The lattice Boltzmann method has become a popular tool for simulating complex flows, including incompressible turbulent flows; however, as an artificial compressibility method, it can generate spurious pressure oscillations whose impact on the statistics of incompressible turbulence has not been systematically examined. In this work, we propose a theoretical approach to analyse the origin of compressibility-induced oscillations (CIOs) and explore ways to suppress or remove them. We begin by decomposing the velocity field and pressure field each into the solenoidal component and the compressive component, and then study the evolution of these two components analytically and numerically. The analysis yields an evolution equation of the mean-square pressure fluctuation which reveals several coupling effects of the two components. The evolution equation suggests that increasing the bulk-to-shear viscosity ratio can suppress CIOs, which is confirmed by numerical simulations. Furthermore, based on the derived evolution equation and data from the simulation, a model is developed to predict the long-term behaviours of the mean-square pressure fluctuations. In the case of decaying turbulence in a periodic domain, we show that the Helmholtz–Hodge decomposition can be used to obtain the solenoidal components reflecting the true evolution of incompressible turbulent flow, from the mesoscopic artificial compressibility approach. The study provides general theoretical guidelines to understand, suppress and even remove CIOs in other related pseudo-compressibility methods.

We investigate flame–acoustic interactions in a turbulent combustor during the state of intermittency before the onset of thermoacoustic instability using complex networks. Experiments are performed in a turbulent bluff-body stabilised dump combustor where the inlet airflow rate is varied quasi-statically and continuously. We construct a natural visibility graph from the local heat release rate fluctuations ($\dot {q}'$) at each location. Comparing the average degree during epochs of high- and low-amplitude acoustic pressure oscillations ($p'$) during the state of intermittency, we detect frequency modulation in $\dot {q}'$. Through this approach, we discover unique spatial patterns of cross-variable coupling between the frequency of $\dot {q}'$ and the amplitude of $p'$. The frequency of $\dot {q}'$ increases in regions of flame anchoring owing to high-frequency excitation of the flow and flame during epochs of high-amplitude $p'$ dynamics. However, the frequency of $\dot {q}'$ decreases in regions associated with flame-front distortions by large coherent vortices. In experiments with continuously varying airflow rates, the spatial pattern of frequency modulation varies with an increase in the average amplitude of $p'$ owing to an increase in the epochs of periodic $p'$ dynamics and the size of vortices forming in the flow. Dynamic shifts in the location of flame anchoring induce low-frequency fluctuations in $\dot {q}'$ during very-high-amplitude intermittent $p'$ dynamics. Our approach using conditional natural visibility graphs thus reveals the spatial pattern of amplitude-frequency coupling between the co-evolving flame and the acoustic field dynamics in turbulent reacting flows.

In this experimental and numerical study, we revisit the question of the onset of the elastic regime in viscoelastic pinch-off. This is relevant to all modern filament thinning techniques, which aim to measure the extensional properties of low-viscosity polymer solutions. Examples are the slow retraction method (SRM) for capillary breakup extensional rheometry (CaBER), or the dripping method, in which a drop detaches from a nozzle. As part of these techniques, a stable liquid bridge is brought slowly to its stability threshold, where capillary-driven thinning starts. This thinning slows down dramatically at a critical radius $h_1$, marking the onset of the elasto-capillary regime, characterised by a filament of nearly uniform radius. While a theoretical scaling exists for this transition in the case of the classical step-strain CaBER protocol, where polymer chains stretch without relaxing during the fast plate separation, we show that this theory is not necessarily valid for a slow protocol such as the SRM. In that case, polymer chains start stretching (beyond their equilibrium coiled configuration) only when the bridge thinning rate becomes comparable to the inverse of their relaxation time. We derive a universal scaling for $h_1$, valid for both low- and high-viscosity polymer solutions. This scaling is validated by CaBER experiments with a slow plate separation protocol using different polymer solutions, plate diameters and sample volumes, as well as by numerical simulations using the FENE-P model.