The effect of fine structure on the stability of planar vortices |
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| Institution: | 1. Department of Otolaryngology, Head and Neck Surgery, Ehime University Graduate School of Medicine, Shitsukawa, Toon, Ehime, Japan;2. Departments of Geriatric Medicine and Neurology, Ehime University Graduate School of Medicine, Shitsukawa, Toon, Ehime, Japan;3. Department of Otolaryngology, Takanoko Hospital, 525-1 Takanoko, Matsuyama, Ehime, Japan;1. University of the Basque Country UPV/EHU, 48080 Bilbao, Spain;2. Beihang University, Beijing 100191, PR China;3. University of Bonn, 53115 Bonn, Germany;4. Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russian Federation;5. Faculty of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic;6. Chiba University, Chiba 263-8522, Japan;7. University of Cincinnati, Cincinnati, OH 45221, USA;8. Deutsches Elektronen–Synchrotron, 22607 Hamburg, Germany;9. Justus-Liebig-Universität Gießen, 35392 Gießen, Germany;10. Gifu University, Gifu 501-1193, Japan;11. SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193, Japan;12. Hanyang University, Seoul 133-791, South Korea;13. University of Hawaii, Honolulu, HI 96822, USA;14. High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan;15. IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Spain;p. Indian Institute of Technology Bhubaneswar, Satya Nagar 751007, India;q. Indian Institute of Technology Madras, Chennai 600036, India;r. Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, PR China;s. Institute for High Energy Physics, Protvino 142281, Russian Federation;t. Institute of High Energy Physics, Vienna 1050, Austria;u. INFN – Sezione di Torino, 10125 Torino, Italy;v. Institute for Theoretical and Experimental Physics, Moscow 117218, Russian Federation;w. J. Stefan Institute, 1000 Ljubljana, Slovenia;x. Kanagawa University, Yokohama 221-8686, Japan;y. Institut für Experimentelle Kernphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany;z. Kennesaw State University, Kennesaw GA 30144, USA;11. King Abdulaziz City for Science and Technology, Riyadh 11442, Saudi Arabia;12. Korea Institute of Science and Technology Information, Daejeon 305-806, South Korea;13. Korea University, Seoul 136-713, South Korea;14. Kyungpook National University, Daegu 702-701, South Korea;15. École Polytechnique Fédérale de Lausanne (EPFL), Lausanne 1015, Switzerland;16. Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia;17. Luther College, Decorah, IA 52101, USA;18. University of Maribor, 2000 Maribor, Slovenia;19. Max-Planck-Institut für Physik, 80805 München, Germany;110. School of Physics, University of Melbourne, Victoria 3010, Australia;111. Moscow Physical Engineering Institute, Moscow 115409, Russian Federation;112. Moscow Institute of Physics and Technology, Moscow Region 141700, Russian Federation;113. Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan;114. Kobayashi–Maskawa Institute, Nagoya University, Nagoya 464-8602, Japan;115. Nara Women''s University, Nara 630-8506, Japan;1p. National Central University, Chung-li 32054, Taiwan;1q. National United University, Miao Li 36003, Taiwan;1r. Department of Physics, National Taiwan University, Taipei 10617, Taiwan;1s. H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342, Poland;1t. Niigata University, Niigata 950-2181, Japan;1u. University of Nova Gorica, 5000 Nova Gorica, Slovenia;1v. Novosibirsk State University, Novosibirsk 630090, Russian Federation;1w. Osaka City University, Osaka 558-8585, Japan;1x. Pacific Northwest National Laboratory, Richland, WA 99352, USA;1y. Peking University, Beijing 100871, PR China;1z. University of Pittsburgh, Pittsburgh, PA 15260, USA;21. University of Science and Technology of China, Hefei 230026, PR China;22. Soongsil University, Seoul 156-743, South Korea;23. Sungkyunkwan University, Suwon 440-746, South Korea;24. School of Physics, University of Sydney, NSW 2006, Australia;25. Department of Physics, Faculty of Science, University of Tabuk, Tabuk 71451, Saudi Arabia;26. Tata Institute of Fundamental Research, Mumbai 400005, India;27. Excellence Cluster Universe, Technische Universität München, 85748 Garching, Germany;28. Toho University, Funabashi 274-8510, Japan;29. Tohoku University, Sendai 980-8578, Japan;210. Earthquake Research Institute, University of Tokyo, Tokyo 113-0032, Japan;211. Department of Physics, University of Tokyo, Tokyo 113-0033, Japan;212. Tokyo Institute of Technology, Tokyo 152-8550, Japan;213. Tokyo Metropolitan University, Tokyo 192-0397, Japan;214. University of Torino, 10124 Torino, Italy;215. CNP, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA;2p. Wayne State University, Detroit, MI 48202, USA;2q. Yamagata University, Yamagata 990-8560, Japan;2r. Yonsei University, Seoul 120-749, South Korea;1. KTH Royal Institute of Technology, Aeronautical and Vehicle Engineering, Teknikringen 8, SE-10044, Stockholm, Sweden;2. Siemens Industry Software, Interleuvenlaan 68, B-3001, Leuven, Belgium;3. Eindhoven University of Technology, Department of Mechanical Engineering, 5600 MB, Eindhoven, the Netherlands |
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| Abstract: | This study considers the linear, inviscid response to an external strain field of classes of planar vortices. The case of a Gaussian vortex has been considered elsewhere, and an enstrophy rebound phenomenon was noted: after the vortex is disturbed enstrophy feeds from the non-axisymmetric to mean flow. At the same time an irreversible spiral wind-up of vorticity fluctuations takes place. A top-hat or Rankine vortex, on the other hand, can support a non-decaying normal mode.In vortex dynamics processes such as stripping and collisions generate vortices with sharp edges and often with bands or rings of fine scale vorticity at their periphery, rather than smooth profiles. This paper considers the stability and response of a family of vortices that vary from a broad profile to a top-hat vortex. As the edge of the vortex becomes sharper, a quasi-mode emerges and vorticity winds up in a critical layer, at the radius where the angular velocity of the fluid matches that of a normal mode on a top-hat vortex. The decay rate of these quasi-modes is proportional to the vorticity gradient at the critical layer, in agreement with theory. As the vortex edge becomes sharper it is found that the rebound of enstrophy becomes stronger but slower.The stability and linear behaviour of coherent vortices is then studied for distributions which exhibit additional fine structure within the critical layer. In particular we consider vorticity profiles with ‘bumps’, ‘troughs’ or ‘steps’ as this fine structure. The modified evolution equation that governs the critical layer is studied using numerical simulations and asymptotic analysis. It is shown that depending on the form of the short-scale vorticity distribution, this can stabilise or destabilise quasi-modes, and it may also lead to oscillatory behaviour. |
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