Only two Betchov homogeneity constraints exist for isotropic turbulence Article Swipe
Maurizio Carbone
,
Michael Wilczek
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1017/jfm.2022.680
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1017/jfm.2022.680
Statistically homogeneous flows obey exact kinematic relations. The Betchov homogeneity constraints (Betchov, J. Fluid Mech. , vol. 1, 1956, pp. 497–504) for the average principal invariants of the velocity gradient are among the most well-known and extensively employed homogeneity relations. These homogeneity relations have far-reaching implications for the coupled dynamics of strain and vorticity, as well as for the turbulent energy cascade. Whether the Betchov homogeneity constraints are the only possible ones or whether additional homogeneity relations exist has not been proven yet. Here we show that the Betchov homogeneity constraints are the only homogeneity constraints for incompressible and statistically isotropic velocity gradient fields. Our analysis also applies to compressible/perceived velocity gradients, and it allows the derivation of homogeneity relations involving the velocity gradient and other dynamically relevant quantities, such as the pressure Hessian and viscous stresses.
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- article
- Language
- en
- Landing Page
- https://doi.org/10.1017/jfm.2022.680
- https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B7E010E18EEE8B1B0646E28DB86A4398/S0022112022006802a.pdf/div-class-title-only-two-betchov-homogeneity-constraints-exist-for-isotropic-turbulence-div.pdf
- OA Status
- hybrid
- Cited By
- 13
- References
- 40
- Related Works
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Only two Betchov homogeneity constraints exist for isotropic turbulenceWork title
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articleOpenAlex work type
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enPrimary language
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2022Year of publication
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2022-09-20Full publication date if available
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Maurizio Carbone, Michael WilczekList of authors in order
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https://doi.org/10.1017/jfm.2022.680Publisher landing page
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https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B7E010E18EEE8B1B0646E28DB86A4398/S0022112022006802a.pdf/div-class-title-only-two-betchov-homogeneity-constraints-exist-for-isotropic-turbulence-div.pdfDirect link to full text PDF
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hybridOpen access status per OpenAlex
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https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B7E010E18EEE8B1B0646E28DB86A4398/S0022112022006802a.pdf/div-class-title-only-two-betchov-homogeneity-constraints-exist-for-isotropic-turbulence-div.pdfDirect OA link when available
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Homogeneity (statistics), Isotropy, Turbulence, Compressibility, Mechanics, Velocity gradient, Hessian matrix, Vorticity, Physics, Homogeneous, Kinematics, Mathematics, Mathematical analysis, Classical mechanics, Vortex, Statistical physics, Applied mathematics, Optics, StatisticsTop concepts (fields/topics) attached by OpenAlex
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13Total citation count in OpenAlex
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2025: 5, 2024: 2, 2023: 6Per-year citation counts (last 5 years)
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