Edge states for the turbulence transition in the asymptotic suction boundary layer
We demonstrate the existence of an exact invariant solution to the Navier–Stokes equations for the asymptotic suction boundary layer. The identified periodic orbit with a very long period of several thousand advective time units is found as a local dynamical attractor embedded in the stability bound...
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| Veröffentlicht in: | Journal of fluid mechanics 2013-07, Vol.726, p.100-122 |
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| container_title | Journal of fluid mechanics |
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| creator | Kreilos, Tobias Veble, Gregor Schneider, Tobias M. Eckhardt, Bruno |
| description | We demonstrate the existence of an exact invariant solution to the Navier–Stokes equations for the asymptotic suction boundary layer. The identified periodic orbit with a very long period of several thousand advective time units is found as a local dynamical attractor embedded in the stability boundary between laminar and turbulent dynamics. Its dynamics captures both the interplay of downstream-oriented vortex pairs and streaks observed in numerous shear flows as well as the energetic bursting that is characteristic for boundary layers. By embedding the flow into a family of flows that interpolates between plane Couette flow and the boundary layer, we demonstrate that the periodic orbit emerges in a saddle–node infinite-period (SNIPER) bifurcation of two symmetry-related travelling-wave solutions of plane Couette flow. Physically, the long period is due to a slow streak instability, which leads to a violent breakup of a streak associated with the bursting and the reformation of the streak at a different spanwise location. We show that the orbit is structurally stable when varying both the Reynolds number and the domain size. |
| doi_str_mv | 10.1017/jfm.2013.212 |
| format | Article |
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The identified periodic orbit with a very long period of several thousand advective time units is found as a local dynamical attractor embedded in the stability boundary between laminar and turbulent dynamics. Its dynamics captures both the interplay of downstream-oriented vortex pairs and streaks observed in numerous shear flows as well as the energetic bursting that is characteristic for boundary layers. By embedding the flow into a family of flows that interpolates between plane Couette flow and the boundary layer, we demonstrate that the periodic orbit emerges in a saddle–node infinite-period (SNIPER) bifurcation of two symmetry-related travelling-wave solutions of plane Couette flow. Physically, the long period is due to a slow streak instability, which leads to a violent breakup of a streak associated with the bursting and the reformation of the streak at a different spanwise location. 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Fluid Mech</addtitle><description>We demonstrate the existence of an exact invariant solution to the Navier–Stokes equations for the asymptotic suction boundary layer. The identified periodic orbit with a very long period of several thousand advective time units is found as a local dynamical attractor embedded in the stability boundary between laminar and turbulent dynamics. Its dynamics captures both the interplay of downstream-oriented vortex pairs and streaks observed in numerous shear flows as well as the energetic bursting that is characteristic for boundary layers. By embedding the flow into a family of flows that interpolates between plane Couette flow and the boundary layer, we demonstrate that the periodic orbit emerges in a saddle–node infinite-period (SNIPER) bifurcation of two symmetry-related travelling-wave solutions of plane Couette flow. Physically, the long period is due to a slow streak instability, which leads to a violent breakup of a streak associated with the bursting and the reformation of the streak at a different spanwise location. 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Fluid Mech</addtitle><date>2013-07-10</date><risdate>2013</risdate><volume>726</volume><spage>100</spage><epage>122</epage><pages>100-122</pages><issn>0022-1120</issn><eissn>1469-7645</eissn><coden>JFLSA7</coden><abstract>We demonstrate the existence of an exact invariant solution to the Navier–Stokes equations for the asymptotic suction boundary layer. The identified periodic orbit with a very long period of several thousand advective time units is found as a local dynamical attractor embedded in the stability boundary between laminar and turbulent dynamics. Its dynamics captures both the interplay of downstream-oriented vortex pairs and streaks observed in numerous shear flows as well as the energetic bursting that is characteristic for boundary layers. By embedding the flow into a family of flows that interpolates between plane Couette flow and the boundary layer, we demonstrate that the periodic orbit emerges in a saddle–node infinite-period (SNIPER) bifurcation of two symmetry-related travelling-wave solutions of plane Couette flow. Physically, the long period is due to a slow streak instability, which leads to a violent breakup of a streak associated with the bursting and the reformation of the streak at a different spanwise location. We show that the orbit is structurally stable when varying both the Reynolds number and the domain size.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/jfm.2013.212</doi><tpages>23</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Asymptotic properties Boundary layer Boundary layers Exact sciences and technology Fluid dynamics Fluid flow Fundamental areas of phenomenology (including applications) Navier-Stokes equations Physics Streak Transition to turbulence Turbulence Turbulent flow Turbulent flows, convection, and heat transfer |
| title | Edge states for the turbulence transition in the asymptotic suction boundary layer |
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