A NOTE ON MEASURES OF DISTURBANCE SIZE FOR SPATIALLY EVOLVING FLOWS

The problem of defining a proper measure for the size of disturbances that evolve spatially is assessed. A model problem serves as a demonstration that the disturbance energy, which is almost exclusively used in a temporal setting, is generally not sufficient as a measure of the disturbance size in the spatial case. It is shown that the specific form of the ''energy'' transferred between Fourier components in the spatial case is not unique, but rather depends on the formulation of the spatial evolution problem. In addition to the model problem, suggestions on how to evaluate spatial ''energy'' transfer in the Navier-Stokes equations are presented.