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@article{Papadakis:2016:10.1103/PhysRevFluids.1.043501,
author = {Papadakis, G and Lu, L and Ricco, P},
doi = {10.1103/PhysRevFluids.1.043501},
journal = {Physical Review Fluids},
title = {Closed-loop control of boundary layer streaks induced by free-stream turbulence},
url = {http://dx.doi.org/10.1103/PhysRevFluids.1.043501},
volume = {1},
year = {2016}
}

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TY  - JOUR
AB  - The central aim of the paper is to carry out a theoretical and numerical study of active wall transpiration control of streaks generated within an incompressible boundary layer by free-stream turbulence. The disturbance flow model is based on the linearized unsteady boundary-region (LUBR) equations, studied by Leib, Wundrow, and Goldstein [J. Fluid Mech. 380, 169 (1999)], which are the rigorous asymptotic limit of the Navier-Stokes equations for low-frequency and long-streamwise wavelength. The mathematical formulation of the problem directly incorporates the random forcing into the equations in a consistent way. Due to linearity, this forcing is factored out and appears as a multiplicative factor. It is shown that the cost function (integral of kinetic energy in the domain) is properly defined as the expectation of a random quadratic function only after integration in wave number space. This operation naturally introduces the free-stream turbulence spectral tensor into the cost function. The controller gains for each wave number are independent of the spectral tensor and, in that sense, universal. Asymptotic matching of the LUBR equations with the free-stream conditions results in an additional forcing term in the state-space system whose presence necessitates the reformulation of the control problem and the rederivation of its solution. It is proved that the solution can be obtained analytically using an extension of the sweep method used in control theory to obtain the standard Riccati equation. The control signal consists of two components, a feedback part and a feed-forward part (that depends explicitly on the forcing term). Explicit recursive equations that provide these two components are derived. It is shown that the feed-forward part makes a negligible contribution to the control signal. We also derive an explicit expression that a priori (i.e., before solving the control problem) leads to the minimum of the objective cost function (i.e., the fundamental pe
AU  - Papadakis,G
AU  - Lu,L
AU  - Ricco,P
DO  - 10.1103/PhysRevFluids.1.043501
PY  - 2016///
SN  - 2469-990X
TI  - Closed-loop control of boundary layer streaks induced by free-stream turbulence
T2  - Physical Review Fluids
UR  - http://dx.doi.org/10.1103/PhysRevFluids.1.043501
UR  - http://hdl.handle.net/10044/1/34245
VL  - 1
ER  -

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