Estimating the size of the regular region of a topographically trapped vortex

References

• Aref , H . 1979 . Motion of three vortices . Phys. Fluids , 22 : 393 – 405 .
   Web of Science ®Google Scholar
• Aref , H . 1984 . Stirring by chaotic advection . J. Fluid Mech. , 143 : 1 – 21 .
   Web of Science ®Google Scholar
• Aref , H . 1990 . Chaotic advection of fluid particles . Philos. Trans. R. Soc. London , 333 : 273 – 288 .
   Google Scholar
• Aref , H and El Naschie , MS . 1994 . Chaos Applied to Fluid Mixing , London : Pergamon .
   Google Scholar
• Baines , PG . 1993 . Topographic Effects in Stratified Flows , Cambridge : Cambridge University Press .
   Google Scholar
• Brown , MG and Samelson , RM . 1994 . Particle motion in vorticity-conserving, two-dimensional incompressible flows . Phys. Fluids , 6 : 2875 – 2876 .
   Web of Science ®Google Scholar
• Chirikov , BV . 1979 . A universal instability of many-dimensional oscillator systems . Phys. Rep. , 52 : 263 – 379 .
   Web of Science ®Google Scholar
• del-Castillo-Negrete , D and Morrison , PJ . 1993 . Chaotic transport by Rossby waves in shear-flow . Phys. Fluids A-Fluid Dyn. , 5 : 948 – 965 .
   Web of Science ®Google Scholar
• Dritschel , DG . 1988 . Contour surgery: a topological reconnection scheme for extended integrations using contour dynamics . J. Comput. Phys. , 77 : 240 – 266 .
   Web of Science ®Google Scholar
• Gledzer , AE . 1999 . Passive pollutant entrainment and release by ocean eddy structures . Izv. Atmos. Oceanic Phys. , 35 : 838 – 845 .
   Google Scholar
• Gryanik , VM and Tevs , MV . 1989 . Dynamics of singular geostrophic vortices in a N-level model of the atmosphere (ocean) . Izv. Atmos. Oceanic Phys. , 25 : 179 – 188 .
   Google Scholar
• Izrailsky , YuG , Kozlov , VF and Koshel , KV . 2004 . Some specific features of chaotization of the pulsating barotropic flow over elliptic and axisymmetric sea-mounts . Phys. Fluids , 2016 : 3173 – 3190 .
   Google Scholar
• Izrailsky , YuG , Koshel , KV and Stepanov , DV . 2008 . Determination of optimal excitation frequency range in background flows . CHAOS , 18 : 1 – 9 .
   Web of Science ®Google Scholar
• Johnson , ER and McDonald , NR . 2004 . The motion of a vortex near two circular cylinders . Proc. R. Soc. Lond. A , 460 : 939 – 954 .
   Web of Science ®Google Scholar
• Johnson , ER and Mcdonald , NR . 2005 . The point island approximation in vortex dynamics . Geophys. Astrophys. Fluid Dyn. , 99 : 49 – 60 .
   Web of Science ®Google Scholar
• Koshel , KV and Prants , SV . 2006 . Chaotic advection in the ocean . PHYS-USP. , 49 : 1151 – 1178 .
   Web of Science ®Google Scholar
• Koshel , KV , Sokolovskiy , MA and Davies , PA . 2008 . Chaotic advection and resonances in an oceanic flow above submerged seamount . Fluid Dyn. Res. , 40 : 695 – 736 .
   Web of Science ®Google Scholar
• Kozlov , VF . 1983a . Models of Topographic Eddies in Ocean , Moscow : Nauka .
   Google Scholar
• Kozlov , VF . 1983b . The method of contour dynamics in model problems of the ocean topographic cyclogenesis . Izv. Atmos. Oceanic Phys. , 19 : 635 – 640 .
   Google Scholar
• Kozlov , VF . 1995 . Background currents in geophysical hydrodynamics . Izv. Atmos. Oceanic Phys. , 31 : 245 – 250 .
   Google Scholar
• Kozlov , VF , Koshel , KV and Stepanov , DV . 2005 . Influence of the boundary on chaotic advection in the simplest model of a topographic vortex . Izv. Atmos. Oceanic Phys. , 41 : 217 – 227 .
   Web of Science ®Google Scholar
• Kuznetsov , L and Zaslavsky , GM . 1998 . Regular and chaotic advection in the flow field of a three-vortex system . Phys. Rev. E , 58 : 7330 – 7349 .
   Web of Science ®Google Scholar
• Kuznetsov , L and Zaslavsky , GM . 2000 . Passive particle transport in three vortex flow . Phys. Rev. E. , 61 : 3777 – 3792 .
   Web of Science ®Google Scholar
• Lamb , H . 1945 . Hydrodynamics, , 6th , New York : Dover Publications .
