SCALING AND CORRELATION OF FLUCTUATING VORTICITY IN TURBULENT WALL LAYERS

Abstract

Asymptotic expansions for the profiles of fluctuating vorticity in boundary layers are proposed based on DNS data. The inner region requires two terms with different scalings; < ! i ! i > /(U 0 u " 3 / # 2 ) and < ! i ! i > /(u " 4 / # 2 ) . The first term decays exponentially and needs no matching term in the outer region. The second term has an overlap behavior of ~ C / y . To match the outer region this requires a third scaling for the outer expansion < ! i ! i > /(u " 3 / #$ ) . This scaling turns out to be the Kolmogorov time scale. INTRODUCTION From a mathematical viewpoint the theory of turbulent wall layers is a singular perturbation problem for large Reynolds numbers. Profiles are expressed as matched asymptotic expansions. There are three parts; an expansion for the outer region, an expansion for the inner region, and a common part that matches the two. The velocity profile is a well-known example. For the outer region the profile has an expansion consisting of two terms.