Compressible mixing layer instabilities are of importance to a wide range of environmental and industrial applications. Past studies have focused on either ideal-gas or real-fluid thermodynamic regimes of single-species mixing layers. However, mixing layers of binary mixtures at supercritical conditions, commonly encountered in fuel injection systems, introduce additional complexities due to the added compositional degree-of-freedom. Moreover, the effect of strong variations in thermodynamic response functions across the Widom line on the binary mixing layer stability remains poorly understood. Thus, the objective of this study is to examine the coupling between the hydrodynamic instability and the real-fluid thermodynamics across the Widom line and its effects on the overall binary mixing layer dynamics. To this end, we develop a linear stability analysis of the full binary-species compressible transport equations coupled with the PC-SAFT equation of state. Analysis shows the existence of a novel instability mechanism that arises from juxtapositioning of the Widom-line transition and the hydrodynamic inflection point. This novel thermodynamically induced instability mechanism has the net effect of destabilizing the binary mixing layer at lowering supercritical conditions towards the critical pressure point. This is in contrast to previous stability analyses of supercritical single-species mixing layers, where increasing pressure destabilizes the flow due to its effect on reducing the density stratification. The discovered thermodynamically induced instability mechanism of binary mixing flows highlights the need for an extension of classical instability criteria to incorporate the effect of strong variations in the thermodynamic response functions across the Widom line on mixing layer instability.

A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for this purpose. Here, we consider a two-dimensional microstructure comprising an array of obstacles of smooth but arbitrary shape, the size and spacing of which can vary along the length of the porous medium. We use homogenisation via the method of multiple scales to systematically upscale a novel problem involving cells of varying area to obtain effective continuum equations for macroscale flow and transport. The equations are characterised by the local porosity, a local anisotropic flow permeability, an effective local anisotropic solute diffusivity and an effective local adsorption rate. These macroscale properties depend non-trivially on the two degrees of microstructural geometric freedom in our problem: obstacle size and obstacle spacing. We exploit this dependence to construct and compare scenarios where the same porosity profile results from different combinations of obstacle size and spacing. We focus on a simple example geometry comprising circular obstacles on a rectangular lattice, for which we numerically determine the macroscale permeability and effective diffusivity. We investigate scenarios where the porosity is spatially uniform but the permeability and diffusivity are not. Our results may be useful in the design of filters or for studying the impact of deformation on transport in soft porous media.

Free-stream turbulence (FST) induced boundary layer transition is an intricate physical process that starts already at the leading edge (LE) with the LE receptivity process dictating how the broad spectrum of FST scales is received by the boundary layer. The importance of the FST integral length scale, apart from the turbulence intensity, has recently been recognized in transition prediction but a systematic variational study of the LE pressure gradient has still not been undertaken. Here, the LE pressure gradient is systematically varied in order to quantify its effect on the transition location. To this purpose, we present a measurement technique for accurate determination of flat-plate boundary layer transition location. The technique is based on electret condenser microphones which are distributed in the streamwise direction with high spatial resolution. All time signals are acquired simultaneously and post-processed giving the full intermittency distribution of the flow over the plate in a few minutes. The technique is validated against a similar procedure using hot-wire anemometry measurements. Our data clearly shows that the LE pressure gradient plays a decisive role in the receptivity process for small integral length scales, at moderate turbulence intensities, leading to variations in the transitional Reynolds number close to 40 %. To our knowledge, this high sensitivity of LE pressure gradient to transition has so far not been reported and our experiments were therefore partly repeated using another LE to ensure set-up independence and result repeatability.

We model the advective Marangoni spreading of insoluble surfactant at the free surface of a viscous fluid that is confined within a two-dimensional rectangular cavity. Interfacial deflections are assumed small, with contact lines pinned to the walls of the cavity, and inertia is neglected. Linearising the surfactant transport equation about the equilibrium state allows a modal decomposition of the dynamics, with eigenvalues corresponding to decay rates of perturbations. Computation of the family of mutually orthogonal two-dimensional eigenfunctions reveals singular flow structures near each contact line, resulting in spatially oscillatory patterns of shear stress and a pressure field that diverges logarithmically. These singularities at a stationary contact line are associated with dynamic compression of the surfactant monolayer. We show how they can be regularised by weak surface diffusion. Their existence highlights the need for careful treatment in computations of unsteady advection-dominated surfactant transport in confined domains.

We analyse the model problem of rigid, spherical pendula impacting on rubber membranes at different Reynolds numbers to understand the contact dynamics in deformable bodies in a viscous fluid. We have investigated the problem both by laboratory and numerical experiments and a new contact model has been developed to perform the simulations. We have found that the collision dynamics depends on many parameters, the most important ones being the impact Stokes number ($St$) and the ratio of the membrane thickness ($e$) to sphere diameter ($2R$). For $e/(2R)=0.1$ the pendulum rebounds for $St \geqslant 18$ and this threshold increases as the membrane thickness decreases. Also, the membrane surface affects the dynamics of the impact by delaying the rebound for smaller membranes.

