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Abstract:

We compute solutions of the Lagrangian-averaged Navier-Stokes α - (LANS α) model 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 the LANS α model. Both fully helical and nonhelical flows are examined, up to Reynolds numbers of ∼1300. Analysis of the third-order structure function scaling supports the predicted l3 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 k1. This latter spectrum is consistent with the absence of stretching in the subfilter scales due to the Taylor frozen-in hypothesis employed as a closure in the derivation of the LANS α model. These two scalings are conjectured to coexist in different spatial portions of the flow. The l3 [E(k)∼ k-1] scaling is subdominant to k1 in the energy spectrum, but the l3 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. From this, we give a methodology either for arriving at grid-independent solutions for the LANS α model, or for obtaining a formulation of the large eddy simulation optimal in the context of the α models. The fully converged grid-independent LANS α model may not be the best approximation to a direct numerical simulation of the Navier-Stokes equations, since the minimum error is a balance between truncation errors and the approximation error due to using the LANS α instead of the primitive equations. Furthermore, the small-scale behavior of the LANS α model contributes to a reduction of flux at constant energy, leading to a shallower energy spectrum for large α. These small-scale features, however, do not preclude the LANS α model from reproducing correctly the intermittency properties of the high-Reynolds-number flow. © 2007 The American Physical Society.

Registro:

Documento: Artículo
Título:Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes α model and their large-eddy-simulation potential
Autor:Graham, J.P.; Holm, D.D.; Mininni, P.D.; Pouquet, A.
Filiación:National Center for Atmospheric Research, P. O. Box 3000, Boulder, CO 80307, United States
Max-Planck-Institut für Sonnensystemforschung, 37191 Katlenburg-Lindau, Germany
Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
Computer and Computational Science Division, Los Alamos National Laboratory, Los Alamos, NM 87545, United States
Departamento de Física, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Palabras clave:Error analysis; Large eddy simulation; Reynolds number; Spectrum analysis; Taylor series; Turbulence; Energy spectrum; Nonhelical flows; Truncation errors; Turbulent solutions; Navier Stokes equations
Año:2007
Volumen:76
Número:5
DOI: http://dx.doi.org/10.1103/PhysRevE.76.056310
Título revista:Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Título revista abreviado:Phys. Rev. E Stat. Nonlinear Soft Matter Phys.
ISSN:15393755
CODEN:PLEEE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v76_n5_p_Graham

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Citas:

---------- APA ----------
Graham, J.P., Holm, D.D., Mininni, P.D. & Pouquet, A. (2007) . Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes α model and their large-eddy-simulation potential. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 76(5).
http://dx.doi.org/10.1103/PhysRevE.76.056310
---------- CHICAGO ----------
Graham, J.P., Holm, D.D., Mininni, P.D., Pouquet, A. "Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes α model and their large-eddy-simulation potential" . Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 76, no. 5 (2007).
http://dx.doi.org/10.1103/PhysRevE.76.056310
---------- MLA ----------
Graham, J.P., Holm, D.D., Mininni, P.D., Pouquet, A. "Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes α model and their large-eddy-simulation potential" . Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 76, no. 5, 2007.
http://dx.doi.org/10.1103/PhysRevE.76.056310
---------- VANCOUVER ----------
Graham, J.P., Holm, D.D., Mininni, P.D., Pouquet, A. Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes α model and their large-eddy-simulation potential. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 2007;76(5).
http://dx.doi.org/10.1103/PhysRevE.76.056310