3 edition of Hopf bifurcation in the driven cavity found in the catalog.
Hopf bifurcation in the driven cavity
John W. Goodrich
by NASA, NASA Lewis Research Center, Institute for Computational Mechanics in Propulsion, For sale by the National Technical Information Service in [Washington, D.C.], [Cleveland, Ohio], [Springfield, Va
Written in English
|Statement||John W. Goodrich, Karl Gustafson, and Kadosha Halasi.|
|Series||NASA technical memorandum -- 102334.|
|Contributions||Gustafson, Karl E., Halasi, Kadosa., United States. National Aeronautics and Space Administration., Lewis Research Center. Institute for Computational Mechanics in Propulsion.|
|The Physical Object|
Moreover, the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are established. Our method is based on the center manifold theory. For the model with no-flux boundary conditions, the diffusion-driven instability of the interior equilibrium is studied. Discussions On Driven Cavity Flow Ercan Erturk Gebze Institute of Technology, the bifurcation of the flow in a driven cavity from a steady regime to an unsteady regime is studied. In these studies a hydrodynamic stability analysis is done and the Reynolds numbers at which a Hopf bifurcation occurs in the flow are presented. Email.
2D lid-driven cavity, from stable linear dynamics to chaotic dynamics. Historically, the rst Hopf bifurcation, characterized by the appearance of a limit cycle, has re-ceived a great deal of attention (Peng et al.,;Shen,;Shankar & Deshpande, ). This paper will characterize a ow’s progression from limit cycle periodicity. Based upon these computations we conclude that a Hopf bifurcation does occur in the aspect ratio two driven cavity for a critical Reynolds number Rec.
Global stability of a lid-driven cavity with through-flow: Flow visualization studies. Phys. Fluids. v3 i9. Google Scholar; 2. Cavity flow dynamics at higher Reynolds number and higher aspect ratio. J. Comput. Phys. v Google Scholar; 3. Hopf bifurcation of the unsteady regularized driven cavity flow. J. Comput. Phys. v The Hopf bifurcation in planar RDEs with small bounded noise is described in the following result. Theorem Consider a family of RDEs depending on one parameter λ, that unfolds, when ε = 0, a supercritical Hopf bifurcation at λ = 0. For small ε > 0 and λ near 0, there is a unique MFI set E λ. There is a single hard bifurcation at λ.
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(PDF) Hopf bifurcation in the driven cavity | Kadosa Halasi - Incompressible two dimensional calculations are reported for the impulsively started lid driven cavity with aspect ratio two.
The algorithm is based on the time dependent streamfunction equation, with a Crank-Nicolson differencing scheme for the. (PDF) Hopf bifurcation in the driven cavity | Kadosa Halasi - is a platform for academics to share research papers.
Based upon these computations we conjecture that the Navier-Stokes equations for the aspect ratio two driven cavity possess a Hopf bifurcation in the driven cavity book bifurcation in the interval ^ Re, since the transition has been computationally by: Abstract To date, there are very few studies on the second Hopf bifurcation in a driven square cavity, although there are intensive investigations focused on the first Hopf bifurcation in literature, due to the difficulties of theoretical analyses and numerical : Tao Wang, Tiegang Liu, Zheng Wang.
Hopf's basic paper  appeared in Although the term "Poincare Andronov-Hopf bifurcation" is more accurate (sometimes Friedrichs is also included), the name "Hopf Bifurcation" seems more common, so we have used it. Hopf's crucial contribution was the extension from two dimensions to higher : Springer-Verlag New York.
The second Hopf bifurcation in lid-driven square cavity Tao Wang et al-Linear instability of the lid-driven flow in a cubic cavity Alexander Yu.
Gelfgat-This content was downloaded from IP address on 06/04/ at Bifurcation analysis of steady-state ﬂows in. Theory And Application Of Hopf Bifurcation book. Read reviews from world’s largest community for readers. The Hopf Bifurcation' describes a phenomenon th /5(1). The procedure to determine the threshold of Hopf bifurcation is the same as that used to compute the threshold of overstabilities in the previous sections for an infinite layer.
