k −1 scaling of the energy spectrum for scales smaller than α. The energy spectrum itself shows a different scaling which goes as k 1 . This latter spectrum is consistent with the absence of stretching in the sub-filter scales due to the Taylor frozen-in hypothesis employed as a closure in the derivation of LANS−α. These two scalings are conjectured to coexist in different spatial portions of the flow. The l 3 (E(k) ∼ k −1 ) scaling is subdominant to k 1 in the energy spectrum, but the l 3 scaling is responsible for the direct energy cascade, as no cascade can result from motions with no internal degrees of freedom. We demonstrate verification of the prediction for the size of the LANS−α attractor resulting from this scaling.