Feedback Control of Transitional Channel Flow using Balanced Proper Orthogonal Decomposition

2008 ◽  
Author(s):  
Milos Ilak ◽  
Clarence Rowley
Keyword(s):  
Feedback Control ◽  
Proper Orthogonal Decomposition ◽  
Channel Flow ◽  
Orthogonal Decomposition ◽  
Balanced Proper Orthogonal Decomposition ◽  
Proper Orthogonal

Proper Orthogonal Decomposition of Turbulent Channel Flow

2001 ◽  
pp. 473-478 ◽  
Author(s):  
Giancarlo Alfonsi ◽  
Leonardo Primavera ◽  
Giuseppe Passoni ◽  
Carlo Restano
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Orthogonal Decomposition ◽  
Proper Orthogonal

scholarly journals Spatio-temporal proper orthogonal decomposition of turbulent channel flow

2019 ◽  
Vol 864 ◽  
pp. 614-639 ◽  
Author(s):  
Srikanth Derebail Muralidhar ◽  
Bérengère Podvin ◽  
Lionel Mathelin ◽  
Yann Fraigneau
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Channel Flow ◽  
Nonlinear Effects ◽  
Turbulent Channel Flow ◽  
Wall Layer ◽  
Orthogonal Decomposition ◽  
Closed Form Expression ◽  
Temporal Decomposition ◽  
Spatio Temporal ◽  
Proper Orthogonal

An extension of proper orthogonal decomposition is applied to the wall layer of a turbulent channel flow ($Re_{\unicode[STIX]{x1D70F}}=590$), so that empirical eigenfunctions are defined in both space and time. Due to the statistical symmetries of the flow, the eigenfunctions are associated with individual wavenumbers and frequencies. Self-similarity of the dominant eigenfunctions, consistent with wall-attached structures transferring energy into the core region, is established. The most energetic modes are characterized by a fundamental time scale in the range 200–300 viscous wall units. The full spatio-temporal decomposition provides a natural measure of the convection velocity of structures, with a characteristic value of 12$u_{\unicode[STIX]{x1D70F}}$ in the wall layer. Finally, we show that the energy budget can be split into specific contributions for each mode, which provides a closed-form expression for nonlinear effects.

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