Detecting and analyzing coherent structures in two-dimensional dynamical systems

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2013.

[1]  George Haller,et al.  Pollution release tied to invariant manifolds: A case study for the coast of Florida , 2005 .

[2]  Gerhard A. Holzapfel,et al.  Nonlinear Solid Mechanics: A Continuum Approach for Engineering Science , 2000 .

[3]  John O. Dabiri,et al.  Transport of inertial particles by Lagrangian coherent structures: application to predator–prey interaction in jellyfish feeding , 2009, Journal of Fluid Mechanics.

[4]  A. Hussain,et al.  Coherent structures and turbulence , 1986, Journal of Fluid Mechanics.

[5]  J. Gollub,et al.  Experimental measurements of stretching fields in fluid mixing. , 2002, Physical review letters.

[6]  Stephen Wiggins,et al.  Intergyre transport in a wind-driven, quasigeostrophic double gyre: An application of lobe dynamics , 2000 .

[7]  J. Marsden,et al.  Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows , 2005 .

[8]  Christopher K. R. T. Jones,et al.  Quantifying transport in numerically generated velocity fields , 1997 .

[9]  G. Haller.  Finding finite-time invariant manifolds in two-dimensional velocity fields. , 2000, Chaos.

[10]  K. Daniels,et al.  Equilibration of granular subsystems , 2010, 1001.5411.

[11]  François Guibault,et al.  Two-dimensional metric tensor visualization using pseudo-meshes , 2006, Engineering with Computers.

[12]  E. Artin.  The theory of braids. , 1950, American scientist.

[13]  D. Lathrop.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering , 2015 .

[14]  George Haller,et al.  Inertial Particle Dynamics in a Hurricane , 2009 .

[15]  W. Large,et al.  Open Ocean Momentum Flux Measurements in Moderate to Strong Winds , 1981 .

[16]  J. Thiffeault,et al.  Braids of entangled particle trajectories. , 2009, Chaos.

[17]  Nicholas T Ouellette,et al.  Lagrangian coherent structures separate dynamically distinct regions in fluid flows. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  G. Budworth.  The Knot Book , 1983 .

[19]  Steven R. Fipke,et al.  Multilateral Wells Reduce Capex of Offshore, Subsea Development in Australia's Northwest Shelf , 2010 .

[20]  Stephen Wiggins,et al.  Chaotic transport in dynamical systems , 1991 .

[21]  H. Koçak,et al.  Invariant-tori-like Lagrangian coherent structures in geophysical flows. , 2010, Chaos.

[22]  Raymond T. Pierrehumbert,et al.  Global Chaotic Mixing on Isentropic Surfaces , 1993 .

[23]  Irina I. Rypina,et al.  Investigating the connection between complexity of isolated trajectories and Lagrangian coherent structures , 2011 .

[24]  F. J. Beron-Vera,et al.  On the Lagrangian Dynamics of Atmospheric Zonal Jets and the Permeability of the Stratospheric Polar Vortex , 2006 .

[25]  G. Haller.  Distinguished material surfaces and coherent structures in three-dimensional fluid flows , 2001 .

[26]  Entropie topologique et représentation de Burau , 1989 .

[27]  George Haller,et al.  Accurate extraction of Lagrangian coherent structures over finite domains with application to flight data analysis over Hong Kong International Airport. , 2010, Chaos.

[28]  George Haller,et al.  Forecasting sudden changes in environmental pollution patterns , 2012, Proceedings of the National Academy of Sciences.

[29]  Jean-Luc Thiffeault,et al.  Topology, braids and mixing in fluids , 2006, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[30]  C. Tresser,et al.  Badly ordered orbits of circle maps , 1984, Mathematical Proceedings of the Cambridge Philosophical Society.

[31]  Phanindra Tallapragada,et al.  Particle segregation by Stokes number for small neutrally buoyant spheres in a fluid. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  T. Sakajo,et al.  Efficient topological chaos embedded in the blinking vortex system. , 2005, Chaos.

[33]  Jacques-Olivier Moussafir.  On computing the entropy of braids , 2006 .

[34]  A. Gordon,et al.  Chaotic Advection in an Archipelago , 2010 .

[35]  Igor Mezic,et al.  Capturing deviation from ergodicity at different scales , 2009 .

[36]  Holger Theisel,et al.  Ridge Concepts for the Visualization of Lagrangian Coherent Structures , 2012 .

[37]  Uang,et al.  The NCEP Climate Forecast System Reanalysis , 2010 .

[38]  Shane D. Ross,et al.  Detection and characterization of transport barriers in complex flows via ridge extraction of the finite time Lyapunov exponent field , 2011 .

[39]  M. Olascoaga,et al.  Isolation on the West Florida Shelf with implications for red tides and pollutant dispersal in the Gulf of Mexico. , 2010, Nonlinear processes in geophysics.

[40]  G. Haller,et al.  Lagrangian coherent structure analysis of terminal winds detected by lidar. Part II: Structure evolution and comparison with flight data , 2011 .

[41]  H. Swinney,et al.  Collective motion and density fluctuations in bacterial colonies , 2010, Proceedings of the National Academy of Sciences.

[42]  Jerrold E. Marsden,et al.  Open-boundary modal analysis: Interpolation, extrapolation, and filtering , 2004 .

[43]  James C. McWilliams,et al.  Correction and commentary for "Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the regional ocean modeling system" by Haidvogel et al., J. Comp. Phys 227, pp 3595-3624 , 2009, J. Comput. Phys..

[44]  J. Ottino.  The Kinematics of Mixing: Stretching, Chaos, and Transport , 1989 .

[45]  W. Thurston.  On the geometry and dynamics of diffeomorphisms of surfaces , 1988 .

[46]  Richard Brinkman,et al.  Seasonal circulation and temperature variability near the North West Cape of Australia , 2012 .

[47]  G. Watabayashi,et al.  Tactical Modeling of Surface Oil Transport During the Deepwater Horizon Spill Response , 2013 .

[48]  Francois Lekien,et al.  The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds. , 2010, Chaos.

[49]  Ryan J. Lowe,et al.  Dynamics of the summer shelf circulation and transient upwelling off Ningaloo Reef, Western Australia , 2013 .