dorsal/arxiv
View SchemaAnisotropy, inhomogeneity and inertial range scalings in turbulent convection
| Authors | Francois Rincon |
|---|---|
| Categories | |
| ArXiv ID | physics/0601198 |
| URL | https://arxiv.org/abs/physics/0601198 |
| DOI | 10.1017/S0022112006000917 |
Abstract
This paper provides a detailed study of scale-by-scale budgets in turbulent Rayleigh-B\'enard convection and aims at testing the applicability of Kolmogorov (1941) and Bolgiano (1959) theories for this flow. Particular emphasis is laid on anisotropic and inhomogeneous effects: the SO(3) decomposition of structure functions (Arad et al 1999) and a method of description of inhomogeneities proposed by Danaila et al (2001) are used to derive inhomogeneous and anisotropic generalizations of Kolmogorov and Yaglom equations applying to RB convection. The various terms in these equations are computed using data from a DNS of turbulent Boussinesq convection at $\rayleigh=10^6$ and $\prandtl=1$ with aspect ratio A=5. The analysis of the isotropic component demonstrates that the shape of the third-order velocity structure function is significantly influenced by buoyancy forcing and large-scale inhomogeneities, while the mixed third-order structure function appearing in Yaglom equation exhibits a clear scaling exponent 1 in a small range of scales. The magnitudes of the various low $\ell$ degree anisotropic components of the equations are also estimated and are shown to be comparable to their isotropic counterparts at moderate to large scales. Finally, a qualitative analysis shows that the influence of buoyancy forcing at scales smaller than the Bolgiano scale is likely to remain important up to $\rayleigh=10^9$, thus preventing Kolmogorov scalings from showing up in convective flows at lower Rayleigh numbers.
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"abstract": "This paper provides a detailed study of scale-by-scale budgets in turbulent\nRayleigh-B\\\u0027enard convection and aims at testing the applicability of\nKolmogorov (1941) and Bolgiano (1959) theories for this flow. Particular\nemphasis is laid on anisotropic and inhomogeneous effects: the SO(3)\ndecomposition of structure functions (Arad et al 1999) and a method of\ndescription of inhomogeneities proposed by Danaila et al (2001) are used to\nderive inhomogeneous and anisotropic generalizations of Kolmogorov and Yaglom\nequations applying to RB convection. The various terms in these equations are\ncomputed using data from a DNS of turbulent Boussinesq convection at\n$\\rayleigh=10^6$ and $\\prandtl=1$ with aspect ratio A=5. The analysis of the\nisotropic component demonstrates that the shape of the third-order velocity\nstructure function is significantly influenced by buoyancy forcing and\nlarge-scale inhomogeneities, while the mixed third-order structure function\nappearing in Yaglom equation exhibits a clear scaling exponent 1 in a small\nrange of scales. The magnitudes of the various low $\\ell$ degree anisotropic\ncomponents of the equations are also estimated and are shown to be comparable\nto their isotropic counterparts at moderate to large scales. Finally, a\nqualitative analysis shows that the influence of buoyancy forcing at scales\nsmaller than the Bolgiano scale is likely to remain important up to\n$\\rayleigh=10^9$, thus preventing Kolmogorov scalings from showing up in\nconvective flows at lower Rayleigh numbers.",
"arxiv_id": "physics/0601198",
"authors": [
"Francois Rincon"
],
"categories": [
"physics.flu-dyn",
"astro-ph"
],
"doi": "10.1017/S0022112006000917",
"title": "Anisotropy, inhomogeneity and inertial range scalings in turbulent convection",
"url": "https://arxiv.org/abs/physics/0601198"
},
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