Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1998-06-09
Nonlinear Sciences
Chaotic Dynamics
48 pages, 17 figures, to appear in Physics of Fluids
Scientific paper
10.1063/1.869709
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, p_N, has a slow-velocity Gaussian component and a significant high-velocity tail caused by close vortex pairs. In the limit for N -> oo, p_N tends to a Gaussian. However, the form of the single-vortex velocity causes very slow convergence with N; for N ~ 10^6 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 sigma_N = sqrt{N ln N /2 pi}. 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.
McWilliams James C.
Provenzale Antonello
Weiss Jeffrey B.
No associations
LandOfFree
Lagrangian Dynamics in High-Dimensional Point-Vortex Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Lagrangian Dynamics in High-Dimensional Point-Vortex Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lagrangian Dynamics in High-Dimensional Point-Vortex Systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-631109