caa a22 4500 469081546 CHVBK 20180323132951.0 cr unu---uuuuu 170328e19920301xx s 000 0 eng 10.1007/BF01170809 doi (NATIONALLICENCE)springer-10.1007/BF01170809 Nonlinear stability of a viscous axisymmetric jet [Elektronische Daten] [J. Horwitz, S. Rosenblat] 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. Springer-Verlag, 1992 Horwitz J. Department of Mathematics, Illinois Institute of Technology, 60616, Chicago, IL, USA aut Rosenblat S. Department of Mathematics, Illinois Institute of Technology, 60616, Chicago, IL, USA aut Acta Mechanica Springer-Verlag 95/1-4(1992-03-01), 131-156 0001-5970 95:1-4<131 1992 95 707 https://doi.org/10.1007/BF01170809 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01170809 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Horwitz J. Department of Mathematics, Illinois Institute of Technology, 60616, Chicago, IL, USA aut NATIONALLICENCE 700 1- Rosenblat S. Department of Mathematics, Illinois Institute of Technology, 60616, Chicago, IL, USA aut NATIONALLICENCE 773 0- Acta Mechanica Springer-Verlag 95/1-4(1992-03-01), 131-156 0001-5970 95:1-4<131 1992 95 707 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer