Fluid mixture models are essential for describing a wide range of physical phenomena, including wave dynamics and spinodal decomposition. However, there is a lack of consensus in the modelling of compressible mixtures, with limited connections between different classes of models. On the one hand, existing compressible two-phase flow models accurately describe wave dynamics, but do not incorporate phase separation mechanisms. On the other hand, phase-field technology in fluid dynamics consists of models incorporating spinodal decomposition; however, a general phase-field theory for compressible mixtures remains largely undeveloped. In this paper we take an initial step toward bridging the gap between compressible two-phase flow models and phase-field models by developing a theory for compressible, isothermal N-phase mixtures. Our theory establishes a system of reduced complexity by formulating N mass balance laws alongside a single momentum balance law, thereby naturally extending the Navier–Stokes Korteweg model to N phases and providing the Navier–Stokes Cahn–Hilliard/Allen–Cahn model for compressible mixtures. Key aspects of the framework include its grounding in continuum mixture theory and its preservation of thermodynamic consistency despite its reduced complexity.

Rapid granular free-surface flows on inclined planes can develop secondary vortices aligned with the dominant flow direction. The reason for their formation remains a subject of research, but plausible mechanisms include instabilities driven by (i) dilatation/compressibility, (ii) normal stress differences and (iii) a self-induced Raleigh–Taylor instability caused by segregation of large–dense and small–light particles. In this paper, a set of novel experiments are performed with large and small particles (of the same bulk density), which form longitudinal stripes due to a combination of secondary recirculation and particle-size segregation. A conceptual model is formulated, in which large particles concentrate in the downwelling sections, small particles concentrate in the upwelling sections and a breaking-size-segregation wave separates the two pure phases from one another. In each secondary vortex, the breaking waves allow the large and small particles to continuously recirculate. Assuming that a series of counter-rotating vortices exist, it is shown that this internal cross-slope structure emerges naturally from solving the gravity-shear-driven segregation-advection equations. When viewed from above, this generates a series of alternating bands of large and small particles, that are sharply separated from one another and are aligned with the downslope direction. Each complete stripe (measured from centre to centre of each large band) is formed by two counter-rotating secondary vortices. Despite the apparent order of the steady-state stripes, it is shown that the individual large and small particle paths form complex interpenetrating co-rotating sub-vortices as they avalanche downslope.

This paper investigates the physical origins of pressure fluctuations on the stationary shroud wall of a mixed-flow pump. A novel ‘triple source model’ is developed and applied to experimental validated stress-blended eddy simulations. The model decomposes stationary-frame pressure fluctuations into three distinct rotating-frame components to disentangle complex tip leakage vortex (TLV) interactions: (i) kinematic ‘non-uniform fluctuation’ ($p_{\textit{NUF}}$) from the steady blade sweep, (ii) dynamic ‘flow synchronous fluctuation’ ($p_{\textit{FSF}}$) phase-locked to rotation, and (iii) ‘flow asynchronous fluctuation’ ($p_{\textit{FAF}}$) from all non-phase-locked phenomena. Analysis reveals that shroud unsteadiness is over 90 % dominated by the synchronous components along the TLV trajectory. Crucially, the model uncovers a counter-intuitive destructive interference mechanism between the kinematic sweep $p_{\textit{NUF}}$ and the dynamic response $p_{\textit{FSF}}$, with local cross-correlation coefficient –0.26, explaining how dynamic instabilities can dampen the steady pressure footprint. Source-term analysis of the pressure Poisson equation establishes a complete causal chain from specific velocity field interactions to pressure signatures: (i) the non-uniform fluctuation is kinematically driven by the mean momentum flux from blade loading, contributing 52.27 % to the local pressure asymmetry; (ii) the flow synchronous fluctuation is generated by periodic vortex–turbulence interaction, contributing 80.22 % of its total source; (iii) and the asynchronous broadband pressure is sourced from the canonical turbulent cascade, contributing 79.33 % of its total source. Spatial correlations confirm the TLV as the common physical nexus for all components. This work establishes a quantitative diagnostic framework that moves beyond qualitative vortex observation, providing a physical basis for the targeted mitigation of turbomachinery unsteadiness.

