Dynamics and invariants of the perceived velocity gradient tensor in homogeneous and isotropic turbulence
| Autor: | Alain Pumir, Haitao Xu, Ping-Fan Yang |
|---|---|
| Přispěvatelé: | Tsinghua University [Beijing] (THU), Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), ANR-16-IDEX-0005,IDEXLYON,IDEXLYON(2016), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
Turbulence Mechanical Engineering Mathematical analysis Isotropy Function (mathematics) Vorticity Condensed Matter Physics Enstrophy 01 natural sciences 010305 fluids & plasmas Physics::Fluid Dynamics Correlation function (statistical mechanics) Mechanics of Materials Vortex stretching 0103 physical sciences Dissipative system [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] 010306 general physics ComputingMilieux_MISCELLANEOUS |
| Zdroj: | Journal of Fluid Mechanics Journal of Fluid Mechanics, 2020, 897, ⟨10.1017/jfm.2020.375⟩ Journal of Fluid Mechanics, Cambridge University Press (CUP), 2020, 897, ⟨10.1017/jfm.2020.375⟩ |
| ISSN: | 0022-1120 1469-7645 |
| DOI: | 10.1017/jfm.2020.375⟩ |
| Popis: | The perceived velocity gradient tensor (PVGT), constructed from four fluid tracers forming a tetrahedron, provides a natural way to study the structure of velocity fluctuations and its dependence on spatial scales. It generalizes and shares qualitatively many properties with the true velocity gradient tensor. Here, we establish the evolution equation for the PVGT, and, for homogeneous and isotropic incompressible turbulent flows, we analyse the dynamics of the PVGT in particular using its second- and third-order invariants. We show that, for PVGT based on regular tetrads with lateral size R₀, the second-order invariants can be expressed solely in terms of the usual second-order velocity structure functions, while the third-order invariants involve the usual third-order longitudinal velocity structure function and a less well known three-point velocity correlation function. For homogeneous and isotropic turbulence, exact relations between the second moments of strain and vorticity, as well as enstrophy production and the third moments of the strain, are derived. These generalized relations are valid for all ranges of R₀, and reduce to classical results for the velocity gradient tensor when R-0 is in the dissipative range. With the help of these relations, we quantify the importance of the various terms, such as vortex stretching, as a function of the scale R₀. Our analysis, which is supported by the results of direct numerical simulations of turbulent flows in the Reynolds-number range 100 ⩽ R(ג) ⩽ 610, allows us to demonstrate that strain prevails over vorticity when R₀ is in the inertial range. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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