• Artale, V., G. Boffetta, A. Celani, M. Cencini, and A. Vulpiani, 1997:Dispersion of passive tracers in closed basins: Beyond the diffusion coefficient. Phys. Fluids.,9, 3162–3171.

  • Backus, R. H., 1986: Biogeographic boundaries in the open ocean. Pelagic Biogeography, UNESCO Tech. Paper Mar. Sci. 49, 9–13. [Available from UNESCO-CSI, 1 rue Miollis, 75732 Paris, France.].

  • Badii, R., and A. Politi, 1997: Complexity: Hierarchical Structures and Scaling in Physics. Cambridge University Press, 318 pp.

  • Bauer, S., M. S. Swenson, A. Griffa, A. J. Mariano, and K. Owens, 1998: Eddy-mean flow decomposition and eddy-diffusivity estimates in the tropical Pacific Ocean. Part 1: Methodology. J. Geophys. Res.,103, 30 855–30 871.

  • Beck, C., and F. Schlögl, 1993: Thermodynamics of Chaotic Systems. Cambridge University Press, 306 pp.

  • Benettin, G., 1984: Power-law behavior of Lyapunov exponents in some conservative dynamical systems. Physica D,13, 211–220.

  • ——, L. Galgani, A. Giorgilli, and J. M. Strelcyn, 1980: Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: A method for computing all of them. Meccanica,15, 9–24.

  • Bower, A. S., 1991: A simple kinematic mechanism for mixing fluid parcels across a meandering jet. J. Phys. Oceanogr.,21, 173–180.

  • ——, and H. T. Rossby, 1989: Evidence of cross-frontal exchange processes in the Gulf Stream based on isopycnal RAFOS float data. J. Phys. Oceanogr.,19, 1177–1190.

  • ——, and M. S. Lozier, 1994: A closer look at particle exchange in the Gulf Stream. J. Phys. Oceanogr.,24, 1399–1418.

  • ——, H. T. Rossby, and J. T. Lillibridge, 1985: The Gulf Stream—Barrier or blender? J. Phys. Oceanogr.,15, 24–32.

  • Brown, M. G., and R. M. Samelson, 1994: Particle motion in vorticity-conserving, two-dimensional incompressible flows. Phys. Fluids,6, 2875–2876.

  • Buffoni, G., P. Falco, A. Griffa, and E. Zambianchi, 1997: Dispersion processes and residence times in a semi-enclosed basin with recirculating gyres. An application to the Tyrrhenian Sea. J. Geophys. Res.,102 (C8), 18 699–18 713.

  • Cecconi, F., and A. Vulpiani, 1995: Approximation of chaotic systems in terms of markovian processes. Phys. Lett. A,201, 326–332.

  • Chandrasekhar, S., 1943: Stochastic problems in physics and astronomy. Rev. Mod. Phys.,15, 1–89.

  • Chirikov, B. V., 1979: A universal instability of many-dimensional oscillator systems. Phys. Rep.,52, 263–379.

  • Colin de Verdière, A., 1983: Lagrangian eddy statistics from surface drifters in the Eastern North Atlantic. J. Mar. Res.,41, 375–398.

  • Cornillon, P., D. Evans, and D. Large, 1986: Warm outbreaks of the Gulf Stream into the Sargasso Sea. J. Geophys. Res.,91, 6583–6596.

  • Crisanti, A., M. Falcioni, G. Paladin, and A. Vulpiani, 1991: Lagrangian chaos: Transport, mixing and diffusion in fluids. La Rivista del Nuovo Cimento,14, 1–80.

  • Davis, R. E., 1991: Observing the general circulation with floats. Deep-Sea Res.,38, S531–S571.

  • del Castillo-Negrete, D., 1998: Asymmetric transport and non-Gaussian statistics of passive scalars in vortices in shear. Phys. Fluids,10, 576–594.

  • Dimas, A. A., and G. S. Triantafylou, 1995: Baroclinic-barotropic instabilities of the Gulf Stream extension. J. Phys. Oceanogr., 25, 825–834.

  • Duan, J., and S. Wiggins, 1996: Fluid exchange across a meandering jet with quasiperiodic variability. J. Phys. Oceanogr.,26, 1176–1188.

  • Dutkiewicz, S., A. Griffa, and D. B. Olson, 1993: Particle diffusion in a meandering jet. J. Geophys. Res.,98, 16 487–16 500.

  • Eckmann, J. P., and D. Ruelle, 1985: Ergodic theory of chaos and strange attractors. Rev. Mod. Phys.,57, 617–655.

  • Feller, W., 1968: An Introduction to Probability Theory and its Applications. Vol. I. Wiley, 528 pp.

  • Fraedrich, K., 1988: El Niño–Southern Oscillation predictability. Mon. Wea. Rev.,116, 1001–1012.

  • ——, and K. Müller, 1983: On single station forecasting: Sunshine and rainfall Markov chains. Beitr. Phys. Atmos.,56, 108–134.

  • Griffa, A., 1996: Applications of stochastic particle models to oceanographic problems. Stochastic Modelling in Physical Oceanography, R. J. Adler, P. Muller, and B. L. Rozovskii, Eds., Birkhäuser, 113–140.

  • ——, K. Owens, L. Piterbarg, and B. Rozowskii, 1995: Estimates of turbulence parameters from Lagrangian data using a stochastic particle model. J. Mar. Res.,53, 371–401.

  • Halliwell, G. R., and C. N. K. Mooers, 1983: Meanders of the Gulf Stream downstream from Cape Hatteras. 1975–1978. J. Phys. Oceanogr.,13, 1275–1292.

  • Khinchin, A. I., 1957: Mathematical Foundations of Information Theory. Dover, 120 pp.

  • Kluiving, R., H. W. Capel, and R. A. Pasmanter, 1992: Symbolic dynamics of fully developed chaos I. Physica A,183, 67–95.

  • Kontoyiannis, H., and D. R. Watts, 1994: Observations on the variability of the Gulf Stream path between 74°W and 70°W. J. Phys. Oceanogr.,24, 1999–2013.

  • Lacorata, G., R. Purini, A. Vulpiani, and E. Zambianchi, 1996: Dispersion of passive tracers in model flows: Effects of the parametrization of small-scale processes. Ann. Geophys.,14, 476–484.

  • Lee, T., 1994: Variability of the Gulf Stream path observed from satellite infrared images. Ph.D. dissertation, University of Rhode Island, 188 pp.

  • Levinson, H. F., 1991: The long-term dynamical behavior of small bodies in the Kuipter belt. Astron. J.,102, 787–794.

  • Lichtenberg, A. J., and M. A. Lieberman, 1992: Regular and Chaotic Dynamics. Springer, 692 pp.

  • MacKay, R. S., J. D. Meiss, and I. C. Percival, 1987: Resonances in area-preserving maps. Physica D,27, 1–20.

  • Mannella, R., and V. Palleschi, 1989: Fast and precise algorithm for computer simulation of stochastic differential equations. Phys. Rev.,A40, 3381–3386.

  • Meiss, J. D., and E. Ott, 1986: Markov tree model of transport in area-preserving maps. Physica D,20, 387–402.

  • Nicolis, C., W. Ebeling, and C. Baraldi, 1997: Markov processes, dynamic entropies and statistical prediction of mesoscale weather regimes. Tellus,49A, 108–118.

  • Okubo, A., 1971: Oceanic diffusion diagrams. Deep-Sea Res.,18, 789–802.

  • Olson, D. B., 1991: Rings in the ocean. Ann. Rev. Earth Planet. Sci.,19, 283–311.

  • Pierrehumbert, R. T., 1991: Chaotic mixing of tracers and vorticity by modulated travelling Rossby waves. Geophys. Astrophys. Fluid Dyn.,58, 285–319.

  • Pope, S. B., 1994: Lagrangian PDF methods for turbulent flows. Ann. Rev. Fluid Mech.,26, 24–63.

  • Poulain, P. -M., and P. P. Niiler, 1989: Statistical analysis of the surface circulation in the California Current System using satellite-tracked drifters. J. Phys. Oceanogr.,19, 1588–1603.

  • Rickman, H., and C. Froeschlè, 1979: Orbital evolution of short-period comets treated as a Markov process. Astron. J.,84, 1910–1917.

  • Risken, H., 1989: The Fokker–Planck Equation. Springer, 472 pp.

  • Samelson, R. M., 1992: Fluid exchange across a meandering jet. J. Phys. Oceanogr.,22, 431–440.

  • Thomson, D. J., 1986: A random walk model of dispersion in turbulent flows and its application to dispersion in a valley. Quart. J. Roy. Meteor. Soc.,112, 511–530.

  • ——, 1987: Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J. Fluid Mech.,180, 529–556.

  • Tracey, K. L., and D. R. Watts, 1986: On Gulf Stream meander characteristics near Cape Hatteras. J. Geophys. Res.,91, 7587–7602.

  • van Dop, H., F. T. M. Niewstadt, and J. C. R. Hunt, 1985: Random walk models for particle displacements in inhomogeneous unsteady turbulent flows. Phys. Fluids,28, 1639–1653.

