Non-Modal Three-Dimensional Optimal Perturbation Growth in Thermally Stratified Mixing Layers
A non-modal transient disturbances growth in a stably stratified mixing layer flow is studied numerically. The model accounts for a density gradient within a shear region, implying a heavier layer at the bottom. Numerical analysis of non-modal stability is followed by a full three-dimensional direct...
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MDPI AG
2021-01-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/6/1/37 |
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| author | Helena Vitoshkin Alexander Gelfgat |
| author_facet | Helena Vitoshkin Alexander Gelfgat |
| author_sort | Helena Vitoshkin |
| collection | DOAJ |
| description | A non-modal transient disturbances growth in a stably stratified mixing layer flow is studied numerically. The model accounts for a density gradient within a shear region, implying a heavier layer at the bottom. Numerical analysis of non-modal stability is followed by a full three-dimensional direct numerical simulation (DNS) with the optimally perturbed base flow. It is found that the transient growth of two-dimensional disturbances diminishes with the strengthening of stratification, while three-dimensional disturbances cause significant non-modal growth, even for a strong, stable stratification. This non-modal growth is governed mainly by the Holmboe modes and does not necessarily weaken with the increase of the Richardson number. The optimal perturbation consists of two waves traveling in opposite directions. Compared to the two-dimensional transient growth, the three-dimensional growth is found to be larger, taking place at shorter times. The non-modal growth is observed in linearly stable regimes and, in slightly linearly supercritical regimes, is steeper than that defined by the most unstable eigenmode. The DNS analysis confirms the presence of the structures determined by the transient growth analysis. |
| first_indexed | 2024-03-09T05:12:00Z |
| format | Article |
| id | doaj.art-739b5278e6d8437a904a76601515a01f |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-09T05:12:00Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-739b5278e6d8437a904a76601515a01f2023-12-03T12:48:25ZengMDPI AGFluids2311-55212021-01-01613710.3390/fluids6010037Non-Modal Three-Dimensional Optimal Perturbation Growth in Thermally Stratified Mixing LayersHelena Vitoshkin0Alexander Gelfgat1Agricultural Research Organization, The Volcani Center, P.O. Box 6, 68 Dereh Hamacabim, Rishon Lezion 5025001, IsraelSchool of Mechanical Engineering, Faculty of Engineering, Tel-Aviv University, Ramat Aviv, Tel-Aviv 6997801, IsraelA non-modal transient disturbances growth in a stably stratified mixing layer flow is studied numerically. The model accounts for a density gradient within a shear region, implying a heavier layer at the bottom. Numerical analysis of non-modal stability is followed by a full three-dimensional direct numerical simulation (DNS) with the optimally perturbed base flow. It is found that the transient growth of two-dimensional disturbances diminishes with the strengthening of stratification, while three-dimensional disturbances cause significant non-modal growth, even for a strong, stable stratification. This non-modal growth is governed mainly by the Holmboe modes and does not necessarily weaken with the increase of the Richardson number. The optimal perturbation consists of two waves traveling in opposite directions. Compared to the two-dimensional transient growth, the three-dimensional growth is found to be larger, taking place at shorter times. The non-modal growth is observed in linearly stable regimes and, in slightly linearly supercritical regimes, is steeper than that defined by the most unstable eigenmode. The DNS analysis confirms the presence of the structures determined by the transient growth analysis.https://www.mdpi.com/2311-5521/6/1/37stratified mixing layernon-modal instabilityKelvin-Helmholtz instabilityHolmboe instability |
| spellingShingle | Helena Vitoshkin Alexander Gelfgat Non-Modal Three-Dimensional Optimal Perturbation Growth in Thermally Stratified Mixing Layers Fluids stratified mixing layer non-modal instability Kelvin-Helmholtz instability Holmboe instability |
| title | Non-Modal Three-Dimensional Optimal Perturbation Growth in Thermally Stratified Mixing Layers |
| title_full | Non-Modal Three-Dimensional Optimal Perturbation Growth in Thermally Stratified Mixing Layers |
| title_fullStr | Non-Modal Three-Dimensional Optimal Perturbation Growth in Thermally Stratified Mixing Layers |
| title_full_unstemmed | Non-Modal Three-Dimensional Optimal Perturbation Growth in Thermally Stratified Mixing Layers |
| title_short | Non-Modal Three-Dimensional Optimal Perturbation Growth in Thermally Stratified Mixing Layers |
| title_sort | non modal three dimensional optimal perturbation growth in thermally stratified mixing layers |
| topic | stratified mixing layer non-modal instability Kelvin-Helmholtz instability Holmboe instability |
| url | https://www.mdpi.com/2311-5521/6/1/37 |
| work_keys_str_mv | AT helenavitoshkin nonmodalthreedimensionaloptimalperturbationgrowthinthermallystratifiedmixinglayers AT alexandergelfgat nonmodalthreedimensionaloptimalperturbationgrowthinthermallystratifiedmixinglayers |