On the adequacy of the ten-dimensional model for the wall layer

In this paper, we provide a numerical validation of the ten-dimensional Proper Orthogonal Decomposition-based model constructed by Aubry [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. (C) 2001 American Institute of Physics.