Academic Journal
Only two Betchov homogeneity constraints exist for isotropic turbulence
| Title: | Only two Betchov homogeneity constraints exist for isotropic turbulence |
|---|---|
| Authors: | Carbone, Maurizio, Wilczek, Michael |
| Superior Title: | Journal of Fluid Mechanics ; volume 948 ; ISSN 0022-1120 1469-7645 |
| Publisher Information: | Cambridge University Press (CUP) |
| Publication Year: | 2022 |
| Subject Terms: | Mechanical Engineering, Mechanics of Materials, Condensed Matter Physics, Applied Mathematics |
| Description: | 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. |
| Document Type: | article in journal/newspaper |
| Language: | English |
| DOI: | 10.1017/jfm.2022.680 |
| Availability: | https://doi.org/10.1017/jfm.2022.680 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112022006802 |
| Rights: | https://creativecommons.org/licenses/by/4.0/ |
| Accession Number: | edsbas.76FA18B7 |
| Database: | BASE |
| Description not available. |