We study the effect of surfactant on the dynamics of a bubble bursting through an interface. We perform fully three-dimensional direct numerical simulations using a hybrid interface-tracking/level-set method accounting for surfactant-induced Marangoni stresses, sorption kinetics and diffusive effects. We select an initial bubble shape corresponding to a large Laplace number and a vanishingly small Bond number in order to neglect gravity, and isolate the effects of surfactant on the flow. Our results demonstrate that the presence of surfactant affects the dynamics of the system through Marangoni-induced flow, driving motion from high to low concentration regions, which is responsible for the onset of a recirculation zone close to the free surface. These Marangoni stresses rigidify the interface, delay the cavity collapse and influence the jet breakup process.

The prediction of the first fluidized path of yield-stress fluids in complex porous media is a challenging yet important task to understand the fundamentals of fluid flow in several industrial and biological processes. In most cases, the conditions that open this first path are known either through experiments or expensive computations. Here, we present a simple network model to predict the first open channel for a yield-stress fluid in a porous medium. For porous media made of non-overlapping discs, we find that the pressure drop ${\rm \Delta} P_c$ required to open the first channel for a given yield stress $\tau _y$ depends on both the relative discs size $R_s$ to the macroscopic length $L$ of the system and the packing fraction $\phi$. The non-dimensional pressure gradient ${\rm \Delta} P_c R_s/ \tau _y L$ (i.e. the critical yield number), however, depends on the packing fraction $\phi$ only, leading to a mastercurve for all examined ratios of $R_s/L$. In the case of non-overlapping discs, we find ${\rm \Delta} P_c R_s/ \tau _y L\sim \phi /(1-\phi )$. We also report the statistics on the arclength of the first open path. Finally, we discuss the implication of our results for the design of porous media used in energy storage applications.

Upscaling the effect of heterogeneities in porous media is crucial for macroscopic flow predictions, with numerous applications in energy and environmental settings. In this study, we derive simple semi-analytical expressions for the upscaling of multiphase flow in a porous medium with a range of vertical heterogeneities. We use this upscaling to give insight into how the flow transitions between a viscous flow regime, in which macroscopic pressure gradients dominate over heterogeneity-driven capillary forces, and a capillary flow regime, in which these capillary forces dominate and set the saturation distribution of the flow. In particular, by studying the dynamics of flow in an aquifer, we demonstrate that different regions lie within the viscous and capillary flow regimes whilst other regions lie in between these regimes. By modifying the classic Buckley–Leverett problem for fluid displacement we demonstrate where and when the flow transitions between these regimes and how this affects flooding speeds. Then, we discuss the implications of these results in the case of carbon dioxide sequestration, making comparisons with field data.

A broad spectrum of internal gravity waves coexist with the geostrophic balanced flow in the world's oceans. Satellite altimeter data sets, in situ observations and global scale ocean model outputs collected over the past one decade reveal significant variability in the balance-to-wave energy ratio in the world's oceans. Notably, wave-dominant regions of the world's oceans are characterized by the internal gravity wave spectrum overtaking the geostrophic balanced flow's spectrum at mesoscales. Inspired by these recent data sets, in this paper we explore turbulent interactions between a broad spectrum of internal gravity waves and the geostrophic balanced flow in different balance-to-wave energy regimes. Our results based on numerical integration of the non-hydrostatic Boussinesq equations reveal that the balanced flow remains unaffected by waves as long as wave energy is not significantly higher than balanced energy. Even in parameter regimes where wave and balanced energies are comparable, balanced flow undergoes an inverse energy flux with energy accumulating in large domain-scale coherent vortices. In contrast, we find that wave-dominant regimes are composed of two-way wave–balance energy exchanges and a forward flux of geostrophic energy. The geostrophic balanced flow in such regimes is composed of fine-scale structures that get dissipated at small scales and show no sign of coherent vortex formation. Our findings reveal that sufficiently high energy waves can reverse the direction of the geostrophic energy flux – from inverse to forward – enhancing geostrophic energy dissipation. Given that the balance-to-wave energy ratio is highly variable in the global ocean, the forward flux and associated small-scale dissipation of balanced energy could play an important role in high wave energy regions of the world's oceans. The prominent mechanisms suggested for dissipating balanced energy in the world's oceans require balanced flow to encounter different forms of boundaries. In contrast, the wave-induced dissipation of balanced energy described in this paper is an attractive mechanism that could dissipate balanced energy in the interior parts of the oceans and away from all forms of boundaries.

This study examines the dynamics of zonally elongated transient flows (ZELTs) in the context of quasi-geostrophic turbulence. Unlike stationary zonal jets considered in previous studies, these flow features do not span the entire oceanic basin and propagate in the zonal direction at a speed slower than baroclinic Rossby waves. The analysis of potential vorticity balance in a statistically steady state shows that ZELTs are maintained by the vorticity flux divergences associated with the eddy–eddy interactions whereas the eddy–mean flow interactions play a secondary role. The divergences of the eddy fluxes of barotropic relative vorticity and buoyancy are shown to be the dominant contributors. The importance of specific eddy–eddy interactions are further studied using a dynamical model with the removed eddy–eddy vorticity flux divergences, which is equivalent to the fluid system with an absent cascade of eddy energy. Simulations with this reduced-dynamics model exhibit a complete disappearance of ZELTs, confirming the expectations from the analysis of the vorticity balance. Additional reduced-dynamics simulations demonstrate that the eddy kinetic energy transport leads to the emergence of ZELTs, with the transport in the baroclinic mode playing the leading role, while the potential energy transport acts to damp them.

Turbulent convection systems are known to give rise to prominent large-scale circulation. At the same time, the ‘background’ (or ‘small-scale’) turbulence is also highly relevant and e.g. carries the majority of the heat transport in the bulk of the flow. Here, we investigate how the small-scale turbulence is interlinked with the large-scale flow organization of Rayleigh–Bénard convection. Our results are based on a numerical simulation at Rayleigh number $Ra = 10^8$ in a large aspect ratio ($\varGamma =32$) cell to ensure a distinct scale separation. We extract local magnitudes and wavenumbers of small-scale turbulence and find significant correlation of large-scale variations in these quantities with the large-scale signal. Most notably, we find stronger temperature fluctuations and increased small-scale transport (by about 10 % of the global Nusselt number $Nu$) in plume impacting regions and opposite trends in the plume emitting counterparts. This concerns wall distances up to $2\delta _\theta$ (thermal boundary layer thickness). Local wavenumbers are generally found to be higher on the plume emitting side compared to the impacting one. A second independent approach by means of conditional averages confirmed these findings and yields additional insight into the large-scale variation of small-scale properties. Our results have implications for the modelling of small-scale turbulence.