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Shear-flow transition: the basin boundary

Shear-flow transition: the basin boundary,Norman R. Lebovitz

Shear-flow transition: the basin boundary   (Citations: 3)
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The structure of the basin of attraction of a stable equilibrium point is investigated for a dynamical system (W97) often used to model transition to turbulence in shear flows. The basin boundary contains not only an equilibrium point Xlb but also a periodic orbit P, and it is the latter that mediates the transition. Orbits starting near Xlb relaminarize. We offer evidence that this is due to the extreme narrowness of the region complementary to basin of attraction in that part of phase space near Xlb. This leads to a proposal for interpreting the 'edge of chaos' in terms of more familiar invariant sets.
Published in 2009.
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    • ...Fig. 4 Figure from [7] representing the basin of the laminar solution for W97 in the hyperplane u = u0, m = m0; the point T = (u0 ,v 0 ,w 0, m0) is the critical disturbance identified in [6] for the W97 model, B indicates the attraction basin of the origin and C its complement...
    • ...The W97 model was investigated in detail in [7], where the structure of the basin boundary of the laminar solution is identified by calculating slices of it by two-dimensional hyperplanes in the phase space at Re = 140 and Re = 190...

    Simone Camarriet al. Further generalized energies for the application of an energy criterio...

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