Properties of the turbulent/non-turbulent layer of a turbulent Boussinesq plume: A study using direct numerical simulation

Abstract

The turbulent/non-turbulent layer (TNTL) in a turbulent Boussinesq plume is analyzed using direct numerical simulations. The Reynolds number (Re) used in the simulation, based on the scales defined at the bottom hot patch, is 2000, and the Reynolds number (Reλ) based on the Taylor microscale (λ) is 114.4 in the self-similar region. The flow is sufficiently resolved till the Kolmogorov scale. The outer edge of the TNTL is detected using the vorticity magnitude. Conditional statistics of various quantities are calculated with reference to the outer edge of the TNTL, which is referred to as the irrotational boundary (IB). The profiles of conditional vorticity magnitude are used to identify the TNTL and determine its thickness. The presence of viscous superlayer (VSL) and turbulent sublayer (TSL) within the TNTL is revealed by exploring the conditional profiles of the enstrophy transport equation. The baroclinic torque, which is a source of vorticity, has been shown to be inconsequential in determining the width of the VSL. The widths of the TNTL and the VSL are determined to be δTNTL≈15η and δVSL≈3.12η, respectively, where η is the Kolmogorov length scale. This gives the width of the TSL as δTSL=δTNTL−δVSL≈13.88η. The invariants of the velocity gradient tensor have been analyzed across the TNTL. The joint probability density function of the invariants Q and R shows a teardrop shape within the turbulent core. The teardrop shape is not fully developed within the TNTL. The TNTL and the turbulent core have a mixed tendency for irrotational dissipation, vortex sheets, and vortex tubes. When normalized by Kolmogorov length and velocity scales, the conditional statistics of the TNTL of the plume are similar to other turbulent flow types, and hence, this provides additional evidence for the universality of small-scale motion within/around the TNTL of various turbulent flows.