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HOMOCLINIC ORBITS IN TRANSITIONAL PLANE COUETTE FLOW
Lustro, Julius Rhoan T.,Kawahara, Genta,van Veen, Lennaert,Shimizu, Masaki Korea Society of Computational Fluids Engineering 2015 한국전산유체공학회지 Vol.20 No.4
Recent studies on wall-bounded shear flow have emphasized the significance of the stable manifold of simple nonlinear invariant solutions to the Navier-Stokes equation in the formation of the boundary between the laminar and turbulent regions in state space. In this paper we present newly discovered homoclinic orbits of the Kawahara and Kida(2001) periodic solution in plane Couette flow. We show that as the Reynolds number decreases a pair of homoclinic orbits move closer to each other until they disappear to exhibit homoclinic tangency.
Homoclinic Orbits in Minimal Plane Couette Flow
Julius Rhoan T. Lustro,Genta Kawahara,Lennaert van Veen,Masaki Shimizu 한국전산유체공학회 2014 한국전산유체공학회 학술대회논문집 Vol.2014 No.10
In wall-bounded shear flow recent studies have pointed the significance of the stable manifold of nonlinear simple invariant solutions, referred to as edge states, to the Navier-Stokes equation in the formation of the laminar-turbulent boundary. Here we present homoclinic orbits of the periodic edge state found by Kawahara and Kida[1] in plane Couette flow. It is observed that these homoclinic orbits collide and disappear to exhibit homoclinic tangency as the Reynolds number decreases.
HOMOCLINIC ORBITS IN TRANSITIONAL PLANE COUETTE FLOW
Julius Rhoan T. Lustro,Genta Kawahara,Lennaert van Veen,Masaki Shimizu 한국전산유체공학회 2015 한국전산유체공학회지 Vol.20 No.4
Recent studies on wall-bounded shear flow have emphasized the significance of the stable manifold of simple nonlinear invariant solutions to the Navier-Stokes equation in the formation of the boundary between the laminar and turbulent regions in state space. In this paper we present newly discovered homoclinic orbits of the Kawahara and Kida(2001) periodic solution in plane Couette flow. We show that as the Reynolds number decreases a pair of homoclinic orbits move closer to each other until they disappear to exhibit homoclinic tangency.