Low dimensional models, the minimal flow unit and control

1999 ◽  
pp. 57-66 ◽  
Author(s):  
J. L. Lumley ◽  
P. N. Blossey ◽  
B. Podvin-Delarue
Keyword(s):  
Flow Unit ◽  
Minimal Flow ◽  
Dimensional Models ◽  
Low Dimensional ◽  
And Control

A low-dimensional approach for the minimal flow unit

1998 ◽  
Vol 362 ◽  
pp. 121-155 ◽  
Author(s):  
BÉRENGÈRE PODVIN ◽  
JOHN LUMLEY
Keyword(s):  
Turbulent Channel Flow ◽  
Dynamical Behaviour ◽  
Flow Unit ◽  
Minimal Flow ◽  
Dimensional Parameters ◽  
Dimensional Models ◽  
Modelling Assumptions ◽  
Low Dimensional ◽  
Proper Orthogonal ◽  
The Relationship

The proper orthogonal decomposition (POD) is applied to the minimal flow unit (MFU) of a turbulent channel flow. Our purpose is to establish a numerical validation of low-dimensional models based on the POD. The simplest (two-mode) model possible is built for the simplified flow in the minimal unit. The dynamical behaviour predicted by the model is compared with that actually occurring in the direct numerical simulation of the flow. The various modelling assumptions which underlie the construction of low-dimensional models are examined and confronted with numerical evidence. The relationship between intermittency in the MFU and intermittent low-dimensional parameters is investigated closely. The agreement observed is quite satisfactory, especially given the crudeness of the truncation considered. To further demonstrate the adequacy of the model, we develop a dynamical filtering procedure to recover information from realistic (partial) measurements. The success obtained illustrates the versatility of the low-dimensional paradigm.

Low Dimensional Models, Wavelet Transforms and Control

1996 ◽  
pp. 271-331 ◽  
Author(s):  
N. Aubry ◽  
G. Berkooz ◽  
B. Coller ◽  
J. Elezgaray ◽  
P. Holmes ◽  
...  
Keyword(s):  
Wavelet Transforms ◽  
Dimensional Models ◽  
Low Dimensional ◽  
And Control

Reduced Order Modelling in Nonlinear Mechanical Oscillators With Energy Pumping

2005 ◽  
Author(s):  
Xianghong Ma ◽  
Alexander F. Vakakis ◽  
Lawrence A. Bergman
Keyword(s):  
Dimensional Model ◽  
Reduced Order ◽  
Energy Pumping ◽  
Weakly Coupled ◽  
Nonlinear Mechanical ◽  
Dimensional Models ◽  
Mechanical Oscillators ◽  
Low Dimensional ◽  
Nonlinear Components ◽  
And Control

Energy pumping in nonlinear mechanical oscillators has been discovered and studied in mechanical systems consisting of weakly coupled, linear and nonlinear components [1–3]. In this paper this phenomenon is further studied and numerically verified on an 11 degree of freedom system. It also presents a technique to create low dimensional models for energy pumping systems using the Karhunen-Loeve (K-L) decomposition method. It is shown that energy pumping can be identified from the dominant K-L modes. The low dimensional models are used to reconstruct the system responses. From the comparisons between the reconstructed and simulated response, we can see that the K-L mode-based low-dimensional model can represent the system responses; it can be used for monitoring, diagnosis and control purposes.

scholarly journals Low-dimensional models of subcritical transition to turbulence

1997 ◽  
Vol 9 (4) ◽  
pp. 1043-1053 ◽  
Author(s):  
Jeffrey S. Baggett ◽  
Lloyd N. Trefethen
Keyword(s):  
Transition To Turbulence ◽  
Dimensional Models ◽  
Low Dimensional
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