12,510 research outputs found
STRANGE ATTRACTOR OF THE MODULATED STOKES WAVE - A UNIVERSAL FORM
No full textThis Rapid Communication argues that the strange attractor recently found in the context of the modulated Stokes wave [H. T. Moon, Phys. Fluids A 3, 2709 (1991)] is a universal form and indeed the asymmetric counterpart of the Lorentz attractor. Furthermore, this form appears to reveal another class of universality in that it follows the evolution pattern set by the tent map. This is in marked contrast to the Rossler attractor, which follows the universal sequence of the logistic map
Soliton turbulence and strange attractor
No full textThis study finds that there exists a set of three basic evolution patterns including a dissipative soliton in the non-Hamiltonian media governed by the Ginzburg-Landau equation. A global analysis in the introduced subspace shows that the soliton is a spiral sink enclosed by a doubly connected homoclinic orbit. The soliton, prior to a turbulent state, breaks up into recurring pulses through a Hopf bifurcation. The strange attractor underlying the turbulence is found and presented with discussion. The Lyapunov number, found from a one-dimensional reduction of the attractor, is given by L almost-equal-to 0.34.
MULTIPLE VORTEX CLUSTERING AND CHAOTIC ADVECTION IN 2 DIMENSIONS
No full textMultiple vortex clustering in a shear layer has been investigated by means of flow visualizations within the context of the two-dimensional Navier-Stokes equations. The study shows that as many as five vortices can cluster together to form a long-lived bound state. This clustering is shown to enhance the shear layer growth drastically. A bound state of six vortices, on the other hand, is difficult to observe when the individual vortices are evolved from the fundamental. In this case, chaotic advection of vortices takes place and destroys the individual vortical structures, which can be diagnosed in terms of a new criterion for structural stability, a C factor
Homoclinic crossings and pattern selection
No full textThe correlations between a homoclinic orbit (HMO) and coherent patterns in the nonlinear Schrödinger model are discussed. In a Hamiltonian situation, two independent patterns are revealed to exist: One corresponds to a motion within an HMO, and the other outside of an HMO. The study further illustrates, when the Hamiltonian constraint is released, the significance of an HMO on the patterns dynamics by presenting the irregular HMO crossings and the resulting chaotic selections between the patterns. © 1990 The American Physical Society
Torus instability in an extended medium
No full textWe investigate the dynamics of quasiperiodic solution in a real flow. Here, a two-mode truncation of the Ginzburg-Landau equation is considered entailing a four-dimensional phase space. We analyze, in particular, the evolution and the instability of single-lobed tori observed in the phase space. One-dimensional return maps are used to investigate the basic characteristics of the dynamics
Significance of the tent map bifurcations in continuous media
No full textThis study provides an incidence where the dynamics of pattern selection is described by the bifurcations of a tent map. This study also shows that the tent map bifurcations in nonlinear systems are structurally stable, implying experimental observability
Complex hysteresis
No full textHysteresis typically refers to subcritical transitions between two stable attractors at two different values of a control parameter. We address here a different form of hysteresis, referred to as complex hysteresis, where a stable attractor and a chaotic attractor coexist. However, depending on the direction of variation of the control parameter, the chaotic state can be observed or cannot be observed. We address the phenomenon of complex hysteresis in one-dimensional maps as well as in a real flow. (c) 2005 Elsevier B.V. All rights reserved
Numerical simulation of the stability of steadily cooled flowing layer
No full textInitiation of longitudinal roll cell convection in a fully developed, steadily cooled flowing layer has been investigated. The upper free surface is subject to convective cooling and the rigid bottom is insulated. The critical Rayleigh number and the associated wavenumber are obtained as functions of the Prandtl number, the dimensionless mass flow rate of main flow and the Plot number at the upper surface. Linear stability theory is not valid in this case. The SIMPLER algorithm with periodic boundary condition is used to directly simulate the flow held numerically in an unsteady manner. In the region of steady bifurcation, the critical Rayleigh number is significantly greater than the results using the linear stability theory: However, when the Prandtl number is greater than 10, the linear stability theory is asymptotically valid, and the critical Rayleigh number and the associated wavenumber are very close to the results from the linear stability theory. Oscillatory motion, or Hopf bifurcation, occurs when the Prandtl number is less than 0.1. (C) 2000 Published by Elsevier Science Ltd
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