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Controlling the onset of turbulence by streamwise travelling waves. Part 1. Receptivity analysis

Published online by Cambridge University Press:  08 September 2010

RASHAD MOARREF  and
MIHAILO R. JOVANOVIĆ
RASHAD MOARREF
Affiliation:
Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA
MIHAILO R. JOVANOVIĆ*
Affiliation:
Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email address for correspondence: mihailo@umn.edu
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Abstract

We examine the efficacy of streamwise travelling waves generated by a zero-net-mass-flux surface blowing and suction for controlling the onset of turbulence in a channel flow. For small-amplitude actuation, we utilize a weakly nonlinear analysis to determine base-flow modifications and assess the resulting net power balance. Receptivity analysis of the velocity fluctuations around this base flow is then employed to design the travelling waves. Our simulation-free approach reveals that, relative to the flow with no control, the downstream travelling waves with properly designed speed and frequency can significantly reduce receptivity, which makes them well suited for controlling the onset of turbulence. In contrast, the velocity fluctuations around the upstream travelling waves exhibit larger receptivity to disturbances. Our theoretical predictions, obtained by perturbation analysis (in the wave amplitude) of the linearized Navier–Stokes equations with spatially periodic coefficients, are verified using full-scale simulations of the nonlinear flow dynamics in the companion paper (Lieu et al., J. Fluid Mech., 2010, doi:10.1017/S002211201000340X).

JFM classification

Flow Control: Flow Control Instability: Transition to turbulence

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 663 , 25 November 2010 , pp. 70 - 99
Copyright
Copyright © Cambridge University Press 2010

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