To study the physics of small-scale properties of homogeneous isotropic turbulence at increasingly high Reynolds numbers, direct numerical simulation results have been obtained for forced isotropic turbulence at Taylor-scale Reynolds number $R_\lambda =2500$ on a $32\,768^3$ three-dimensional periodic domain using a GPU pseudo-spectral code on a 1.1 exaflop GPU supercomputer (Frontier). These simulations employ the multi-resolution independent simulation (MRIS) technique (Yeung & Ravikumar 2020, Phys. Rev. Fluids, vol. 5, 110517) where ensemble averaging is performed over multiple short segments initiated from velocity fields at modest resolution, and subsequently taken to higher resolution in both space and time. Reynolds numbers are increased by reducing the viscosity with the large-scale forcing parameters unchanged. Although MRIS segments at the highest resolution for each Reynolds number last for only a few Kolmogorov time scales, small-scale physics in the dissipation range is well captured – for instance, in the probability density functions and higher moments of the dissipation rate and enstrophy density, which appear to show monotonic trends persisting well beyond the Reynolds number range in prior works in the literature. Attainment of range of length and time scales consistent with classical scaling also reinforces the potential utility of the present high-resolution data for studies of short-time-scale turbulence physics at high Reynolds numbers where full-length simulations spanning many large-eddy time scales are still not accessible. A single snapshot of the $32\,768^3$ data is publicly available for further analyses via the Johns Hopkins Turbulence Database.

The breakup of viscous liquid threads is governed by a complex interplay of inertial, viscous and capillary stresses. Theoretical predictions near the point of breakup suggest the emergence of a finite-time singularity, leading to universal power laws describing the breakup, characterised by a universal prefactor. Recent stability analyses indicate that, due to the presence of complex eigenvalues, achieving similarity may only be possible through time-damped oscillations, making it unclear when and how self-similar regimes are reached for both visco-inertial and viscous regimes. In this paper, we combine experiments with unprecedented spatio-temporal resolution and highly resolved numerical simulations to investigate the evolution of the liquid free surface during the pinching of a viscous capillary bridge. We experimentally show for the first time that, for viscous fluids the approach to the self-similar solution is composed of a large overshoot of the instantaneous shrinking speed before the system converges to the nonlinear pinch-off similarity solution. In the visco-inertial case, the convergence to the stable solution is oscillatory, whereas in the viscous case, the approach to singularity is monotonic. While our experimental and numerical results are in good agreement in the viscous regime, systematic differences emerge in the visco-inertial regime, potentially because of effects such as polymer polydispersity, which are not incorporated into our numerical model.

Layer formation can occur within stratified fluids, often associated with the effect of ‘double diffusion’ where the fluid buoyancy depends on two components with differing molecular diffusivities (e.g. heat and salt in seawater). However, since layering also occurs in one-component stratified fluids, the generation mechanism for layers is often unclear. In this paper, we present a framework that unifies multiple-layer generation mechanisms across both one- and two-component stratified fluids. We demonstrate how these mechanisms can be assessed using simulations of double-diffusive intrusions. Our simulations illustrate the importance of the negative turbulent diffusivity for buoyancy in contributing to layer formation.

Transient growth mechanisms operating on streaky shear flows are believed important for sustaining near-wall turbulence. Of the three individual mechanisms present – Orr, lift-up and ‘push over’ – Lozano-Duran et al. 2021 (J. Fluid Mech. 914, A8) have recently observed that both Orr and push over need to be present to sustain turbulent fluctuations given streaky (streamwise-independent) base fields whereas lift-up does not. We show here, using Kelvin’s model of unbounded constant shear augmented by spanwise-periodic streaks, that this is because the push-over mechanism can act in concert with a Orr mechanism based upon the streaks to produce much-enhanced transient growth. The model clarifies the transient growth mechanism originally found by Schoppa & Hussain (2002 J. Fluid Mech. 453, 57–108) and finds that this is one half of a linear instability mechanism centred at the spanwise inflexion points observed originally by Swearingen & Blackwelder (1987 J. Fluid Mech. 182, 255–290). The instability and even transient growth acting on its own are found to have the correct nonlinear feedback to generate streamwise rolls which can then re-energise the assumed streaks through lift-up indicating a sustaining cycle. Our results therefore support the view that, while lift-up is believed central for the roll-to-streak regenerative process, it is Orr and push-over mechanisms that are both key for the streak-to-roll regenerative process in near-wall turbulence.