This paper employs the ensemble-based data assimilation method to develop a closed-form correction term for the Spalart–Allmaras (S–A) turbulence model to enhance predictive accuracy in separated flows through model-form uncertainty reduction. A compact radial-basis-function expression is proposed as correction model to supersede conventional modification procedures in classic field inversion and machine learning frameworks, achieving computational economy through spatially bounded correction regions. The correction model is derived via the Ensemble Kalman method with effective utilisation of synthesised observations based on the multi-fidelity data aggregation. The modified compact expression trained on a single case is systematically evaluated against unseen separation scenarios and the results show that the developed model can improve the prediction accuracy of flow separation in different validation cases, and the effectiveness of the method is verified. Compared with other black-box models, the correction based on the radial-basis-function form offers reduced complexity and high suitability for direct integration into numerical solvers. This approach facilitates cost-effective data assimilation and enables dynamic adaptation of the correction, thereby enhancing the generalisation capability for similar flow separation conditions.

The Taylor–Green vortex (TGV) serves as a canonical benchmark for studying the transition from laminar to turbulent flow in the absence of solid boundaries. Despite its widespread use in turbulence model validation, the degree to which the TGV exhibits true isotropy and homogeneity, particularly at late stages of decay, remains insufficiently examined. This study employs high-order numerical simulations to investigate these properties for both the standard and isotropic variants of the TGV. Statistical measures, including Reynolds stress anisotropy, coherent structure functions, homogeneity indices and integral length scales, are used to assess flow behaviour over time. Results show that the standard TGV remains anisotropic and inhomogeneous even during late decay stages, with unequal longitudinal length scales and directionally dependent homogeneity indices. The isotropic TGV maintains isotropy by design but still deviates from the characteristics of ideal homogeneous isotropic turbulence, exhibiting larger transverse than longitudinal length scales. Both configurations reveal persistent spatial inhomogeneities manifested as fixed peaks in turbulent kinetic energy and the coherent structure function of plane-averaged statistics. The findings highlight that while the isotropic TGV provides a more balanced and symmetric configuration, neither flow achieves fully homogeneous isotropic turbulence.

The onset of vortex breakdown in supersonic flows remains an unsolved problem in physics. In this study, a sufficient condition for spiral vortex breakdown to occur in supersonic flows was derived from the conserved total enthalpy at the vortex axis under complete supersonic inflow conditions. The theoretical threshold was simply determined by the relationship between the magnitudes of the kinetic and internal energies (i.e. axial velocity squared and static temperature, respectively) downstream. In addition, it was found that the squared velocity and static temperature in the sufficient condition were closely related to a rapid reduction in the helicity, which indicated that vortex breakdown occurred. Numerical simulations confirmed that the theoretical threshold corresponds to the onset of spiral vortex breakdowns in supersonic flows.

Marangoni spreading is frequently observed in nature and is utilised in industrial processes, including contaminant removal, drug delivery, and fabrication of complex structures. The spreading of a hydrophilic organic droplet on the free surface of an aqueous solution represents a convenient reference process. Spreading on an infinitely miscible interface is known to reach a quasi-steady state, with the spreading diameter determined by molecular diffusion into the bulk. However, the coupled effects of the spreading flow, the interface’s solubility, and the evaporation of the volatile droplet are not well understood. In this work, we experimentally investigate the Marangoni spreading of a hydrophilic organic droplet on the surface of a saline solution. Widely available salts are often used to reduce the solubility of non-electrolytes in water by exploiting the salting-out effect, which controls the spreading of the organic droplet on the free surface of the saline. Quasi-static spreading-diameter measurements are used to quantify this spreading. The free surface’s height, measured using the transmission speckle method, indicates that a high-concentration saline solution renders the interface temporarily non-miscible. Schlieren images capture the structure of the evaporative field, demonstrating that the evaporation is significantly reduced by mixing between the spreading droplet and the bulk fluid. It can, however, be retained through partial mixing due to the salting-out effect. A scaling law is deduced to interpret variations of the spreading diameter controlled by the salting-out effect. This work presents an effective experimental method for determining the salting-out constant, a crucial parameter in regulating interfacial reactions.