  • Vazquez, J., and D. R. Watts, 1985: Observations on the propagation, growth and predictability of Gulf Stream meanders. J. Geophys. Res.,90, 7143–7151.

  • Verron, J., and K. D. Nguyen, 1989: Lagrangian diffusivity estimates from a gyre-scale numerical experiment on float tracking. Oceanol. Acta,12, 167–176.

  • Watts, D. R., 1983: Gulf Stream variability. Eddies in Marine Science, A. Robinson, Ed., Springer Verlag, 114–144.

  • Wiggins, S., 1992: Chaotic Transport in Dynamical Systems. Springer, 352 pp.

  • Yang, H., 1996: Chaotic transport and mixing by ocean gyre circulation. Stochastic Modelling in Physical Oceanography, R. J. Adler, P. Muller, and B. L. Rozovskii, Eds., Birkhäuser, 439–466.

  • Yeung, P. K., and S. B. Pope, 1989: Lagrangian statistics from direct numerical simulations of isotropic turbulence. J. Fluid Mech.,207, 531–586.

  • Zambianchi, E., and A. Griffa, 1994a: Effects of finite scales of turbulence on dispersion estimates. J. Mar. Res.,52, 129–148.

  • ——, and ——, 1994b: On the applicability of a stochastic model for particle motion to drifter data in the Brazil–Malvinas extension. Annali Ist. Univ. Navale,61, 75–90.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 169 169 13
PDF Downloads 74 74 13

Mixing in a Meandering Jet: A Markovian Approximation

View More View Less
  • 1 Dipartimento di Fisica, Università “la Sapienza,” and Istituto Nazionale Fisica della Materia, Unità di Roma, Rome, Italy
  • | 2 Dipartimento di Fisica, Università dell’ Aquila, Coppito, and Istituto di Fisica dell’Atmosfera—CNR, Rome, Italy
  • | 3 Dipartimento di Fisica, Università “la Sapienza,” and Istituto Nazionale Fisica della Materia, Unità di Roma, Rome, Italy
  • | 4 Istituto di Meteorologia e Oceanografia, Istituto Universitario Navale, Naples, Italy
© Get Permissions Rent on DeepDyve
Restricted access

Abstract

Mixing and transport in correspondence of a meandering jet are investigated. The large-scale flow field is a kinematically assigned streamfunction. Two basic mixing mechanisms are considered separately and in combination: deterministic chaotic advection induced by a time dependence of the flow, and turbulent diffusion described by means of a stochastic model for particle motion.

Rather than looking at the details of particle trajectories, fluid exchange is studied in terms of Markovian approximations. The 2D physical space accessible to fluid particles is subdivided into regions characterized by different Lagrangian behavior. From the observed transitions between regions it is possible to derive a number of relevant quantities characterizing transport and mixing in the studied flow regime, such as residence times, meridional mixing, and correlation functions. These estimated quantities are compared to the corresponding ones resulting from the actual simulations. The outcome of the comparison suggests the possibility of describing in a satisfactory way at least some of the mixing properties of the system through the very simplified approach of a first-order Markovian approximation, whereas other properties exhibit memory patterns of higher order.

Corresponding author address: Dr. Enrico Zambianchi, Istituto di Meteorologia e Oceanografia, Istituto Universitario Navale, Via Acton 38, 80133 Napoli, Italy.

Email: enrico@naval.uninav.it

Abstract

Mixing and transport in correspondence of a meandering jet are investigated. The large-scale flow field is a kinematically assigned streamfunction. Two basic mixing mechanisms are considered separately and in combination: deterministic chaotic advection induced by a time dependence of the flow, and turbulent diffusion described by means of a stochastic model for particle motion.

Rather than looking at the details of particle trajectories, fluid exchange is studied in terms of Markovian approximations. The 2D physical space accessible to fluid particles is subdivided into regions characterized by different Lagrangian behavior. From the observed transitions between regions it is possible to derive a number of relevant quantities characterizing transport and mixing in the studied flow regime, such as residence times, meridional mixing, and correlation functions. These estimated quantities are compared to the corresponding ones resulting from the actual simulations. The outcome of the comparison suggests the possibility of describing in a satisfactory way at least some of the mixing properties of the system through the very simplified approach of a first-order Markovian approximation, whereas other properties exhibit memory patterns of higher order.

Corresponding author address: Dr. Enrico Zambianchi, Istituto di Meteorologia e Oceanografia, Istituto Universitario Navale, Via Acton 38, 80133 Napoli, Italy.

Email: enrico@naval.uninav.it

Save