LOW-DIMENSIONAL APPROACH FOR THE MINIMAL FLOW UNIT

The proper orthogonal decomposition (POD) is applied to the minimal fl ow unit (MFU) of a turbulent channel flow. Our purpose is to establish a numerical validation of low-dimensional models based on the POD. Th e 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 simulat ion of the flow. The various modelling assumptions which underlie the construction of low-dimensional models are examined and confronted wit h numerical evidence. The relationship between intermittency in the MF U and intermittent low-dimensional parameters is investigated closely. The agreement observed is quite satisfactory, especially given the cr udeness of the truncation considered. To further demonstrate the adequ acy of the model, we develop a dynamical filtering procedure to recove r information from realistic (partial) measurements. The success obtai ned illustrates the versatility of the low-dimensional paradigm.