For this situation, the basic solution Ψ b; T b, and S b is given by equation ().To validate the present numerical procedure, the results of Kimura et al.
() for thermal convection are considered. The system has a Hopf bifurcation at µ = 0. We have ω = −1, d = 1 2 and a = −1 8, so the bifurcation is supercritical and there is a stable isolated periodic orbit (limit cycle) if µ > 0 for each suﬃciently small µ (see Fig.
Hopf bifurcation for maps There is a discrete-time counterpart of the Hopf bifurcation. It occurs when a. unstable equilibrium point, the bifurcation is called a supercritical Hopf bifurcation.
If the limit cycle is unstable and surrounds a stable equilibrium point, then the bifurcation is called a subcritical Hopf bifurcation (cf. , p. Before stating the theorem, we look at an example of a Hopf bifurcation on a two-dimensional. Get this from a library.
Hopf bifurcation in the driven cavity. [John W Goodrich; Karl E Gustafson; Kadosa Halasi; United States. National Aeronautics and Space Administration.; Lewis Research Center. Institute for Computational Mechanics in Propulsion.]. driven cavity flow. We presented there some preliminary results which indicated that Hopf bifurcations occurred at Re = 12, Due to a limitation of the computing source, the approximating solutions presented there had not been developed in final asymptotic states.
In this paper, we continue the investigation. A Hopf bifurcation arises when these two eigenvalues cross the imaginary axis because of a variation of the system parameters.
Routh–Hurwitz criterion [ edit ] Routh–Hurwitz criterion (section I of ) gives necessary conditions so that a Hopf bifurcation occurs.
Abstract Abstract Two-dimensional (2D) flow inside a lid driven cavity (LDC) is shown to display multi-modal behavior in a consistent manner. Hopf bifurcation in the driven cavity.
By Kadosa Halasi, Karl Gustafson and John W. Goodrich. Abstract. The algorithm employed in the present incompressible two-dimensional calculations of an impulsively-started lid-driven cavity has its basis in the time-dependent stream-function equation.
While a Crank-Nicholson differencing scheme is used. Then, utilizing bifurcation analysis on the system of ODE’s, we succeeded in establishing the early transition to an oscillatory motion as a supercritical Hopf-bifurcation, and in particular we also estimated the critical Reynolds number within % of the Reynolds number due to the full numerical system in degrees of freedom.
Hopf Bifurcation of the Unsteady Regularized Driven Cavity Flow. Shen, Jie. Abstract. A numerical simulation of the unsteady incompressible flow in the unit cavity is performed by using a Chebyshev-Tau approximation for the space variables. referred to as the Hopf bifurcation with applications to spe cific problems, including stability calculations.
Historical ly, the subject had its origins in the works of Poincare  around and was extensively discussed by Andronov and Witt  and their co-workers starting around Hopf's basic paper  appeared in Rich and complex buoyancy-driven flow field due to natural convection will be studied numerically over a wide range of Rayleigh numbers in a cubic cavity by virtue of the simulated bifurcation.
hopf bifurcation unsteady regularized driven cavity flow reynolds number critical value reliable result unsteady incompressible flow stationary state unit cavity space variable moderate number condensed distribution high accuracy high reynolds number chebyshev-tau approximation spectral method re re2 time periodicity numerical simulation.
Abstract A comprehensive study of the two-dimensional incompressible shear-driven flow in an open square cavity is carried out. Two successive bifurcations lead to two limit cycles with different frequencies and different numbers of structures which propagate along the top of the cavity and circulate in its interior.A numerical study is performed on the flow of an incompressible fluid driven in a square cavity.
The behavior of unsteady flows beyond the first Hopf bifurcation is investigated. The first Hopf bifurcation is localized at Re cr1 =±% with the fundamental frequency f B =, in good agreement with the previous studies.The `Hopf Bifurcation' describes a phenomenon that occurs widely in nature: the birth of a family of oscillations as a controlling parameter is varied.