Mixing and heat transfer rates are typically enhanced in high-pressure transcritical turbulent flow regimes. This is largely due to the rapid variation of thermophysical properties near the pseudo-boiling region, which can significantly amplify velocity fluctuations and promote flow destabilisation. The stability conditions are influenced by the presence of baroclinic torque, primarily driven by steep, localised density gradients across the pseudo-boiling line; an effect intensified by differentially heated wall boundaries. As a result, enstrophy levels increase compared with equivalent low-pressure systems, and flow dynamics diverge from those of classical wall-bounded turbulence. In this study the dynamic equilibrium of these instabilities is systematically analysed using linear stability theory. It is shown that under isothermal wall transcritical conditions, the nonlinear thermodynamics near the pseudo-boiling region favour destabilisation more readily than in subcritical or supercritical states; though this typically requires high-Mach-number regimes. The destabilisation is further intensified in non-isothermal wall configurations, even at low Brinkman and significantly low Mach numbers. In particular, the sensitivity of neutral curves to Brinkman number variations, along with the modal and non-modal perturbation profiles of hydrodynamic and thermodynamic modes, offer preliminary insight into the conditions driving early destabilisation. Notably, a non-isothermal set-up (where walls are held at different temperatures) is found to be a necessary condition for triggering destabilisation in low-Mach, low-Reynolds-number regimes. For the same Brinkman number, such configurations accelerate destabilisation and enhance algebraic growth compared with isothermal wall cases. As a consequence, high-pressure transcritical flows exhibit increased kinetic energy budgets, driven by elevated production rates and reduced viscous dissipation.

Biological soil crusts (biocrusts) are key components of dryland ecosystems worldwide, contributing to soil stabilization, nutrient cycling and enhancing ecosystem resilience. Despite their ecological importance, biocrusts in the Arabian Peninsula are largely underexplored, with much of the region’s biocrust diversity and functionality remaining undocumented. This review synthesizes current knowledge on biocrusts across the Arabian Peninsula, focusing on their major taxonomic groups (cyanobacteria, fungi, lichens, mosses and algae), their ecological roles and distribution patterns. It also discusses the potential for biocrust restoration through strategies such as cyanobacterial inoculation and passive protection, which could contribute to land degradation and desertification control in the Arabian Peninsula. Our work identifies significant research gaps in biocrust biodiversity, ecophysiology and their role in ecosystem functioning within this region, and calls for more focused research to integrate biocrusts into land management strategies for the Arabian Peninsula.

The Boltzmann kinetic equation is considered to compute the transport coefficients associated with the mass flux of intruders in a granular gas. Intruders and granular gas are immersed in a gas of elastic hard spheres (molecular gas). We assume that the granular particles are sufficiently rarefied so that the state of the molecular gas is not affected by the presence of the granular gas. Thus, the gas of elastic hard spheres can be considered as a thermostat (or bath) at a fixed temperature $T_g$. In the absence of spatial gradients, the system achieves a steady state where the temperature of the granular gas $T$ differs from that of the intruders $T_0$ (energy non-equipartition). Approximate theoretical predictions for the temperature ratio $T_0/T_g$ and the kurtosis $c_0$ associated with the intruders compare very well with Monte Carlo simulations for conditions of practical interest. For states close to the steady homogeneous state, the Boltzmann equation for the intruders is solved by means of the Chapman–Enskog method to first order in the spatial gradients. As expected, the diffusion transport coefficients are given in terms of the solutions of a set of coupled linear integral equations which are approximately solved by considering the first Sonine approximation. In dimensionless form, the transport coefficients are nonlinear functions of the mass and diameter ratios, the coefficients of restitution and the (reduced) bath temperature. Interestingly, previous results derived from a suspension model based on an effective fluid–solid interaction force are recovered when $m/m_g\to \infty$ and $m_0/m_g\to \infty$, where $m$, $m_0$ and $m_g$ are the masses of the granular particles, intruders and molecular gas particles, respectively. Finally, as an application of our results, thermal diffusion segregation is exhaustively analysed.

Linear-stability modelling suggests that all sufficiently large riblets promote maximally growing spanwise rollers (García-Mayoral & Jiménez 2011 J. Fluid Mech. vol. 678, 317–347), yet direct numerical simulations (DNS) have shown that this is not the case (Endrikat et al. 2021 J. Fluid Mech. vol. 913, A37) some riblet shapes do not form spanwise rollers at all. Thus, the drag-reduction breakdown across all riblet shapes cannot be solely attributed to maximally growing spanwise rollers, prompting a reappraisal of the modelling. In this paper, comparing DNS data with riblet-resolving linear-stability predictions shows that the spanwise rollers are actually marginal modes, not maximally growing instabilities. This riblet-resolved linear analysis also predicts that not all riblet shapes promote spanwise rollers, in agreement with DNS, and unlike earlier linear-stability modelling, which relied on a one-dimensional (1-D) mean flow and on an over-simplified effective wall-admittance boundary condition. These riblet-resolved calculations further inform how to capture the effect of the riblet shape in a 1D model. Once captured, predictions with an effective boundary condition match riblet-resolved results, but still do not indicate what features of the riblet geometry promote the roller instability. Thus, the wall admittance is measured near the riblet crests, in both the riblet-resolved linear analysis and DNS, to show that the in-groove dynamics is dominated by a balance between the overlying pressure and unsteady inertia, and not viscous diffusion, as previously assumed. This pressure–unsteady-inertia balance sets the linear scaling of the wall admittance with riblet size, as observed in DNS, and is a key factor in setting the streamwise wavelength of the spanwise rollers. Furthermore, modelling this pressure–unsteady-inertia balance in the wall admittance reveals the role of riblet slenderness in promoting spanwise rollers, which provides the missing link in previous correlations between the riblet geometry and the presence or lack of rollers.

We investigate Lighthill’s proposed turbulent mechanism for near-wall concentration of spanwise vorticity by calculating mean flows conditioned on motion away from or toward the wall in an (friction Reynolds number) ${\textit{Re}}_\tau =1000$ database of plane-parallel channel flow. Our results corroborate Lighthill’s proposal throughout the entire logarithmic layer, but extended by counter-flows that help explain anti-correlation of vorticity transport by advection and by stretching/tilting. We present evidence also for Lighthill’s hypothesis that the vorticity transport in the log layer is a ‘cascade process’ through a scale hierarchy of eddies, with intense competition between transport outward from and inward to the wall. Townsend’s model of attached eddies of hairpin-vortex type accounts for half of the vorticity cascade, whereas we identify necklace type or ’shawl vortices’ that envelop turbulent sweeps as supplying the other half.