{"title":"Synchronization of Traveling Waves within a Hollow-Core Vortex","authors":"H. Ait Abderrahmane, M. Fayed, H. D. Ng, G. H. Vatistas","volume":124,"journal":"International Journal of Mechanical and Mechatronics Engineering","pagesStart":742,"pagesEnd":747,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10006754","abstract":"
The present paper expands details and confirms the transition mechanism between two subsequent polygonal patterns of the hollow-core vortex. Using power spectral analysis, we confirm in this work that the transition from any N-<\/em>gon to (N+1)-<\/em>gon pattern observed within a hollow-core vortex of shallow rotating flows occurs in two steps. The regime was quasi-periodic before the frequencies lock (synchronization). The ratios of locking frequencies were found to be equal to (N-1)\/N<\/em>.<\/p>\r\n","references":"[1]\tH. Ait Abderrahmane, K. Siddiqui, and G. H. Vatistas, \u201cTransition between Kelvin\u2019s equilibria,\u201d Phys. Rev. E, 2009, no.80, 066305. \r\n[2]\tP. Berg\u00e9, Y. Pomeau, and C. Vidal, \u201cOrder Within Chaos,\u201d Hermann, Paris, 1984.\r\n[3]\tJ. M. Chomaz, M. Rabaud, C. Basdevant, and Y. Couder, \u201cExperimental and numerical investigation of a forced circular shear layer,\u201d J. Fluid Mech., 1988, 187, pp. 115-140.\r\n[4]\tR. Hide, and C. W. Titman, \u201cDetached shear layers in a rotating fluid.\u201d J. Fluid Mech., 1967, vol. 29, pp. 39-60.\r\n[5]\tT. R. N. Jansson, M. P Haspang, K. H. Jensen, P. Hersen, and T. Bohr, \u201cPolygons on a rotating fluid surface,\u201d Phys. Rev. Lett., 2006, no. 96. \r\n[6]\tH. Niino, and N. Misawa, \u201cAn experimental and theoretical study of barotropic instability.\u201d J. Atmos. Sci. 1984, vol. 41, pp. 1992-2011.\r\n[7]\tS. Poncet and M. P Chauve, \u201cShear-layer instability in a rotating system,\u201d J. Flow Visualization and Image Processing, 2007, no. 14 (1), pp. 85-105.\r\n[8]\tM. Rabaud, and Y. Couder, \u201cInstability of an annular shear layer,\u201d J. Fluid Mech., 1983, vol. 136, pp. 291\u2013319. \r\n[9]\tG. H. Vatistas, H. Ait Abderrahmane, and K. Siddiqui, \u201cAn experimental confirmation of Kelvin\u2019s equilibria,\u201d Phys. Rev. Lett., 2008, no. 100, 17450.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 124, 2017"}