Using direct numerical simulations, we systematically investigate the inner-layer turbulence of a turbulent vertical buoyancy layer (a model for a vertical natural convection boundary layer) at a constant Prandtl number of $0.71$. Near-wall streaky structures of streamwise velocity fluctuations, synonymous with the buffer layer streaks of canonical wall turbulence, are not evident at low and moderate Reynolds numbers (${\textit{Re}}$) but manifest at high ${\textit{Re}}$. At low ${\textit{Re}}$, the turbulent production in the near-wall region is negligible; however, this increases with increasing ${\textit{Re}}$. By using domains truncated in the streamwise, spanwise and wall-normal directions, we demonstrate that the turbulence production in the near-wall region at moderate and high ${\textit{Re}}$ is largely independent of large-scale motions and outer-layer turbulence. On a fundamental level, the near-wall turbulence production is autonomous and self-sustaining, and a well-developed bulk is not needed to drive the inner-layer turbulence. Near-wall streaks are also not essential for this autonomous process. The type of thermal boundary condition only marginally influences the velocity fluctuations, revealing that the turbulence dynamics are primarily governed by the mean-shear induced by the buoyancy field and not by the thermal fluctuations, despite the current flow being solely driven by buoyancy. In the inner layer, the spanwise wavelength of the eddies responsible for positive shear production is remarkably similar to that of canonical wall turbulence at moderate and high ${\textit{Re}}$ (irrespective of near-wall streaks). Based on these findings, we propose a mechanistic model that unifies the near-wall shear production of vertical buoyancy layers and canonical wall turbulence.

We derive a mathematical model for the overflow fusion glass manufacturing process. In the limit of zero wedge angle, the model leads to a canonical fluid mechanics problem in which, under the effects of gravity and surface tension, a free-surface viscous flow transitions from lubrication flow to extensional flow. We explore the leading-order behaviour of this problem in the limit of small capillary number, and find that there are four distinct regions where different physical effects control the flow. We obtain leading-order governing equations, and determine the solution in each region using asymptotic matching. The downstream behaviour reveals appropriate far-field conditions to impose on the full problem, resulting in a simple governing equation for the film thickness that holds at leading order across the entire domain.

Induced diffusion (ID), an important mechanism of spectral energy transfer due to interacting internal gravity waves (IGWs), plays a significant role in driving turbulent dissipation in the ocean interior. In this study, we revisit the ID mechanism to elucidate its directionality and role in ocean mixing under varying IGW spectral forms, with particular attention to deviations from the standard Garrett–Munk spectrum. The original interpretation of ID as an action diffusion process, as proposed by McComas et al., suggests that ID is inherently bidirectional, with its direction governed by the vertical-wavenumber spectral slope $\sigma$ of the IGW action spectrum, $n \propto m^\sigma$. However, through the direct evaluation of the wave kinetic equation, we reveal a more complete depiction of ID, comprising both a diffusive and a scale-separated transfer rooted in the energy conservation within wave triads. Although the action diffusion may reverse direction depending on the sign of $\sigma$ (i.e. red or blue spectra), the net transfer by ID consistently leads to a forward energy cascade at the dissipation scale, contributing positively to turbulent dissipation. This supports the viewpoint of ID as a dissipative mechanism in physical oceanography. This study presents a physically grounded overview of ID, and offers insights into the specific types of wave–wave interactions responsible for turbulent dissipation.