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

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...

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Autor principal: Mininni, Pablo Daniel
Publicado: 2007
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Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v76_n5_p_Graham
http://hdl.handle.net/20.500.12110/paper_15393755_v76_n5_p_Graham
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spelling paper:paper_15393755_v76_n5_p_Graham2023-06-08T16:20:34Z Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes α model and their large-eddy-simulation potential Mininni, Pablo Daniel Error analysis Large eddy simulation Reynolds number Spectrum analysis Taylor series Turbulence Energy spectrum Nonhelical flows Truncation errors Turbulent solutions Navier Stokes equations 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. Fil:Mininni, P.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2007 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v76_n5_p_Graham http://hdl.handle.net/20.500.12110/paper_15393755_v76_n5_p_Graham
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Error analysis
Large eddy simulation
Reynolds number
Spectrum analysis
Taylor series
Turbulence
Energy spectrum
Nonhelical flows
Truncation errors
Turbulent solutions
Navier Stokes equations
spellingShingle Error analysis
Large eddy simulation
Reynolds number
Spectrum analysis
Taylor series
Turbulence
Energy spectrum
Nonhelical flows
Truncation errors
Turbulent solutions
Navier Stokes equations
Mininni, Pablo Daniel
Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes α model and their large-eddy-simulation potential
topic_facet Error analysis
Large eddy simulation
Reynolds number
Spectrum analysis
Taylor series
Turbulence
Energy spectrum
Nonhelical flows
Truncation errors
Turbulent solutions
Navier Stokes equations
description 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.
author Mininni, Pablo Daniel
author_facet Mininni, Pablo Daniel
author_sort Mininni, Pablo Daniel
title Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes α model and their large-eddy-simulation potential
title_short Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes α model and their large-eddy-simulation potential
title_full Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes α model and their large-eddy-simulation potential
title_fullStr Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes α model and their large-eddy-simulation potential
title_full_unstemmed Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes α model and their large-eddy-simulation potential
title_sort highly turbulent solutions of the lagrangian-averaged navier-stokes α model and their large-eddy-simulation potential
publishDate 2007
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v76_n5_p_Graham
http://hdl.handle.net/20.500.12110/paper_15393755_v76_n5_p_Graham
work_keys_str_mv AT mininnipablodaniel highlyturbulentsolutionsofthelagrangianaveragednavierstokesamodelandtheirlargeeddysimulationpotential
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