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Three-dimensional dynamics and transition to turbulence in the wake of bluff objects. (English) Zbl 0754.76043
A 3-D wake flow behind a circular bluff body was investigated by a numerical simulation of the Navier-Stokes-equations with a high-order time accurate mixed spectral/spectral element method. The authors reported that at \(\text{Re}=175\) the introduced 3-D noise will die out and the flow will return to its 2-D state in their numerical experiments, but at \(\text{Re}=225\) the noise will be amplified in time and evolves into 3-D coherent structures. The computational results also show that the time trace of the \(w\)-component has a much stronger modulated form than that of the \(u\)- and \(v\)-components, which exhibit weaker modulation. Moreover, at \(\text{Re}=300\), the bifurcation in the wake flow occurs, which implies that the flow leads to a periodic state with an oscillation period twice the fundamental one exhibited at \(Re=225\). The occurrence of subharmonics of the fundamental frequency in the power- spectrum of the velocity signal means that there is a period-doubling bifurcation in the phase space. So, the key finding of this paper is that the route to chaos in a 3-D wake flow behind a stationary circular cylinder is the Feigenbaum scenario which has not been reported by others in the past. The paper also noted that the period-doubling bifurcation in the wake flow does not lead to merging of the vortex in the wake flow, but however still retains its basic coherent structures. The authors also found that the wake flow at \(\text{Re}=333\) is transitional, which was computed from the velocity field at \(\text{Re}=300\). When the Reynolds number is subsequently increased to \(\text{Re}=500\), then the simulation experiment reaches a turbulent field. But, the Reynolds number Re=300 of the transition to chaos by numerical simulation seems somehow to be larger than that of the present available experimental data, \(\text{Re}\simeq 185\). In addition, the Feigenbaum route from laminar state to chaos is only observed by experiments in the wake flow behind an oscillating circular cylinder. The cause of the difference between the computational results and the experimental data is still unknown.

76F10 Shear flows and turbulence
76F20 Dynamical systems approach to turbulence
76E99 Hydrodynamic stability
76D25 Wakes and jets
76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: DOI
[1] Chu, Theor. Comp. Fluid Dynamics 165 pp 79– (1991)
[2] DOI: 10.1017/S0022112082000044 · Zbl 0479.76056
[3] DOI: 10.1103/PhysRevLett.57.2157
[4] DOI: 10.1016/0021-9991(84)90128-1 · Zbl 0535.76035
[5] DOI: 10.1017/S0022112086003014 · Zbl 0596.76047
[6] DOI: 10.1017/S0022112064000726 · Zbl 0119.41703
[7] DOI: 10.1017/S0022112083000518 · Zbl 0556.76039
[8] DOI: 10.1146/annurev.fl.20.010188.002043
[9] DOI: 10.1016/S0889-9746(87)90323-9 · Zbl 0619.76052
[10] DOI: 10.1103/PhysRevLett.57.2160
[11] DOI: 10.1017/S0022112087002866 · Zbl 0638.76060
[12] DOI: 10.1017/S0022112088001181
[13] DOI: 10.1016/0021-8928(72)90163-3 · Zbl 0263.76037
[14] DOI: 10.1063/1.857473
[15] Lasheras, Phys. Fluids A2 pp 371– (1990)
[16] Konig, Phys. Fluids A2 pp 1607– (1990)
[17] DOI: 10.1016/0022-460X(85)90445-6
[18] Karniadakis, AIAA 199 pp 441– (1990)
[19] Karniadakis, J. Fluid Mech. 199 pp 441– (1989)
[20] DOI: 10.1016/0021-9991(91)90007-8 · Zbl 0738.76050
[21] Zores, Tech. Rep. 206 pp 579– (1989)
[22] Williamson, J. Fluid Mech. 206 pp 579– (1989)
[23] DOI: 10.1016/0168-9274(89)90056-1 · Zbl 0678.76050
[24] DOI: 10.1063/1.866925
[25] DOI: 10.1017/S0022112088001429
[26] Kaiktsis, J. Fluid Mech. 231 pp 521– (1991)
[27] DOI: 10.1063/1.864557 · Zbl 0548.76051
[28] DOI: 10.1016/0021-9991(87)90035-0 · Zbl 0617.76062
[29] DOI: 10.1017/S0022112086000976
[30] DOI: 10.1063/1.857716
[31] DOI: 10.1146/annurev.fl.20.010188.002415
[32] Hanneman, J. Fluid Mech. 199 pp 55– (1989)
[33] DOI: 10.1063/1.857306
[34] DOI: 10.1002/fld.1650040703 · Zbl 0559.76031
[35] DOI: 10.1007/BF01061059
[36] Feigenbaum, Phys. Lett. 74A pp 375– (1979)
[37] DOI: 10.1007/BF01020332 · Zbl 0509.58037
[38] Strykowski, J. Fluid Mech. 218 pp 71– (1990)
[39] Squire, Proc. R. Soc. Lond. 142 pp 621– (1933)
[40] Deane, Phys. Fluids 3 pp 2337– (1991) · Zbl 0746.76021
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