Adrian, R. J. 1991 Particle-imaging techniques for experimental fluid-mechanics. Annu. Rev. Fluid Mech. 23, 261–304.
Aref, H. 2002 The development of chaotic advection. Phys. Fluids 14 (4), 1350–1325.
Arratia, P. E., Voth, G. A. & Gollub, J. P. 2005 Stretching and mixing of non-Newtonian fluids in time-periodic flows. Phys. Fluids 17 (5), 053102.
Chella, R. & Ottino, J. M. 1985 Stretching in some classes of fluid motions and asymptotic mixing efficiencies as a measure of flow classification. Arch. Rat. Mech. Anal. 90, 15–42.
Dabiri, J. O. 2005 On the estimation of swimming and flying forces from wake measurements. J. Exp Biol. 208, 3519–3532.
Dabiri, J. O. & Gharib, M. 2004 Fluid entrainment by isolated vortex rings. J. Fluid Mech. 511, 311–331.
Didden, N. 1979 On the formation of vortex rings: rolling-up and production of circulation. Z. Angew. Math. Phys. 30, 101–116.
Dudley, R. 2002 The Biomechanics of Insect Flight: Form, Function, Evolution. Princeton University Press.
Eckart, C. 1948 An analysis of the stirring and mixing processes in incompressible fluids. J. Mar. Res. 7, 265–275.
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.
Green, M. A., Rowley, C. W. & Haller, G. 2007 Detection of Lagrangian coherent structures in three-dimensional turbulence. J. Fluid Mech. 572, 111–120.
Haller, G. 2001 Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D 149, 248–277.
Haller, G. 2002 Lagrangian coherent structures from approximate velocity data. Phys. Fluids 14 (6), 1851–1861.
Haller, G. & Poje, A. C. 1998 Finite time transport in aperiodic flows. Physica D 119, 352–380.
Haller, G. & Yuan, G. 2000 Lagrangian coherent structures and mixing in two-dimensional turbulence. Physica D 147, (3–4), 352–370.
Jones, C. K. R. T. & Winkler, S. 2002 Invariant manifolds and Lagrangian dynamics in the ocean and atmosphere. In Handbook of Dynamical Systems (ed. Fiedler, B.), vol. 2, pp. 55–92. Elsevier.
Joseph, B. & Legras, B. 2002 Relation between kinematic boundaries, stirring, and barriers for the Antarctic polar vortex. J. Atmos. Sci. 59, 1198–1212.
Khakhar, D. V. & Ottino, J. M. 1986 Fluid mixing (stretching) by time periodic sequences of weak flows. Phys. Fluids 29 (11), 3503–3505.
Khakhar, D. V., Rising, H. & Ottino, J. M. 1986 Analysis of chaotic mixing in two model systems. J. Fluid Mech. 172, 419–451.
Koh, T. Y. & Legras, B. 2002 Hyperbolic lines and the stratospheric polar vortex. Chaos 12, 382–394.
Krasny, R. & Nitsche, M. 2002 The onset of chaos in vortex sheet flow. J. Fluid Mech. 454, 47–69.
Lekien, F., Coulliette, C., Mariano, A. J., Ryan, E. H., Shay, L. K., Haller, G. & Marsden, J. 2005 Pollution release tied to invariant manifolds: a case study for the coast of Florida. Physica D 210, 1–20.
Leonard, A., Rom-Kedar, V. & Wiggins, S. 1987 Fluid mixing and dynamical systems. Proc. Intl Conf. on the Physics of Chaos and Systems Far from Equilibium, Nuclear Physics B 2, 179–190.
Lugt, H. J. 1983 Vortex Flow in Nature and Technology. John Wiley.
Malhotra, N., Mezić, I. & Wiggins, S. 1998 Patchiness: a new diagnostic for Lagrangian trajectory analysis in time-dependent fluid flows. Intl J. Bifurcation Chaos 8, 1053–1093.
Mancho, A. M., Small, D., Wiggins, S. & Ide, K. 2003 Computation of stable and unstable manifolds of hyperbolic trajectories in two-dimensional, aperiodically time-dependent vector fields. Physica D 182, 188–222.
Mathiew, G., Mezić, I. & Petzold, L. 2005 A multiscale measure for mixing. Physica D 211, 23–46.
Maxworthy, T. 1977 Some experimental studies of vortex rings. J. Fluid Mech. 81, 465–495.
Mezić, I. & Wiggins, S. 1999 A method for visualization of invariant sets of dynamical systems based on the ergodic partition. Chaos 9, 213–218.
Moore, D. W. & Saffman, P. G. 1973 Axial flow in laminar trailing vortices. Proc. R. Soc. Lond. A 333, 491–508.
Müller, E. A. & Didden, N. 1980 Zur erzeugung der zirkulation bei der bildung eines ringwirbels an einer dusenmundung. Stroj. Casop. 31, 363–372.
Nitsche, M. & Krasny, R. 1994 A numerical study of vortex ring formation at the edge of a circular tube. J. Fluid Mech. 276, 139–161.
Ottino, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge University Press.
Ottino, J. M. 1990 Mixing, chaotic advection, and turbulence. Annu. Rev. Fluid Mech. 22, 207–253.
Padberg, K. 2005 Numerical analysis of chaotic transport in dynamical systems. PhD thesis, University of Paderborn.
Pierrehumbert, R. T. & Yang, H. 1993 Global chaotic mixing on isentropic surfaces. J. Atmos. Sci. 50, 2462–2480.
Poje, A. C. & Haller, G. 1999 Geometry of cross-stream mixing in a double-gyre ocean model. J. Phys. Oceanogr. 29, 1649–1665.
Pullin, D. I. 1979 Vortex ring formation at tube and orifice openings. Phys. Fluids 22, 401–403.
Pullin, D. I. & Saffman, P. G. 1998 Vortex dynamics in turbulence. Annu. Rev. Fluid Mech. 30, 31–51.
Romkedar, V., Leonard, A. & Wiggins, S. 1990 An analytical study of transport, mixing and chaos in an unsteady vortical flow. J. Fluid Mech. 214, 347–394.
Rosenfeld, M., Rambod, E. & Gharib, M. 1998 Circulation and formation number of laminar vortex rings. J. Fluid Mech. 376, 297–318.
Saffman, P. G. 1978 The number of waves on unstable vortex rings. J. Fluid Mech. 84, 721–733.
Shadden, S. C. 2006 A dynamical systems approach to unsteady systems. PhD thesis, California Institute of Technology.
Shadden, S. C., Lekien, F. & Marsden, J. E. 2005 Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 212, 271–304.
Shadden, S. C., Dabiri, J. O. & Marsden, J. E. 2006 Lagrangian analysis of fluid transport in empirical vortex rings. Phys. Fluids 18 (4), 0471051–11.
Shariff, K. & Leonard, A. 1992 Vortex rings. Annu. Rev. Fluid Mech. 24, U235–U279.
Spedding, G. R., Rosen, M. & Hedenstrom, A. 2003 A family of vortex wakes generated by a thrush nightingale in free flight in a wind tunnel over its entire natural range of flight speeds. J. Exp. Biol. 206, 2313–2344.
Tambasco, M. & Steinman, D. A. 2002 On assessing the quality of particle tracking through computational fluid dynamic models. J. Biomech. Engng 124, 166–175.
Voth, G. A., Haller, G. & Gollub, J. P. 2002 Experimental measurements of stretching fields in fluid mixing. Phys. Rev. Lett. 88, 254501.
Weihs, D. 1973 Hydromechanics of fish schooling. Nature 241, 290–291.
Wiggins, S. 2005 The dynamical systems approach to Lagrangian transport in oceanic flows. Annu. Rev. Fluid Mech. 37, 295–328.
Willert, C. E. & Gharib, M. 1991 Digital particle image velocimetry. Exps Fluids 10 (4), 181–193.
Zabusky, N. J. 1999 Vortex paradigm for accelerated inhomogeneous flows: visiometrics for the Rayleigh–Taylor and Richtmyer–Meshkov environments. Annu. Rev. Fluid Mech. 31, 495–536.