The dynamical behaviors of coherent structures in countercurrent axisymmetric shear flows are experimentally studied.The forward velocity U1 and the velocity ratio R=(U1-U2)/(U1+U2),where U2 denotes the suction veloci...The dynamical behaviors of coherent structures in countercurrent axisymmetric shear flows are experimentally studied.The forward velocity U1 and the velocity ratio R=(U1-U2)/(U1+U2),where U2 denotes the suction velocity,are consldered as the control parameters.Two kinds of vortex structures,i.e.,axisymmetric and helical structures,were discovered with respect to different reginmes in the R versus U1 diagram .In the case of U1 rangjing from 3 to 20m/s and R from 1 to 3,the axisymmetric structures plan an important role.Based on the dynamical behaviors of axisymmetric structures,a critical forward velocity U1cr=6.8m/s was defined,subsequently,the subcritical velocity regime:U1>U1cr and the supercritical velocity regime:U1<U1er,In the subcritical velocity regine,the flow system contains shear layer self-excited oscillations in a certain range of the velocity ratio with respect to any forward velocity.In the supercritical velocity regime,the effect of the velocity ratio could be explained by the relative movement and the spatial evolution of the axisymmetric structure undergoes the following stages:(1) Kelvin-Helmholtz instability leading to vortex rolling up,(2) first time vortex agglomeration.(3) jet colunn self-excited oscillation,(4) shear layer self-excited oscillation,(5)"ordered tearing",(6) turbulence in the case of U1<4m/s (the "ordered tearing" does not exist when U1>4m/s),correspondingly,the spatial evolution of the temporal asymptotic behavior of a dynamical system can be described as follows:(1) Hopt bifurcation,(5) chaos("weak turbulence")in the case of U1<4m/s(superharmonic bifurcation does not exist when U1>4m/s).The proposed new terms,superharmonic and reversed superbarmonic bifurcations,are characterized of the frequency doubling rather than the period doubling.A kind of unfamiliar vortices referred to as the helical structure was discovered experimentally when the forward velocity around 2m/s and the velocity range from 1.1 to 2.3,There are two base frequencies contained in the flow system and they could coexist as indicated by the Wigner-Ville-Distribution and the temporal asymptotic behavior of the dynamical system corresponding to the helical vortex could be described as 2-torus as indicted by the 3D reconstructed phase trajectory and correlation dimension.The scenario of the spatial evolution of helical structures could be described as follows:the jet column is separated into two parts at a certain spatial location and they entangle each other to form the helical vortex until the occurrence of those separated jet columns to reconnect further downstream with the result that the flow system evolves into turbulence in a catastrophic form.Correspondingly,the dynamical system evolves directly into 2-tiorus through the supercritical Hopf bifurcation followed by a transition from a quasi-periodic attractor to a strange attractor.In the case of U1=2m/s,the parametric evolution of the temporal asymptotic behavior of the dynamical system as the velocity ratio increases from 1 to 3 could be described as follows:(1)2-torus(Hopf bifurcation),(2) limit cycle(reversed Hopf bifurcation),(3) strange attractor (subbarmonic bifurcation).展开更多
The coherent structures and the chaotic phenomena in the transition of the axisymmetric countercurrent mixing shear flow were investigated experimentally. Two kinds of self-excited oscillation modes could exist in the...The coherent structures and the chaotic phenomena in the transition of the axisymmetric countercurrent mixing shear flow were investigated experimentally. Two kinds of self-excited oscillation modes could exist in the axisymmetric countercurrent mixing shear flow. One is the shear layer self-excited oscillation mode corresponding to the high Reynolds number regime and the other is the jet column self-excited oscillation mode corresponding to the low Reynolds number regime in the case of the velocity ratio ranging from I to 1.5. Analyzing the auto-power spectrum, self-correlation-function and three dimensional reconstructed phase trajectory, the route to chaos through three Hopf bifurcations intercepted by an intermittence of the dynamical system corresponding to the axisymmetric countercurrent mixing shear flow was discovered when the velocity ratio is equal to 1.32.展开更多
