Overview of a Methodology for Scaling the Indeterminate Equations of Wall Turbulence

Recent efforts by the present authors have focused on the fundamental multiscaling behaviors of the time averaged dynamical equations of wall-turbulence. These efforts have generated a number of new results relating to dynamical structure, as well as a new mathematical foundation. Central to this has been the development of the so-called method of scaling patches. This method provides a formalism for determining the scaling behaviors directly from the indeterminate equations. A general description of this methodology is provided herein, and in doing so its connections to well-established scaling notions are identified. Example problems for which the method has been successfully applied includes turbulent boundary layer, pipe and channel flows, turbulent Couette-Poiseuille flow, and fully developed turbulent heat transfer in a channel.