   Google Scholar
• Leoncini , X , Kuznetsov , L and Zaslavsky , GM . 2000 . Motion of three vortices near collapse . Phys. Fluids , 12 : 1911 – 1927 .
   Web of Science ®Google Scholar
• Lichtenberg , A and Lieberman , M . 1983 . Regular and Stochastic Motion , New York : Springer .
   Google Scholar
• Makarov , VG and Bulgakov , SN . 2008 . Regimes of near-wall vortex dynamics in potential flow through gaps . Phys. Fluids , 20 : 086605
   Web of Science ®Google Scholar
• Meleshko , VV and van Heijst , GJF . 1994 . Interacting 2-dimensional vortex structures – point vortices, contour kinematics and stirring properties . Chaos Solitons Fractals , 4 : 977 – 1010 .
   Web of Science ®Google Scholar
• Noack , BR , Mezic , I , Tadmor , G and Banaszuk , A . 2004 . Optimal mixing in recirculation zones . Phys. Fluids , 16 : 867 – 888 .
   Web of Science ®Google Scholar
• Pedlosky , J . 1987 . Geophysical Fluid Dynamics, , 2 , New York : Springer .
   Google Scholar
• Pierrehumbert , RT . 1991 . Chaotic mixing of tracer and vorticity by modulated travelling Rossby waves . J. Geophys. Astrophys. Fluid Dyn. , 58 : 285 – 319 .
   Web of Science ®Google Scholar
• Pierrehumbert , RT and Yang , H . 1992 . Global chaotic mixing on isentropic surfaces . J. Atmospheric Sci. , 50 : 2462 – 2480 .
   Web of Science ®Google Scholar
• Polvani , LM . 1991 . Two-layer geostrophic vortex dynamics. Part 2. Alignment and two-layer V-states . J. Fluid Mech. , 225 : 241 – 270 .
   Web of Science ®Google Scholar
• Provenzale , A . 1999 . Transport by coherent barotropic vortices . Annu. Rev. Fluid Mech. , 31 : 55 – 93 .
   Web of Science ®Google Scholar
• Rhines , PB and Young , WR . 1982 . Homogenization of Potential Vorticity in Planetary Gyres . J. Fluid Mech. , 122 : 347 – 367 .
   Web of Science ®Google Scholar
• Rom-Kedar , V , Leonard , A and Wiggins , A . 1990 . An analytical study of transport, mixing and chaos in unsteady vortical flow . J. Fluid Mech. , 214 : 347 – 394 .
   Web of Science ®Google Scholar
• Rom-Kedar , V and Poje , AC . 1999 . Universal properties of chaotic transport in the presence of diffusion . Phys. Fluids , 11 : 2044 – 2057 .
   Web of Science ®Google Scholar
• Ryzhov , EA , Koshel , KV and Stepanov , DV . 2010 . Background current concept and chaotic advection in an oceanic vortex flow . Theor. Comput. Fluid Dyn. , 24 : 59 – 64 .
   Web of Science ®Google Scholar
• Shevchenko , II . 2008 . The width of a chaotic layer . Phys. Lett. A , 372 : 808 – 816 .
   Web of Science ®Google Scholar
• Sokolovskiy , MA and Verron , J . 2000 . Finite-core hetons: Stability and interactions . J. Fluid Mech. , 423 : 127 – 154 .
   Web of Science ®Google Scholar
• Sokolovskiy , MA , Zyryanov , VN and Davies , PA . 1998 . On the influence of an isolated submerged obstacle on a barotropic tidal flow . Geophys. Astrophys. Fluid Dyn. , 88 : 1 – 30 .
   Web of Science ®Google Scholar
• Stoer , J and Bulirsch , R . 1993 . Introduction to Numerical Analysis , New York : Springer-Verlag .
   Google Scholar
• Verron , J . 1986 . Topographic eddies in temporally varying oceanic flows . Geophys. Astrophys. Fluid Dyn. , 35 : 257 – 276 .
   Web of Science ®Google Scholar
• Vosbeek , PWC , van Geffen , JHGM , Meleshko , VV and van Heijst , GJF . 1997 . Collapse interactions of finite-sized two-dimensional vortices . Phys. Fluids , 9 : 3315 – 3322 .
   Web of Science ®Google Scholar
• Wiggins , S . 2005 . The dynamical systems approach to Lagrangian transport in oceanic flows . Annu. Rev. Fluid Mech. , 37 : 295 – 328 .
   Web of Science ®Google Scholar
• Zabusky , NJ , Hughesand , M and Roberts , KV . 1979 . Contour dynamics for the Euler equations in two dimensions . J. Comput. Phys. , 30 : 96 – 106 .
   Web of Science ®Google Scholar
• Zaslavsky , GM . 2007 . Physics of Chaos in Hamiltonian Systems , London : Imperial College Press .
   Google Scholar
• Zyryanov , VN . 1995 . Topographic eddies in sea currents dynamics , Moscow : IPM RAN .
   Google Scholar