NONLINEAR-ANALYSIS OF HIGH-REYNOLDS-NUMBER FLOWS OVER A BUOYANT AXISYMMETRICAL BODY

Data from experiments on the turbulent boundary layer around an axisymmetric vehicle rising under its own buoyancy are described in detail and analyzed using tools developed in nonlinear dynamics. Arguments are given that in this experiment the size of the wall mounted pressure sensors would make the data sensitive to the dynamics of about ten or so coherent structures in the turbulent boundary layer. Analysis of a substantial number of large, well sampled data sets indicates that the (integer) dimension of the embedding space required to capture the dynamics of the observed flows in the laminar regime is very large. This is consistent with there being no pressure fluctuations expected here and the signal being dominated by instrumental ''noise.'' In a consistency check we find that data from the ambient state of the vehicle before buoyant rise occurs and data from an accelerometer mounted in the prow are also consistent with this large dimension. The time scales in those data are also unrelated to fluid dynamic phenomena. In the transition and turbulent regions of the flow we find the pressure fluctuation time scales to be consistent with those of the fluid flow (about 250 musec) and determine the dimension required for embedding the data to be about 7-8 for the transitional region and about 8-9 for the turbulent regime. These results are examined in detail using both global and local false nearest-neighbor methods as well as mutual information aspects of the data. The results indicate that the pressure fluctuations are determined in these regimes by the coherent structures in the turbulent boundary layer. Applications and further investigations suggested by these results are discussed.