Heijst, van, G.J.F.

Kamp, L.P.J.

Kizner, Z.

Makarov, V.

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Instability of a shear flow around a circular island and emission of vortex dipoles

Kizner, Z Ziv

Makarov, V

Kamp, LPJ Leon

Heijst, GJF Gert-Jan  van

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 Instability of a shear flow around a circular island andemission of vortex dipolesCitation for published version (APA):Kizner, Z., Makarov, V., Kamp, L. P. J., & Heijst, van, G. J. F. (2013). Instability of a shear flow around a circularisland and emission of vortex dipoles. In Proceedings of the General Assembly of the European GeosciencesUnion (EGU 2013), 7-12 April 2013, Vienna, Austria (pp. 11634-). (Geophysical research abstracts; Vol. 15).Copernicus.Document status and date:Published: 01/01/2013Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 17. Nov. 2023Geophysical Research AbstractsVol. 15, EGU2013-11634-1, 2013EGU General Assembly 2013© Author(s) 2013. CC Attribution 3.0 License.Instability of a shear flow around a circular island and emission of vortexdipolesZiv Kizner (1), Vyacheslav Makarov (2), Leon Kamp (3), and GertJan van Heijst (3)(1) Bar-Ilan University, Department of Physics, Ramat-Gan, Israel (zinovyk@mail.biu.ac.il), (2) National PolytechnicInstitute, Interdisciplinary Center of Marine Sciences, La Paz, Mexico, (3) Eindhoven University of Technology, FluidDynamics Laboratory, Eindhoven, The NetherlandsLaboratory experiments suggest that the instability of a circular flow with alternating vorticity around a cylinderculminates in shedding of two or three vortex dipoles. These observations lead us to the following questions: Whatare the conditions for a flow around a cylinder (island) to be stable? If the flow is unstable, how long can it survive,i.e. what are the growth rates of its unstable modes, and what vortical patterns emerge due to the instability?This topic is of oceanographic significance, since coastal waters near islands are usually rich in chemical and bi-ological material, whereas vortex dipoles are normally quite robust and can serve as carriers of the trapped material.To answer the above-posted questions we apply both analytical and numerical approaches. First we estab-lish analytically the conditions for the linear instability of a two-dimensional azimuthally symmetric flowaround a rigid circular boundary. To simplify the problem, we assume the unperturbed velocity profile tocorrespond to two concentric neighboring rings of uniform but different vorticity, with the inner ring touchingthe cylinder. As the next step, based on the analytical results, we carry out numerical simulations aiming to studythe long-term, nonlinear evolution of the linearly unstable flow and to follow the formation of new vortical patterns.At the analytical stage, we remain in the contour-dynamics framework, i.e. regard the fluid to be inviscidand consider the perturbations that affect the free edges of the two rings only. At the numerical stage, we runcontour-dynamics simulations, which are made feasible by using the Green function for the Laplace operatoron a plane with a circular cut-out, and high Reynolds number simulations. In the latter case, a finite-elementNavier–Stokes module of COMSOL software is used.Fixing the ratio of the vorticity in the two rings, assuming the scaled cylinder radius to be 1, and denotingthe outer radii of the inner and outer vorticity rings a and b, we determine analytically the regions on the (a,b)-plane, where azimuthal modes m = 2, 3, . . . are unstable, and calculate the growth rates of these modes asfunctions of a and b. For each mode m > 2, apart from the region where this mode and all the lower modes areunstable (we call it the regular instability region), a closed finite-size region is found, in which only mode m isunstable (the unique instability region). In the latter case, the inner ring is much thinner than the outer one. Forthe ordinary instability regions, the two numerical techniques yield qualitatively the same result, the emergence ofm dipoles. However, for the unique instability regions, no dipole emergence is observed in the contour-dynamicssimulations.This approach is extended to the two-layer quasigeostrophic model, where one vorticity ring is located inthe upper layer, and the other ring, in the lower layer. Here, as in the barotropic case, both analytical and numericalmethods are exploited.

Instability of a shear flow around a circular island and emission of vortex dipoles

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