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

In this paper, we provide a numerical validation of the ten-dimensional Pro per Orthogonal Decomposition-based model constructed by Aubry [J. Fluid Mec h. 192, 115 (1988)] for the wall region of the turbulent boundary layer. Un der certain conditions, this model was shown to display intermittent featur es highly reminiscent of the experimental observations of the bursting proc ess in the wall layer, which makes it a potential key player in understandi ng 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, 12 1 (1998)], we carried out a numerical simulation of a channel flow with rel atively small horizontal dimensions which matched those in the 10-D model. The closure hypotheses used to build up the model were confronted with nume rical results. Time histories of the modes in the model were compared to th ose of the simulation. Emphasis was put on identifying long-term characteri stics such as a "mean" intermittency period. Our model, quite similar to Au bry's, was found to display the same heteroclinic cycles under conditions c onsistent with the numerical experiment. The intermittency period in the mo del 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 wi th streamwise modes (32-D) and found evidence of increasing complexity in t he bursts displayed. (C) 2001 American Institute of Physics.