Anisotropy in turbulence profiles of stratified wakes

Abstract

At sufficiently high values of the Reynolds number (Re⩾4.5×103) and internal Froude number (F⩾4), initially turbulent bluff body wakes evolve in the presence of a stable background density gradient with wake-averaged mean and turbulence length and velocity scales that are independent of Re and F for at least two orders of magnitude extension in both parameters. The way in which the initially three-dimensional motions transition to the characteristic (and Re- and F-independent) late wakes (where vertical velocities, w≪u,v) is both of great practical interest, and complex, hence somewhat unclear. Here, digital particle imaging velocimetry type measurements on towed-sphere wakes are described, so that the development of anisotropy can be measured by the time development of turbulence profiles in horizontal and vertical centerplanes. The observed anisotropies can be associated with energy transfer to internal wave modes, and suppression of other vertical displacements, that contrasts with sphere wakes at similar Re in a homogeneous fluid. Maximum Reynolds stresses occur at the boundary of a sinuous undulation of the wake, which increases in amplitude up to Nt≈60 (N is the buoyancy frequency that characterizes the strength of the stratification). Although an intrinsic wake profile instability cannot be excluded, the observed wake element spacings can be accounted for by known spiral and Kelvin–Helmholtz instabilities in the near wake.