Bifurcation Cascade in a Diverging Flow

  • Vladimir Shtern
  • Fazle Hussain
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


We study the nonlinear instability of a radially divergent flow and find a bifurcation cascade that corresponds to the subsequent halving of length scales of the disturbance motion like in the (inverse) Feigenbaum and the Richardson-Kolmogorov cascades. The initial axisymmetric flow is driven by surface stresses and related to the Marangoni convention in the half-space of viscous incompressible fluid with a high Prandtl number. The cascade causes splitting of the initial flow into m = 2n, n = 1,2,…, radial near-surface jets separated by inflows at the critical Reynolds number (defined as the product of the mean radial velocity at the surface and the distance from the origin divided by the velocity) Re * = 46 * 4 n as n tends to infinity. The derived boundary layer equations are found to be invariant to the scaling transformation.


Radial Velocity Critical Reynolds Number Marangoni Convection Axisymmetric Flow Disturbance Motion 
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Copyright information

© Springer-Verlag, Berlin Heidelberg 1994

Authors and Affiliations

  • Vladimir Shtern
    • 1
  • Fazle Hussain
    • 1
  1. 1.University of HoustonHoustonUSA

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