Pore-resolved direct numerical simulations are performed to investigate the interactions between streamflow turbulence and groundwater flow through a randomly packed porous sediment bed for three permeability Reynolds numbers, $Re_K=2.56$, 5.17 and 8.94, representative of natural stream or river systems. Time–space averaging is used to quantify the Reynolds stress, form-induced stress, mean flow and shear penetration depths, and mixing length at the sediment–water interface (SWI). The mean flow and shear penetration depths increase with $Re_K$ and are found to be nonlinear functions of non-dimensional permeability. The peaks and significant values of the Reynolds stresses, form-induced stresses, and pressure variations are shown to occur in the top layer of the bed, which is also confirmed by conducting simulations of just the top layer as roughness elements over an impermeable wall. The probability distribution functions (p.d.f.s) of normalized local bed stress are found to collapse for all Reynolds numbers, and their root-mean-square fluctuations are assumed to follow logarithmic correlations. The fluctuations in local bed stress and resultant drag and lift forces on sediment grains are mainly a result of the top layer; their p.d.f.s are symmetric with heavy tails, and can be well represented by a non-Gaussian model fit. The bed stress statistics and the pressure data at the SWI potentially can be used in providing better boundary conditions in modelling of incipient motion and reach-scale transport in the hyporheic zone.

When surface waves interact with ambient turbulence, the two affect each other mutually. Turbulent eddies get redirected, intensified and periodically stretched and compressed, while the waves suffer directional scattering. We study these mutual interactions experimentally in the water channel laboratory at the Norwegian University of Science and Technology (NTNU) Trondheim. Long groups of waves were propagated upstream on currents with identical mean flow but different turbulence properties, created by an active grid at the current inlet. The subsurface flow in the spanwise–vertical plane was measured with stereo particle-image velocimetry. Comparing the subsurface velocity fields before and after the passage of a wave group, a strong enhancement of streamwise vorticity is observed which increases rapidly towards the surface for $k_0z\gtrsim -0.3$ ($z$, vertical distance from still surface; $k_0$, carrier wavenumber) in qualitative agreement with theory. Next, we measure the broadening of the directional wave spectrum at increasing propagation distance. The rate of directional diffusion is greatest for the turbulent case with the highest energy at the longest length scales whereas the highest total turbulent kinetic energy overall did not produce the most scattering. The variance of directional spectra is found to increase linearly as a function of propagation time.

The dynamics of turbulent flow structures in the wakes of barchan dunes is investigated to understand the complex, long-range interactions that occur between these three-dimensional bedforms. High-frame-rate stereo-particle image velocimetry measurements are collected from the cross-stream plane in a refractive-index-matched flume, wherein rigid models are immersed in the logarithmic region of a turbulent boundary layer. Through application of Taylor's hypothesis, limited-domain pseudo-three-dimensional reconstructions of the flow are made, wherein coherent structures are identified in the wake of an isolated barchan that resemble hairpin-like vortices. Amplitude modulation analysis, based on wavelet decomposition of velocity fluctuations and swirling strength, suggests a correlation between the shedding of these coherent structures and the passage of large-scale motions (LSMs) aloft in the turbulent boundary layer within which the barchan dune is immersed. Impulse analysis of shear stress events shows that, while the hairpin-like structures predominantly induce ejections of low-momentum fluid, the intermittent passage of an overlying high-momentum LSM yields intense sweep events as they impact the wall. Similar flow dynamics is found in dune–dune collision configurations involving barchan dunes arranged in tandem, with the exception that significant flow asymmetries are introduced, resulting in structures resembling single-legged hairpin-like (or ‘cane’) vortices being identified in conditional averages. These results provide insight into both the morphodynamics of dune interactions as well as the interactions between boundary-layer structure and roughness elements protruding into the log layer.

Soft corals, such as the bipinnate sea plume Antillogorgia bipinnata, are colony building animals that feed by catching food particles brought by currents. Because of their flexible skeleton, they bend and sway back and forth with the wave swell. In addition to this low-frequency sway of the whole colony, branches of A. bipinnata vibrate at high frequency with small amplitude and transverse to the flow as the wave flow speed peaks. In this paper, we investigate the origin of these yet unexplained vibrations and consider their effect on soft corals. Estimation of dynamical variables along with finite element implementation of the wake-oscillator model favour vortex-induced vibrations (VIVs) as the most probable origin of the observed rapid dynamics. To assess the impact of the dynamics on filter feeding, we simulated particles advected by the flow around a circular cylinder and calculated the capture rate with an in-house monolithic fluid–structure interaction (FSI) finite element solver and Python code. We observe that vibrating cylinders can capture up to 40 % more particles than fixed cylinders at frequency lock-in. Therefore, VIVs plausibly offer soft corals a better food capture.

