COHERENT STRUCTURES IN DEVELOPING FLOW OVER A WAVY WALL

The present study focuses on the case of developing flow with in a channel containing a long array of sinusoidal waves (2a/${\lambda}$=0.1, ${\lambda}$=h, ${\lambda}$ is the wavelength, 2a is the wave height, h is the mean channel depth) at the bottom wall. The Reynolds number defined with channel height, h and the mean velocity, U, is Re=6,700. The channel is sufficiently long such that transition is completed and the flow is fully developed over the downstream half of the channel. For the case of an incoming steady flow with no resolved turbulence, the instantaneous flow fields in the transition region are characterized by the formation of arrays of highly-organized large-scale hairpin vortices whose dimensions scale with that of the roughness elements. The paper explains the mechanism for the formation of these arrays of hairpin vortices and shows these eddies play the primary role in the formation of the large-scale streaks of high and low velocity over the wavy wall region. The presence of resolved turbulence in the incoming flow, reduces the streamwise distance needed for the streaks to develop over the wavy region, but does not affect qualitatively the transition process. In the fully-developed region, isolated and trains of large-scale hairpins play an important role in the dynamics of the streaks over the wavy wall.

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