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  • 1
    Electronic Resource
    Electronic Resource
    Anisotropic geophysical vortices (1994)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 4 (1994), S. 305-311 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A survey is made of many types of coherent vortices in the Earth's ocean and atmosphere. These vortices often occur with strong, environmentally induced anisotropy in their velocity and vorticity fields. We propose a definition of the essential characteristics of coherent vortices and formulate hypotheses concerning their dynamical role in complex, anisotropic fluid motions. Finally, we analyze numerical solutions both for uniformly rotating, stably stratified three-dimensional flow and for two-dimensional flow for the phenomena of enstrophy cascade and dissipation, intermittency, isotropy in the appropriate coordinate frame, coherent vortex emergence, vortex population dynamics, and approach to a nonturbulent end state.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166010
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  • 2
    Electronic Resource
    Electronic Resource
    Lagrangian dynamics in high-dimensional point-vortex systems (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 1929-1941 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We study the Lagrangian dynamics of systems of N point vortices and passive particles in a two-dimensional, doubly periodic domain. The probability distribution function of vortex velocity, pN, has a slow-velocity Gaussian component and a significant high-velocity tail caused by close vortex pairs. In the limit for N→∞, pN tends to a Gaussian. However, the form of the single-vortex velocity causes very slow convergence with N; for N(approximate)106 the non-Gaussian high-velocity tails still play a significant role. At finite N, the Gaussian component is well modeled by an Ornstein-Uhlenbeck (OU) stochastic process with variance σN=N ln N/2π. Considering in detail the case N=100, we show that at short times the velocity autocorrelation is dominated by the Gaussian component and displays an exponential decay with a short Lagrangian decorrelation time. The close pairs have a long correlation time and cause nonergodicity over at least the time of the integration. Due to close vortex dipoles the absolute dispersion differs significantly from the OU prediction, and shows evidence of long-time anomalous dispersion. We discuss the mathematical form of a new stochastic model for the Lagrangian dynamics, consisting of an OU model combined with long-lived close same-sign vortices engaged in rapid rotation and long-lived close dipoles engaged in ballistic motion. From a dynamical-systems perspective this work indicates that systems of dimension O(100) can have behavior which is a combination of both low-dimensional behavior, i.e., close pairs, and extremely high-dimensional behavior described by traditional stochastic processes. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869709
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  • 3
    Electronic Resource
    Electronic Resource
    A wavelet-packet census algorithm for calculating vortex statistics (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 1988-1999 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A generalized wavelet-packet based technique for decomposing signals into coherent and noncoherent parts is presented. The method is tested on the vorticity field of numerical simulations of weakly decaying two-dimensional turbulence. The easily recognizable coherent vortex structures that emerge are systematically filtered from the solution. Once extracted, various properties of the vortices, such as their number, size, circulation, and peak value are computed. The results compare well with a similar study [J. Fluid Mech. 219, 361 (1990); Phys. Fluids 5, 608 (1993)], which employs a complex pattern recognition technique based exclusively on a priori knowledge of the properties of the solution—that is, the features typical of the resulting vortex structures. The similarity of the results is encouraging, suggesting that the wavelet packet technique, by absorbing much of the complexity into the mathematical features of the transform itself, can provide an efficient, standardized tool that is readily extendible to more complex problems in two and three dimensions. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869318
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  • 4
    Electronic Resource
    Electronic Resource
    Nonergodicity of point vortices (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 835-844 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The motion of N point vortices in a two-dimensional fluid is a Hamiltonian dynamical system with a 2N-dimensional phase space. The equations of motion for point vortices in a two-dimensional square doubly periodic domain are derived from those for an open domain. The Hamiltonian has three known constants of the motion and is thus believed to be nonintegrable for four or more vortices. Trajectories are numerically integrated from several initial conditions containing six vortices with varying total energy. Ergodicity on the surface defined by the constants of the motion is directly tested by comparing time-average and ensemble-average vortex pair statistics. It is found that the dynamics is not ergodic. There is evidence that the nonergodicity is not due to a gross fragmentation of phase space as might result from a broken symmetry. Vortex pair statistics are also used to test the randomness of the chaotic motion. It is found that the time-averaged statistics of the vortices are clearly distinct from those of independent random walkers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858014