We simulated laminar flow through a hexagonal sphere pack driven by a sinusoidal volume force using direct numerical simulation. We vary two independent parameters, the Hagen and Womersley numbers, representing the amplitude and frequency of the forcing. First, we determine for which regions in the parameter space nonlinear effects have to be considered. We judge the presence of nonlinear effects from the departure of the superficial velocity and kinetic energy from a linear behaviour as well as from the presence of higher harmonics in the discrete Fourier transform of the velocity field. We discuss the asymptotic behaviour of the onset of nonlinearity in the limits of low and high Womersley number, and we delineate approximately the parameter region that can be described using the linear theory. Second, we document the changes of instantaneous velocity fields with Hagen and Womersley numbers. We show that the onset of nonlinearity is accompanied by a loss of fore–aft symmetry of the flow, and subsequently, we employ the deviation from this symmetry to quantify the strength of nonlinear effects in the instantaneous velocity fields. Based on this analysis, we demonstrate that for higher Womersley numbers, the strongest nonlinear effects occur during the deceleration of the superficial velocity; consequently, the development of the nonlinearity is not in phase with the superficial velocity. Finally, we describe the leading-order nonlinear effects in the frequency domain and the interaction among the nonlinear Fourier modes that leads to a temporal variation in the strength of nonlinear effects.

We investigate the fundamental time scales that characterise the statistics of fragmentation under homogeneous isotropic turbulence for air–water bubbly flows at moderate to large bubble Weber numbers, $We$. We elucidate three time scales: $\tau _r$, the characteristic age of bubbles when their subsequent statistics become stationary; $\tau _\ell$, the expected lifetime of a bubble before further fragmentation; and $\tau _c$, the expected time for the air within a bubble to reach the Hinze scale, radius $a_H$, through the fragmentation cascade. The time scale $\tau _\ell$ is important to the population balance equation (PBE), $\tau _r$ is critical to evaluating the applicability of the PBE no-hysteresis assumption, and $\tau _c$ provides the characteristic time for fragmentation cascades to equilibrate. By identifying a non-dimensionalised average speed $\bar {s}$ at which air moves through the cascade, we derive $\tau _c=C_\tau \varepsilon ^{-1/3} a^{2/3} (1-(a_{max}/a_H)^{-2/3})$, where $C_\tau =1/\bar {s}$ and $a_{max}$ is the largest bubble radius in the cascade. While $\bar {s}$ is a function of PBE fragmentation statistics, which depend on the measurement interval $T$, $\bar {s}$ itself is independent of $T$ for $\tau _r \ll T \ll \tau _c$. We verify the $T$-independence of $\bar {s}$ and its direct relationship to $\tau _c$ using Monte Carlo simulations. We perform direct numerical simulations (DNS) at moderate to large bubble Weber numbers, $We$, to measure fragmentation statistics over a range of $T$. We establish that non-stationary effects decay exponentially with $T$, independent of $We$, and provide $\tau _r=C_{r} \varepsilon ^{-1/3} a^{2/3}$ with $C_{r}\approx 0.11$. This gives $\tau _r\ll \tau _\ell$, validating the PBE no-hysteresis assumption. From DNS, we measure $\bar {s}$ and find that for large Weber numbers ($We>30$), $C_{\tau }\approx 9$. In addition to providing $\tau _c$, this obtains a new constraint on fragmentation models for PBE.

We experimentally investigate the surface drag characteristics of a staggered-distributed cube array and its interaction with the turbulent structure of the overlying flow. Instantaneous maps of the pressure field, inferred from in-plane velocity data are used to estimate the forces acting on a target roughness element. Coupled statistics of the force in combination with conditional flow analysis and extended proper orthogonal decomposition (POD) of the pressure field, based on the velocity POD modes, elucidate the relevant mechanisms responsible for surface drag generation. The results show that turbulent motions, at different scales, leave an imprint on the pressure field. Specifically, positive and negative fluctuations are generally associated with flow regions experiencing a local deceleration and acceleration, respectively. Although large-scale motions were found to be the single greatest contributor to the fluctuating pressure field, their direct influence on the surface drag fluctuations appears to be mitigated by the relative size of the considerably smaller roughness obstacles. We hypothesise that a pressure wave induced by the passage of alternating high- and low-momentum regions evenly affects the flow field over a broad region, coupling the forces on the windward and leeward sides of the cube, which, in turn, partially cancel each other out. Uncorrelated, intermediate and small-scale pressure events are thus more important to the overall drag fluctuations. While the direct influence of the large-scale structures on the surface drag may be smaller than expected, the results suggest that they are still significant for the role they play in modulating the small-scale pressure events in the canopy region.