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.

We analyse the long-time dynamics of trajectories within the stability boundary between laminar and turbulent square duct flow. If not constrained to a symmetric subspace, the edge trajectories exhibit a chaotic dynamics characterised by a sequence of alternating quiescent phases and intense bursting episodes. The dynamics reflects the different stages of the well-known near-wall streak–vortex interaction. Most of the time, the edge states feature a single streak with a number of flanking vortices attached to one of the four surrounding walls. The initially straight streak undergoes a linear instability and eventually breaks in an intense bursting event. At the same time, the downstream vortices give rise to a new low-speed streak at one of the neighbouring walls, thereby causing the turbulent activity to ‘switch’ from one wall to the other. If the edge dynamics is restricted to a single or twofold mirror-symmetric subspace, the bursting and wall-switching episodes become self-recurrent in time, representing the first periodic orbits found in square duct flow. In contrast to the chaotic edge states in the non-symmetric case, the imposed symmetries enforce analogue bursting cycles to simultaneously appear at two parallel opposing walls in a mirror-symmetric configuration. Both the localisation of turbulent activity to one or two walls and the wall-switching dynamics are shown to be common phenomena in marginally turbulent duct flows. We argue that such episodes represent transient visits of marginally turbulent trajectories to some of the edge states detected here.

Symmetry-based analyses of multiscale velocity gradients highlight that strain self-amplification (SS) and vortex stretching (VS) drive forward energy transfer in turbulent flows. By contrast, a strain–vorticity covariance mechanism produces backscatter that contributes to the bottleneck effect in the subinertial range of the energy cascade. We extend these analyses by using a normality-based decomposition of filtered velocity gradients in forced isotropic turbulence to distinguish contributions from normal straining, pure shearing and rigid rotation at a given scale. Our analysis of direct numerical simulation (DNS) data illuminates the importance of shear layers in the inertial range and (especially) the subinertial range of the cascade. Shear layers contribute significantly to SS and VS and play a dominant role in the backscatter mechanism responsible for the bottleneck effect. Our concurrent analysis of large-eddy simulation (LES) data characterizes how different closure models affect the flow structure and energy transfer throughout the resolved scales. We thoroughly demonstrate that the multiscale flow features produced by a mixed model closely resemble those in a filtered DNS, whereas the features produced by an eddy viscosity model resemble those in an unfiltered DNS at a lower Reynolds number. This analysis helps explain how small-scale shear layers, whose imprint is mitigated upon filtering, amplify the artificial bottleneck effect produced by the eddy viscosity model in the inertial range of the cascade. Altogether, the present results provide a refined interpretation of the flow structures and mechanisms underlying the energy cascade and insight for designing and evaluating LES closure models.