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A STREAMWISE-CONSTANT MODEL OF TURBULENT PIPE FLOW

Jean-Loup Bourguignon
Graduate Aerospace Laboratories California Institute of Technology 1200 E. California Blvd, Pasadena, California 91125, U.S.A.

Beverley J. McKeon
Department of Aeronautics, Imperial College London, SW7 2AZ, UK; Graduate Aerospace Laboratories California Institute of Technology Pasadena, CA 91125, USA

Аннотация

We present a streamwise-constant model of turbulent pipe flow forced by stochastic noise and focus particularly on the influence of the no-slip boundary condition in the azimuthal direction on the flow behavior. With a no-slip boundary condition at the wall, our model captures the formation of "streamwise-constant puffs", so-called due to the good agreement between the temporal evolution of their velocity field and the projection of the velocity field associated with three-dimensional puffs in a frame of reference moving at the bulk velocity. The three-dimensional puffs were observed experimentally by Hof et al. (2004) and Nishi et al. (2008), and simulated numerically by Shimizu & Kida (2009). When we allow for slip in the azimuthal direction, we no longer observe the quasi-periodic generation of puffs, instead the flow stays away from the laminar state for extended periods of time. We observe that, for a given forcing amplitude, a larger blunting of the velocity profile is realized when we allow for slip in the azimuthal direction and we relate this larger amplification to the existence of self-sustained solutions of the linearized streamfunction equation with slip at the wall.