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  • 1
    Electronic Resource
    Electronic Resource
    Lagrangian and Eulerian view of the bursting period (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 433-437 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Low-dimensional models for the turbulent wall layer display an intermittent phenomenon with an ejection phase and a sweep phase that strongly resembles the bursting phenomenon observed in experimental flows. The probability distribution of inter-burst times has the observed shape [E. Stone and P. J. Holmes, Physica D 37, 20 (1989); SIAM J. Appl. Math. 50, 726 (1990); Phys. Lett. A 5, 29 (1991); P. J. Holmes and E. Stone, in Studies in Turbulence, edited by T. B. Gatski, S. Sarkar, and C. G. Speziale (Springer, Heidelberg, 1992)]. However, the time scales both for bursts and interburst durations are unrealistically long, a fact that was not appreciated until recently. We believe that the long time scales are due to the model's inclusion of only a single coherent structure, when in fact a succession of quasi-independent structures are being swept past the sensor in an experiment. A simple statistical model of this situation restores the magnitude of the observed bursting period, although there is a great deal of flexibility in the various parameters involved. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869137
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  • 2
    Electronic Resource
    Electronic Resource
    Low-order models for the flow in a differentially heated cavity (2001)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 13 (2001), S. 3204-3214 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The proper orthogonal decomposition (P.O.D.) is applied to the flow in a differentially heated cavity. The fluid considered is air, and the aspect ratio of the cavity is 4. At a fixed Rayleigh number, P.O.D. empirical functions are extracted, and low-dimensional models are built and compared to the numerical simulation. Generally speaking, low-D models provide a coarse picture of the flow, which is also quick, cheap, and easy to understand. They can help pinpoint leading instability mechanisms. They are potentially key players in a number of applications such as optimization and control. Our goal in this study is to determine how well the flow can be represented by very low-dimensional models. Two moderately complex situations are examined. In the first case, at some distance from the bifurcation point, the dynamics can still be reduced down to two modes, although it is necessary to account for the effect of higher-order modes in the model. In the second case, farther away from the bifurcation, the flow is chaotic. A ten-dimensional model successfully captures the essential dynamics of the flow. The procedure was seen to be robust. It clearly illustrates the power of the P.O.D. as a reduction tool. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1408919
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  • 3
    Electronic Resource
    Electronic Resource
    On the adequacy of the ten-dimensional model for the wall layer (2001)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 13 (2001), S. 210-224 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In this paper, we provide a numerical validation of the ten-dimensional Proper Orthogonal Decomposition-based model constructed by Aubry et al. [J. Fluid Mech. 192, 115 (1988)] for the wall region of the turbulent boundary layer. Under certain conditions, this model was shown to display intermittent features highly reminiscent of the experimental observations of the bursting process in the wall layer, which makes it a potential key player in understanding and possibly controlling the dynamics of wall-bounded flows. In the same spirit as in our previous study [Podvin and Lumley, J. Fluid Mech. 362, 121 (1998)], we carried out a numerical simulation of a channel flow with relatively small horizontal dimensions which matched those in the 10-D model. The closure hypotheses used to build up the model were confronted with numerical results. Time histories of the modes in the model were compared to those of the simulation. Emphasis was put on identifying long-term characteristics such as a "mean" intermittency period. Our model, quite similar to Aubry's, was found to display the same heteroclinic cycles under conditions consistent with the numerical experiment. The intermittency period in the model was found to agree well with that found in the simulation. However, the well-ordered character of 10-D bursts is significantly different from the simulation. To try and understand this discrepancy, we simulated a model with streamwise modes (32-D) and found evidence of increasing complexity in the bursts displayed. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1328741
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  • 4
    Electronic Resource
    Electronic Resource
    Reconstructing the flow in the wall region from wall sensors (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 1182-1190 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In this paper we examine how the flow in the wall region can be predicted from realistic (partial) measurements. The underlying motivation of this study is the improvement of control schemes for near-wall flows. We propose a method based on the proper orthogonal decomposition which provides estimated amplitudes for the coherent structures (i.e., the large scales) of the flow from wall measurements. The method is tested for the direct numerical simulation of a minimal flow unit. The large scales obtained by reconstruction from wall data are compared to those of the velocity field in the wall layer. The dominant structures—the streamwise streaks—are well recovered, the cross-stream motions less so since they are associated with higher-order structures unaccounted for in our truncation. We defined "rescaled" eigenfunctions to try to improve the representation of the cross-stream components of the flow. Aliasing effects due to realistic (large) sensor spacings were examined. We find that the spanwise spacing is the limiting factor for the estimation, so that a realistic grid will affect the reconstruction by at least 20% compared to full wall information. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869642
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