[Show abstract][Hide abstract]ABSTRACT: We introduce a spatially localized inhomogeneity into the two-dimensional complex Ginzburg-Landau equation. We observe that this can produce two types of target wave patterns: stationary and breathing. In both cases, far from the target center, the field variables correspond to an outward propagating periodic traveling wave. In the breathing case, however, the region in the vicinity of the target center experiences a periodic temporal modulation at a frequency, in addition to that of the wave frequency of the faraway outward waves. Thus at a fixed point near the target, the breathing case yields a quasiperiodic time variation of the field. We investigate the transition between stationary and breathing targets, and note the existence of hysteresis. We also discuss the competition between the two types of target waves and spiral waves.
Preview · Article · Jan 2001 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
[Show abstract][Hide abstract]ABSTRACT: The power law exponent for the wavenumber power spectrum of a passive scalar field with finite lifetime in Lagrangian chaotic flows and the enstrophy spectrum of two-dimensional Navier–Stokes turbulence with drag are investigated. The power law exponents are related to the distribution of finite-time Lyapunov exponents and the finite lifetime (or the drag coefficient).
No preview · Article · Dec 2000 · Physica A: Statistical Mechanics and its Applications
[Show abstract][Hide abstract]ABSTRACT: We investigate the effect of drag force on the enstrophy cascade of two-dimensional Navier-Stokes turbulence. We find a power law decrease of the energy wave number (k) spectrum that is faster than the classical (no-drag) prediction of k(-3). It is shown that the enstrophy cascade with drag can be analyzed by making use of a previous theory for finite lifetime passive scalars advected by a Lagrangian chaotic fluid flow. Using this we relate the power law exponent of the energy wave number spectrum to the distribution of finite time Lyapunov exponents and the drag coefficient.
Preview · Article · Jun 2000 · Physical Review Letters
[Show abstract][Hide abstract]ABSTRACT: In this paper the power spectrum of passive scalars transported in two dimensional chaotic fluid flows is studied theoretically. Using a wave-packet method introduced by Antonsen et al., several model flows are investigated, and the fact that the power spectrum has the k(-1)-scaling predicted by Batchelor is confirmed. It is also observed that increased intermittency of the stretching tends to make the roll-off of the power spectrum at the high k end of the k(-1) scaling range more gradual. These results are discussed in light of recent experiments where a k(-1) scaling range was not observed. (c) 2000 American Institute of Physics.
[Show abstract][Hide abstract]ABSTRACT: The power law exponent for the wave number power spectrum of a passive scalar field in Lagrangian chaotic flows is found to differ from the classical value of -1 (Batchelor's law) when the passive particles have a finite lifetime for exponential decay. A theory based on the chaotic dynamics of the passive scalar is developed and compared to numerical simulation results.
Preview · Article · Oct 1999 · Physical Review Letters
[Show abstract][Hide abstract]ABSTRACT: The effect of adding a chiral symmetry breaking term to the two-dimensional complex Ginzburg-Landau equation is investigated. We find that this term causes a shift in the frequency of the spiral wave solutions and that the sign of this shift depends on the topological charge (handedness) of the spiral. For parameters such that nearly stationary spiral domains form (called a “frozen” state), we find that, due to this charge-dependent frequency shift, the boundary between oppositely charged spiral domains moves, resulting in the domination of one domain of charge over the other. In addition, we introduce a quantity which measures the chirality of patterns and use it to characterize the transition between frozen and turbulent states. We also find that, depending on parameters, this transition occurs in two qualitatively distinct ways.
No preview · Article · Jul 1998 · Physica D Nonlinear Phenomena
[Show abstract][Hide abstract]ABSTRACT: In this paper we investigate the stability of a straight vortex filament with phase twist described by the three-dimensional complex Ginzburg-Landau equation CGLE. The results of the linear stability analysis show that the straight filament is stable in a limited region of the two parameter space of the CGLE. The stable region is dependent on the phase twist imposed on the filament and shrinks in size as the phase twist is increased. It is also shown numerically that the nonlinear evolution of an unstable initial straight filament can lead to a helical filament.
Preview · Article · Mar 1998 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics