Revisiting turbulence small-scale behavior using velocity gradient triple decomposition
Turbulence small-scale behavior has been commonly investigated in literature by decomposing the velocity-gradient tensor ( A _ij ) into the symmetric strain-rate ( S _ij ) and anti-symmetric rotation-rate ( W _ij ) tensors. To develop further insight, we revisit some of the key studies using a tripl...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2020-01-01
|
| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ab8ab2 |
| _version_ | 1797750319124316160 |
|---|---|
| author | Rishita Das Sharath S Girimaji |
| author_facet | Rishita Das Sharath S Girimaji |
| author_sort | Rishita Das |
| collection | DOAJ |
| description | Turbulence small-scale behavior has been commonly investigated in literature by decomposing the velocity-gradient tensor ( A _ij ) into the symmetric strain-rate ( S _ij ) and anti-symmetric rotation-rate ( W _ij ) tensors. To develop further insight, we revisit some of the key studies using a triple decomposition of the velocity-gradient tensor. The additive triple decomposition formally segregates the contributions of normal-strain-rate ( N _ij ), pure-shear ( H _ij ) and rigid-body-rotation-rate ( R _ij ). The decomposition not only highlights the key role of shear, but it also provides a more accurate account of the influence of normal-strain and pure rotation on important small-scale features. First, the local streamline topology and geometry are described in terms of the three constituent tensors in velocity-gradient invariants’ space. Using direct numerical simulation (DNS) data sets of forced isotropic turbulence, the velocity-gradient and pressure field fluctuations are examined at different Reynolds numbers. At all Reynolds numbers, shear contributes the most and rigid-body-rotation the least toward the velocity-gradient magnitude ( A ^2 ≡ A _ij A _ij ). Especially, shear contribution is dominant in regions of high values of A ^2 (intermittency). It is shown that the high-degree of enstrophy intermittency reported in literature is due to the shear contribution toward vorticity rather than that of rigid-body-rotation. The study also provides an explanation for the non-intermittent nature of pressure-Laplacian, despite the strong intermittency of enstrophy and dissipation fields. The study further investigates the alignment of the rotation axis with normal strain-rate and pressure Hessian eigenvectors. Overall, it is demonstrated that triple decomposition offers unique and deeper understanding of velocity-gradient behavior in turbulence. |
| first_indexed | 2024-03-12T16:31:00Z |
| format | Article |
| id | doaj.art-f576c37d34364e39a03899f58c0dead8 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:31:00Z |
| publishDate | 2020-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-f576c37d34364e39a03899f58c0dead82023-08-08T15:31:23ZengIOP PublishingNew Journal of Physics1367-26302020-01-0122606301510.1088/1367-2630/ab8ab2Revisiting turbulence small-scale behavior using velocity gradient triple decompositionRishita Das0https://orcid.org/0000-0001-9785-5109Sharath S Girimaji1Aerospace Engineering, Texas A&M University , College Station, TX 77843, United States of AmericaOcean Engineering, Texas A&M University , College Station, TX 77843, United States of AmericaTurbulence small-scale behavior has been commonly investigated in literature by decomposing the velocity-gradient tensor ( A _ij ) into the symmetric strain-rate ( S _ij ) and anti-symmetric rotation-rate ( W _ij ) tensors. To develop further insight, we revisit some of the key studies using a triple decomposition of the velocity-gradient tensor. The additive triple decomposition formally segregates the contributions of normal-strain-rate ( N _ij ), pure-shear ( H _ij ) and rigid-body-rotation-rate ( R _ij ). The decomposition not only highlights the key role of shear, but it also provides a more accurate account of the influence of normal-strain and pure rotation on important small-scale features. First, the local streamline topology and geometry are described in terms of the three constituent tensors in velocity-gradient invariants’ space. Using direct numerical simulation (DNS) data sets of forced isotropic turbulence, the velocity-gradient and pressure field fluctuations are examined at different Reynolds numbers. At all Reynolds numbers, shear contributes the most and rigid-body-rotation the least toward the velocity-gradient magnitude ( A ^2 ≡ A _ij A _ij ). Especially, shear contribution is dominant in regions of high values of A ^2 (intermittency). It is shown that the high-degree of enstrophy intermittency reported in literature is due to the shear contribution toward vorticity rather than that of rigid-body-rotation. The study also provides an explanation for the non-intermittent nature of pressure-Laplacian, despite the strong intermittency of enstrophy and dissipation fields. The study further investigates the alignment of the rotation axis with normal strain-rate and pressure Hessian eigenvectors. Overall, it is demonstrated that triple decomposition offers unique and deeper understanding of velocity-gradient behavior in turbulence.https://doi.org/10.1088/1367-2630/ab8ab2turbulencevelocity gradient dynamicsintermittency |
| spellingShingle | Rishita Das Sharath S Girimaji Revisiting turbulence small-scale behavior using velocity gradient triple decomposition New Journal of Physics turbulence velocity gradient dynamics intermittency |
| title | Revisiting turbulence small-scale behavior using velocity gradient triple decomposition |
| title_full | Revisiting turbulence small-scale behavior using velocity gradient triple decomposition |
| title_fullStr | Revisiting turbulence small-scale behavior using velocity gradient triple decomposition |
| title_full_unstemmed | Revisiting turbulence small-scale behavior using velocity gradient triple decomposition |
| title_short | Revisiting turbulence small-scale behavior using velocity gradient triple decomposition |
| title_sort | revisiting turbulence small scale behavior using velocity gradient triple decomposition |
| topic | turbulence velocity gradient dynamics intermittency |
| url | https://doi.org/10.1088/1367-2630/ab8ab2 |
| work_keys_str_mv | AT rishitadas revisitingturbulencesmallscalebehaviorusingvelocitygradienttripledecomposition AT sharathsgirimaji revisitingturbulencesmallscalebehaviorusingvelocitygradienttripledecomposition |