文摘The dynamical behaviors of coherent structures in countercurrent axisymmetric shear flows are experimentally studied.The forward velocity U1 and the velocity ratio R=(U1-U2)/(U1+U2),where U2 denotes the suction velocity,are consldered as the control parameters.Two kinds of vortex structures,i.e.,axisymmetric and helical structures,were discovered with respect to different reginmes in the R versus U1 diagram .In the case of U1 rangjing from 3 to 20m/s and R from 1 to 3,the axisymmetric structures plan an important role.Based on the dynamical behaviors of axisymmetric structures,a critical forward velocity U1cr=6.8m/s was defined,subsequently,the subcritical velocity regime:U1>U1cr and the supercritical velocity regime:U1<U1er,In the subcritical velocity regine,the flow system contains shear layer self-excited oscillations in a certain range of the velocity ratio with respect to any forward velocity.In the supercritical velocity regime,the effect of the velocity ratio could be explained by the relative movement and the spatial evolution of the axisymmetric structure undergoes the following stages:(1) Kelvin-Helmholtz instability leading to vortex rolling up,(2) first time vortex agglomeration.(3) jet colunn self-excited oscillation,(4) shear layer self-excited oscillation,(5)"ordered tearing",(6) turbulence in the case of U1<4m/s (the "ordered tearing" does not exist when U1>4m/s),correspondingly,the spatial evolution of the temporal asymptotic behavior of a dynamical system can be described as follows:(1) Hopt bifurcation,(5) chaos("weak turbulence")in the case of U1<4m/s(superharmonic bifurcation does not exist when U1>4m/s).The proposed new terms,superharmonic and reversed superbarmonic bifurcations,are characterized of the frequency doubling rather than the period doubling.A kind of unfamiliar vortices referred to as the helical structure was discovered experimentally when the forward velocity around 2m/s and the velocity range from 1.1 to 2.3,There are two base frequencies contained in the flow system and they could coexist as indicated by the Wigner-Ville-Distribution and the temporal asymptotic behavior of the dynamical system corresponding to the helical vortex could be described as 2-torus as indicted by the 3D reconstructed phase trajectory and correlation dimension.The scenario of the spatial evolution of helical structures could be described as follows:the jet column is separated into two parts at a certain spatial location and they entangle each other to form the helical vortex until the occurrence of those separated jet columns to reconnect further downstream with the result that the flow system evolves into turbulence in a catastrophic form.Correspondingly,the dynamical system evolves directly into 2-tiorus through the supercritical Hopf bifurcation followed by a transition from a quasi-periodic attractor to a strange attractor.In the case of U1=2m/s,the parametric evolution of the temporal asymptotic behavior of the dynamical system as the velocity ratio increases from 1 to 3 could be described as follows:(1)2-torus(Hopf bifurcation),(2) limit cycle(reversed Hopf bifurcation),(3) strange attractor (subbarmonic bifurcation).
文摘The coherent structures and the chaotic phenomena in the transition of the axisymmetric countercurrent mixing shear flow were investigated experimentally. Two kinds of self-excited oscillation modes could exist in the axisymmetric countercurrent mixing shear flow. One is the shear layer self-excited oscillation mode corresponding to the high Reynolds number regime and the other is the jet column self-excited oscillation mode corresponding to the low Reynolds number regime in the case of the velocity ratio ranging from I to 1.5. Analyzing the auto-power spectrum, self-correlation-function and three dimensional reconstructed phase trajectory, the route to chaos through three Hopf bifurcations intercepted by an intermittence of the dynamical system corresponding to the axisymmetric countercurrent mixing shear flow was discovered when the velocity ratio is equal to 1.32.
基金Projects support by National Nature Science Foundation of China(11172069)undergraduate key reform project Curriculum system of theories and applications of modern continuum mechanics issued by Shanghai Municipal Education Commission in 2011
