Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows

Physica D: Nonlinear Phenomena - Tập 212 - Trang 271-304 - 2005
Shawn C. Shadden1, Francois Lekien2, Jerrold E. Marsden1
1Control and Dynamical Systems, California Institute of Technology, United States
2Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, United States

Tài liệu tham khảo

Barreira, 2002, Lyapunov Exponents and Smooth Ergodic Theory, vol. 23 Coppel, 1978, Dichotomies in Stability Theory, vol. 629 Cottet, 2000 Coulliette, 2000, Intergyre transport in a wind-driven, quasigeostrophic double gyre: An application of lobe dynamics, Nonlinear Process. Geophys., 7, 59, 10.5194/npg-7-59-2000 Doerner, 1999, Stable manifolds and predictability of dynamical systems, Chaos Solitons Fractals, 10, 1759 Eldredge, 2002, A vortex particle method for two-dimensional compressible flow, J. Comput. Phys., 179, 371, 10.1006/jcph.2002.7060 J.D. Eldredge, Efficient tools for the simulation of flapping wing flows, AIAA Paper 2005–0085 Guckenheimer, 1983, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, vol. 42 Haller, 2000, Finite-time transport in aperiodic flows, Physica D, 119, 352, 10.1016/S0167-2789(98)00091-8 Haller, 2000, Lagrangian coherent structures and mixing in two-dimensional turbulence, Chaos, 10, 99, 10.1063/1.166479 Haller, 2000, Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D, 147, 352, 10.1016/S0167-2789(00)00142-1 Haller, 2001, Distinguished material surfaces and coherent structures in 3d fluid flows, Physica D, 149, 248, 10.1016/S0167-2789(00)00199-8 Haller, 2001, Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence, Phys. Fluids A, 13, 3368 Haller, 2002, Lagrangian coherent structures from approximate velocity data, Phys. Fluids A, 14, 1851, 10.1063/1.1477449 Haller, 2004, Exact theory of unsteady separation for two-dimensional flows, J. Fluid Mech., 512, 257, 10.1017/S0022112004009929 Hartman, 1973 T. Inanc, S.C. Shadden, J.E. Marsden, Optimal trajectory generation in ocean flows, in: Proc. of 24th American Control Conference, Portland, USA, June 2005 Jones, 2002, Invariant manifolds and Lagrangian dynamics in the ocean and atmosphere, 55, 10.1016/S1874-575X(02)80023-6 Joseph, 2002, Relation between kinematic boundaries, stirring, and barriers for the Antarctic polar vortex, J. Atmospheric Sci., 59, 1198, 10.1175/1520-0469(2002)059<1198:RBKBSA>2.0.CO;2 Koh, 2002, Hyperbolic lines and the stratospheric polar vortex, Chaos, 12, 382, 10.1063/1.1480442 F. Lekien, N. Leonard, Dynamically consistent Lagrangian coherent structures, in: American Institute of Physics: 8th Experimental Chaos Conference, vol. 742, 2004, pp. 132–139 Lekien, 2005, Tricubic interpolation in three dimensions, Internat. J. Numer. Methods Engrg., 63, 455, 10.1002/nme.1296 Lekien, 2005, Pollution release tied to invariant manifolds: A case study for the coast of Florida, Physica D, 210, 1, 10.1016/j.physd.2005.06.023 F. Lekien, C. Coulliette, G. Haller, J. Paduan, J.E. Marsden, Optimal pollution release in Monterey Bay based on nonlinear analysis of coastal radar data, Environ. Sci. Technol. 2005 (under review) Liapunov, 1966 Malhotra, 1998, Patchiness: A new diagnostic for Lagrangian trajectory analysis in time-dependent fluid flows, Internat. J. Bifur. Chaos, 8, 1073, 10.1142/S0218127498000875 Mancho, 2003, Computation of stable and unstable manifold of hyperbolic trajectories in two-dimensional, aperiodically time-dependent vector fields, Physica D, 182, 188, 10.1016/S0167-2789(03)00152-0 Marsden, 1993 Mezic, 1999, A method for visualization of invariant sets of dynamical systems based on the ergodic partition, Chaos, 9, 213, 10.1063/1.166399 O’Neill, 1997 Oseledec, 1968, A multiplicative ergodic theorem: Ljapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc., 19, 197 Ottino, 1989 Peters, 2002, Current variability on a narrow shelf with large ambient vorticity, J. Geophys. Res.-Oceans, 107, 10.1029/2001JC000813 Pierrehumbert, 1991, Large-scale horizontal mixing in planetary atmospheres, Phys. Fluids A, 3, 1250, 10.1063/1.858053 Pierrehumbert, 1993, Global chaotic mixing on isentropic surfaces, J. Atmospheric Sci., 50, 2462, 10.1175/1520-0469(1993)050<2462:GCMOIS>2.0.CO;2 Poje, 1999, Geometry of cross-stream mixing in a double-gyre ocean model, J. Phys. Oceanogr., 29, 1649, 10.1175/1520-0485(1999)029<1649:GOCSMI>2.0.CO;2 Prandle, 1987, The fine-structure of nearshore tidal and residual circulations revealed by HF radar surface current measurements, J. Phys. Oceanogr., 17, 231, 10.1175/1520-0485(1987)017<0231:TFSONT>2.0.CO;2 Provenzale, 1999, Transport by coherent barotropic vortices, Annu. Rev. Fluid Mech., 31, 55, 10.1146/annurev.fluid.31.1.55 Rogerson, 1999, Lagrangian motion and fluid exchange in a barotropic meandering jet, J. Phys. Oceanogr., 29, 2635, 10.1175/1520-0485(1999)029<2635:LMAFEI>2.0.CO;2 Rom-Kedar, 1990, Transport rates of a class of two-dimensional maps and flows, Physica D, 43, 229, 10.1016/0167-2789(90)90135-C Rom-Kedar, 1990, An analytical study of transport, mixing, and chaos in unsteady vortical flow, J. Fluid Mech., 214, 347, 10.1017/S0022112090000167 Rom-Kedar, 1991, Transport in two-dimensional maps: Concepts, examples, and a comparison of the theory of Rom-Kedar and Wiggins with the Markov model of Mackay, Meiss, Ott, and Percival, Physica D, 51, 248, 10.1016/0167-2789(91)90237-4 Shay, 1995, Mesoscale ocean surface current structure detected by HF radar, J. Atmos. Ocean. Technol., 12, 881, 10.1175/1520-0426(1995)012<0881:MOSCSD>2.0.CO;2 Shay, 2000, VHF radar detects oceanic submesoscale vortex along the Florida coast, EOS Trans. Am. Geophys. Union, 81, 209, 10.1029/00EO00143 Shay, 2002, Very high frequency radar mapping of the surface currents, IEEE J. Oceanogr. Engin., 27, 155, 10.1109/JOE.2002.1002470 Stewart, 1974, HF radio measurements of surface currents, Deep-Sea Res., 21, 1039 Truesdell, 1954 Verhulst, 1996 von Hardenberg, 2000, Transient chaotic mixing during a baroclinic life cycle, Chaos, 10, 122, 10.1063/1.166491 Voth, 2002, Experimental measurements of stretching fields in fluid mixing, Phys. Rev. Lett., 88, 254501.1, 10.1103/PhysRevLett.88.254501 K.C. Wang, On current controversy of unsteady separation, in: Symposium on Numerical and Physical Aspects of Aerodynamic Flows, Long Beach, CA, January 19–21, 1981 Wiggins, 1992 Wiggins, 2005, The dynamical systems approach to Lagrangian transport in ocean flows, Annu. Rev. Fluid Mech., 37, 295, 10.1146/annurev.fluid.37.061903.175815 Yuan, 2002, Barrier destruction and Lagrangian predictability at depth in a meandering jet, Dyn. Atmos. Oceans, 35, 41, 10.1016/S0377-0265(01)00082-3