Nonlinear evolution of two vortex sheets moving separately in uniform shear flows with opposite direction
It has been considered that two close vortex sheets become unstable and evolve simultaneously when sufficiently strong uniform shears exist. However, Moore (Mathematika, 1976) suggested in his linear analysis that a vortex sheet evolves just as if the other vortex sheet were absent under certain con...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-03-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2022093?viewType=HTML |
| _version_ | 1828338186260054016 |
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| author | Chihiro Matsuoka |
| author_facet | Chihiro Matsuoka |
| author_sort | Chihiro Matsuoka |
| collection | DOAJ |
| description | It has been considered that two close vortex sheets become unstable and evolve simultaneously when sufficiently strong uniform shears exist. However, Moore (Mathematika, 1976) suggested in his linear analysis that a vortex sheet evolves just as if the other vortex sheet were absent under certain conditions. In the current study, we investigate how the two vortex sheets evolve in the nonlinear region when they satisfy Moore's condition. We also consider density stratification, which is not included in Moore's analysis. Moore's estimate is only valid within linear theory; however, a motion suggested by Moore appears even in the nonlinear regime when Moore's condition is satisfied. We found that there is a case that a vortex sheet hardly deforms, even though the other sheet becomes unstable and largely deforms. We also show that there is a case that Moore's analysis is not effective even the condition is satisfied when a density instability exists in the system. |
| first_indexed | 2024-04-13T22:24:20Z |
| format | Article |
| id | doaj.art-fa84056c76354e87aec9af5e39ef32e8 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-13T22:24:20Z |
| publishDate | 2022-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-fa84056c76354e87aec9af5e39ef32e82022-12-22T02:27:06ZengAIMS PressElectronic Research Archive2688-15942022-03-013051836186310.3934/era.2022093Nonlinear evolution of two vortex sheets moving separately in uniform shear flows with opposite directionChihiro Matsuoka01. Laboratory of Applied Mathemetics, Graduate School of Engineering, Osaka City University, Sugimoto, Sumiyoshi, Osaka 5588585, Japan 2. Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka City University, Sugimoto, Sumiyoshi, Osaka 5580022, Japan 3. Osaka City University Advanced Mathematical Institute (OCAMI), Sugimoto, Sumiyoshi, Osaka 5580022, JapanIt has been considered that two close vortex sheets become unstable and evolve simultaneously when sufficiently strong uniform shears exist. However, Moore (Mathematika, 1976) suggested in his linear analysis that a vortex sheet evolves just as if the other vortex sheet were absent under certain conditions. In the current study, we investigate how the two vortex sheets evolve in the nonlinear region when they satisfy Moore's condition. We also consider density stratification, which is not included in Moore's analysis. Moore's estimate is only valid within linear theory; however, a motion suggested by Moore appears even in the nonlinear regime when Moore's condition is satisfied. We found that there is a case that a vortex sheet hardly deforms, even though the other sheet becomes unstable and largely deforms. We also show that there is a case that Moore's analysis is not effective even the condition is satisfied when a density instability exists in the system.https://www.aimspress.com/article/doi/10.3934/era.2022093?viewType=HTMLtwo vortex sheetsmulti-layer flowkelvin-helmholtz instabilitydensity stratificationvortex method |
| spellingShingle | Chihiro Matsuoka Nonlinear evolution of two vortex sheets moving separately in uniform shear flows with opposite direction Electronic Research Archive two vortex sheets multi-layer flow kelvin-helmholtz instability density stratification vortex method |
| title | Nonlinear evolution of two vortex sheets moving separately in uniform shear flows with opposite direction |
| title_full | Nonlinear evolution of two vortex sheets moving separately in uniform shear flows with opposite direction |
| title_fullStr | Nonlinear evolution of two vortex sheets moving separately in uniform shear flows with opposite direction |
| title_full_unstemmed | Nonlinear evolution of two vortex sheets moving separately in uniform shear flows with opposite direction |
| title_short | Nonlinear evolution of two vortex sheets moving separately in uniform shear flows with opposite direction |
| title_sort | nonlinear evolution of two vortex sheets moving separately in uniform shear flows with opposite direction |
| topic | two vortex sheets multi-layer flow kelvin-helmholtz instability density stratification vortex method |
| url | https://www.aimspress.com/article/doi/10.3934/era.2022093?viewType=HTML |
| work_keys_str_mv | AT chihiromatsuoka nonlinearevolutionoftwovortexsheetsmovingseparatelyinuniformshearflowswithoppositedirection |