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  • 5
    Electronic Resource
    Electronic Resource
    Temporal scaling behavior of decaying two-dimensional turbulence (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 608-621 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Decaying two-dimensional turbulence is characterized by the emergence of coherent vortices, which subsequently dominate the evolution. The temporal scaling behavior of the flow is analyzed using a scaling theory, a long-time integration of the fluid equations, and a dissipative, modified point-vortex model that represents the turbulence as a system of interacting coherent structures. Good agreement is found in the behavior of average vortex properties, low-order moments of the flow fields, and the form of self-similar evolution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858647
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  • 6
    Electronic Resource
    Electronic Resource
    Transport and mixing in traveling waves (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 1379-1384 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An iterated map is constructed that captures the essential features of particle trajectories in a class of quasiperiodic traveling waves: large-amplitude single-frequency traveling waves with two-dimensional structure perturbed by a wave with a second frequency. The map provides an efficient method for numerical calculation of the transport and mixing properties of such waves, and is used here to study the properties of a chaotic separatrix layer. It is found that the average position increases linearly with time indicating the existence of a well-defined transport velocity. The transport velocity grows faster than linearly as the perturbation parameter k increases. The mixing takes the form of anomalous diffusion where the mean-square deviation of position grows as tν, with ν〉1. The data is consistent with the diffusion exponent ν growing linearly with k.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858068
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  • 7
    Electronic Resource
    Electronic Resource
    Volume Visualizing High-Resolution Turbulence Computations (1998)
    Springer
    Theoretical and computational fluid dynamics 11 (1998), S. 195-211 
    Details
    ISSN: 1432-2250
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract: Using several volume-visualization packages including a new package we developed called Volsh, we investigate a 25-Gbyte dataset from a 2563 computation of decaying quasi-geostrophic turbulence. We compare surface fitting and direct volume rendering approaches, as well as a number of techniques for producing feature-revealing spatial cues. We also study the pros and cons of using batch and interactive tools for visualizing the data and discuss the relative merits of using each approach. We find that each tool has its own advantages and disadvantages, and a combination of tools is most effective at exploring large four-dimensional scalar datasets. The resulting visualizations show several new phenomena in the dynamics of coherent vortices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001620050089
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  • 8
    Electronic Resource
    Electronic Resource
    A stochastic return map for stochastic differential equations (1990)
    Springer
    Journal of statistical physics 58 (1990), S. 863-883 
    Details
    ISSN: 1572-9613
    Keywords: Stochastic map ; stochastic differential equation ; limit cycle ; Gaussian colored noise
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A method is presented for constructing a stochastic return map from a stochastic differential equation containing a locally stable limit cycle and small-amplitude [O(ε)] additive Gaussian colored noise. The construction is valid provided the correlation time isO(ε) orO(1). The effective noise in the return map has nonzeroO(ε 2) mean and is state dependent. The method is applied to a model dynamical system, illustrating how the effective noise in the return map depends on both the original noise process and the local deterministic dynamics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01026555
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  • 9
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    Merger and alignment in a reduced model for three-dimensional quasigeostrophic ellipsoidal vortices (2006)
    American Institute of Physics
    Details
    Publication Date: 2006-05-01
    Print ISSN: 1070-6631
    Electronic ISSN: 1089-7666
    Topics: Physics
    Published by American Institute of Physics
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  • 10
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    Dispersion and Mixing in Quasigeostrophic Turbulence (2004)
    American Physical Society
    Details
    Publication Date: 2004-02-25
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
    Published by American Physical Society
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