ISSN:
1619-6937
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
Notes:
Summary The nonlinear temporal stability of a viscous axisymmetric jet is studied with respect to axisymmetric disturbances. The weakly nonlinear Stuart Watson perturbation expansion is used to study the self interaction of the fundamental in a neighborhood of the critical Reynolds number (R c). The Landau constant is positive indicating there is a supercritical Hopf bifurcation. In order to extend these results pastR∼R c, a severely truncated Fourier modal expansion using the Stuart Watson functions to represent ther dependence, exponentials inz and unknown amplitudes in time is substituted into the Navier-Stokes equation. A projection onto an appropriate subspace leads to a low dimensional (five) system of amplitude equations for the disturbance of the fundamental, harmonic and distortion to the mean flow. Numerical results show that the periodic solution is stable for 55.3〈R〈72.3. There is a secondary bifurcation atR=72.3 to a quasiperiodic solution with 2 incommensurate frequenciesf 1 andf 2. Each peak in the Fourier spectrum can be indexed according tof=f 1+nf 2 forn=0,±1,±2,... AsR increases pastR=78 there is a transition through another periodic regime and then finally a transition to intermittency for 100〈R〈1000. No chaotic solutions were observed in this low dimensional model.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01170809
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