The classical Prats problem of flow instability in a horizontal porous channel saturated by a fluid subject to a buoyancy force is reconsidered. In the original formulation, the driving buoyancy force results from thermal diffusion. This study, however, substitutes thermal diffusion with mass diffusion. Furthermore, the usual scheme of mass diffusion is extended to comprehend also the anomalous phenomena of superdiffusion and subdiffusion. Such phenomena are modelled via a time-dependent mass diffusivity which yields a significant change in the formulation of the stability eigenvalue problem. In particular, the ordinary differential equations governing the time evolution of the perturbations acting on the base throughflow become non-autonomous. This makes a significant difference in the discussion of the conditions leading to instability, with a marked effect of the anomaly in the mass diffusion process. The transition from convective to absolute instability for subdiffusion processes is also addressed.

Experiments were conducted to investigate the characteristics of turbulent spots formed in transitional boundary layers developed over a flat plate and an axisymmetric cone placed in similar hypersonic free-stream environment of Mach number 5.85. The free-stream unit Reynolds number in the present work varied in the range of $(3.0{-}6.0)\times 10^6$ m−1. Heat transfer measurement along the surface of both the test models was used to ascertain the state of boundary layer and to calculate the intermittency associated with the transitional boundary layer. Turbulent spots generated in the transitional boundary layer were characterised in terms of their leading–trailing-edge velocities, their streamwise length scales and their generation rates on both the test models. The leading edge of the turbulent spots developed over both the test models were found to be convecting at a speed equivalent to 90 % of the boundary layer edge speed. The trailing edge of the spots developed on a planar boundary layer traversed at a lower speed than its axisymmetric counterpart. Streamwise length scales of a turbulent spot developed in a planar boundary layer grew at a higher rate when compared with the axisymmetric boundary layer. Turbulent spot generation rates for both planar and axisymmetric boundary layers was found to be in the range of $10\,00\,000{-}30\,00\,000$ spots m−1/s−1.

This study presents an in-depth analysis of the energy dissipation and momentum balance during a laminar planar hydraulic jump in a viscous free surface flow, with shallow flow theory used to estimate the relevant jump parameters. The inclusion of momentum and kinetic energy correction factors incorporates the influence of the fluid nature. The fluid is described by the generalised Herschel–Bulkley model with Papanastasiou regularisation, which reduces to the Bingham plastic, power-law and Newtonian models under relevant limiting conditions. The analysis, extensively validated against experimental and simulated data, is explored to understand the physics of free surface flow during jump formation. Energy dissipation increases with an increase in the flow behaviour index n, flow consistency index k and yield stress τo since each of them increases the apparent viscosity. Interestingly, it is higher in the supercritical (upstream) compared with the subcritical (downstream) zone. For constant discharge rate and film thickness, the specific energy depends on the velocity profile and is thus a function of n and τo but not k, and the mechanism of influence of n and τo are also different. For a generalised approach, energy dissipation and jump parameters are discussed as a function of relevant non-dimensional numbers obtained from SFT. Energy dissipation during a hydraulic jump in non-Newtonian liquids is a hitherto unexplored aspect. In fact, energy dissipation during a planar jump in a viscous Newtonian liquid is also rare, although hydraulic jumps are primarily used as energy dissipators in free surface flows.

The interaction between turbulence and shock waves significantly modulates the frequency and amplitude of hydrodynamic fluctuations experienced by aerospace vehicles during low-altitude hypersonic flight. In these high-speed flows, intrinsic compressibility effects arise alongside high-enthalpy phenomena manifested through internal-energy excitation. The present study compares direct numerical simulation and linear interaction analysis (LIA) to characterise the influence of solenoidal and dilatational fluctuations, as well as endothermic processes, on a Mach 5 canonical shock–turbulence interaction (STI). Whilst the computational approach involves directly resolving all relevant length scales and potential nonlinear interactions, the LIA framework models the upstream compressible turbulence as a superposition of weakly vortical, entropic and acoustic fluctuations, with the thermal non-equilibrium thickness assumed to be much thinner than the turbulence scales. Both the numerical and theoretical methods reveal that increasing upstream compressibility enhances the turbulent kinetic energy (TKE) across the STI for varying turbulent Mach numbers. The effect of vibrational excitation is shown to further amplify the TKE downstream of the shock. The influence of upstream dilatational disturbances on the postshock turbulent spectra is also analysed, and an improved LIA-based estimate of the Kolmogorov length scale across the shock is obtained.