Energy dynamics in a turbulent channel ow using the Karhunen-Lo eve approach

The dynamical equations for the energy in a turbulent channel ow have been developed by using the Karhunen-Lo eve modes to represent the velocity eld. The energy balance equations show that all the energy in the ow originates from the applied pressure gradient acting on the mean ow. Energy redistribution occurs through triad interactions, which is basic to understanding the dynamics. Each triad interaction determines the rate of energy transport between source and sink modes via a catalyst mode. The importance of the proposed method stems from the fact that it can be used to determine both the rate of energy transport between modes as well as the direction of energy ow. The e ectiveness of the method in determining the mechanisms by which the turbulence sustains itself is demonstrated by performing a detailed analysis of triad interactions occurring during a turbulent burst in a minimal channel ow. The impact on ow modi cation is discussed. Copyright ? 2002 John Wiley & Sons, Ltd.