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 ofthe 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 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, fully developed turbulent heat transfer in a channel, and favorable pressure gradient boundary layers.Recent efforts by the present authors have focused on the fundamental multiscaling behaviors ofthe 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 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, fully developed turbulent heat transfer in a channel, and favorable pressure gradient boundary layers.