Reynolds Number Dependence, Scaling, and Dynamics of Turbulent Boundary Layers

Abstract

The past two decades (approximately 1990 to 2010) have witnessed an ever-quickening pace of new findings pertaining to the Reynolds number dependencies, scaling, and dynamics of turbulent boundary layer flows (and wall-bounded turbulent flows in general). Given this, an important objective of the present effort is to provide a review that enables researchers new to the field (e.g., graduate students) to gain an appreciation for, and an understanding of, the prevalent research themes currently under investigation. Thus, the emphasis is more on laying a contextual foundation rather than, for example, comprehensively reporting all of the research findings of the past 20 years. The review begins with a brief exposition of scaling concepts and the normalizing parameters used in exploring Reynolds number dependence. An overall focus of the effort is to describe the scaling problem in relation to the underlying behaviors of the governing transport equations. For this reason, a number of relevant equations are concisely presented. The technical challenges associated with reliably exploring Reynolds number dependence are nontrivial and are of central importance. Thus, a separate section is devoted to this topic. Similarly, since they factor importantly relative to understanding and organizing the data trends, the attributes, strengths, and weaknesses of the various theoretical approaches and models (both physical and mathematical) are briefly reviewed. The statistical data presented primarily focus on means and variances since these quantities most directly relate to the time-averaged equations. Recent results pertaining to the spatial structure of turbulent boundary layers provide a useful context for describing instantaneous dynamics, often involving coherent vortical motions and including the so-called inner/outer interaction. Overall, the cumulative evidence increasingly supports a paradigm in which the scaling behaviors of the statistical profiles stem from the existence of an internal hierarchy of motions that approach a dynamically self-similar state as the Reynolds number becomes large.