Corpus ID: 117978571

Is a Direct Numerical Simulation of Chaos or Turbulence Possible: A Study of a Model Non-Linearity

@article{Yao2005IsAD,
  title={Is a Direct Numerical Simulation of Chaos or Turbulence Possible: A Study of a Model Non-Linearity},
  author={L. Yao},
  journal={arXiv: Fluid Dynamics},
  year={2005}
}
  • L. Yao
  • Published 2005
  • Physics, Mathematics
  • arXiv: Fluid Dynamics
There are many subtle issues associated with solving the Navier-Stokes equations. In this paper, several of these issues, which have been observed previously in research involving the Navier-Stokes equations, are studied within the framework of the one-dimensional Kuramoto-Sivashinsky (KS) equation, a model nonlinear partial-differential equation. This alternative approach is expected to more easily expose major points and hopefully identify open questions that are related to the Navier-Stokes… Expand

References

SHOWING 1-10 OF 12 REFERENCES
Nonlinear instability of travelling waves with a continuous spectrum
Abstract The nonlinear evolution of a continuous spectrum of travelling waves resulting from the growth of unstable disturbances in fully-developed fluid flows is studied. The disturbance isExpand
A resonant wave theory
Analysis is used to show that a solution of the Navier–Stokes equations can be computed in terms of wave-like series, which are referred to as waves below. The mean flow is a wave of infinitely longExpand
Taylor-Couette Instability With a Continuous Spectrum
Nonlinear evolution of a continuous spectrum of unstable waves near the first bifurcation point in circular Couette flow has been investigated. The disturbance is represented by a Fourier integralExpand
Computed Chaos or Numerical Errors
  • L. Yao
  • Mathematics, Physics
  • 2005
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful toExpand
On the non-linear mechanics of wave disturbances in stable and unstable parallel flows Part 1. The basic behaviour in plane Poiseuille flow
This paper considers the nature of a non-linear, two-dimensional solution of the Navier-Stokes equations when the rate of amplification of the disturbance, at a given wave-number and Reynolds number,Expand
On the non-linear mechanics of wave disturbances in stable and unstable parallel flows Part 2. The development of a solution for plane Poiseuille flow and for plane Couette flow
In Part 1 by Stuart (1960), a study was made of the growth of an unstable infinitesimal disturbance, or the decay of a finite disturbance through a stable infinitesimal disturbance to zero, in planeExpand
Taylor-gortler vortices in fully developed or boundary-layer flows: Linear theory
The stability characteristics of some fluid flows at high Taylor or Gortler numbers are determined using perturbation methods. In particular, the stability characteristics of some fully developedExpand
Wave-number selection at finite amplitude in rotating Couette flow
Measurements have been made of the wavelength of Taylor vortices between rotating cylinders. It is shown that the relaxation time of such a vortex system is approximately L 2 /6 v , where L is theExpand
Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: analysis and computations
Abstract We evaluate several alternative methods for the approximation of inertial manifolds for the one-dimensional Kuramoto-Sivashinsky equation (KSE). A method motivated by the dynamics originallyExpand
TRANSITION IN CIRCULAR COUETTE FLOW
Two distinct kinds of transition have been identified in Couette flow between concentric rotating cylinders. The first, which will be called transition by spectral evolution, is characteristic ofExpand
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