KARHUNEN-LOEVE DECOMPOSITION OF MINIMAL CHANNEL FLOW

Minimal channel flow is analyzed by means of the Karhunen-Loeve (KL) d ecomposition. It is shown that the most energetic modes are streamwise rollers followed by outward tilted quasi-streamwise vortices. Both of these mode types have a strong similarity to structures seen in physi cal experiments. Temporal plots of roll energy, propagating energy, bu lk velocity, and representational entropy have been obtained. Study of the evolution of these variables shows a consistent pattern of growth and decay in which entropy plays a key role in describing the events in the turbulent process. The roll and propagating modes are also show n to make independent contributions to the Reynolds stress with the ro ll modes dominating the profile near the walls and the propagating mod es having larger values towards the channel center. A comparison of th e KL dimension of this flow and a full channel flow shows that the dim ension scales with box size, i.e., it confirms the assertion that dime nsion is an extensive variable. (C) 1997 American Institute of Physics .