Non-modal linear stability analysis results are presented for hypersonic flow over an elliptic cone with an aspect ratio of two at zero angle of attack, completing earlier modal instability analysis of flow around the same geometry. The theoretical framework to perform transient growth analysis of compressible flows on a generalized two-dimensional frame of reference is developed for the first time and is then applied to solve the initial-value problem governing non-modal linear instability on planes perpendicular to the cone axis, taken at successive streamwise locations along the elliptic cone. Parameter ranges examined here are chosen so as to model flight of the Hypersonic International Flight Research Experimentation 5 (HIFiRE-5) test geometry at altitudes of 21 km and 33 km, corresponding to Mach numbers 7.45 and 8.05 and unit Reynolds numbers $Re' = 1.07\times 10^7$ and $1.89\times 10^6$, respectively. Results obtained indicate that the significance of the non-modal growth for laminar–turbulent transition increases with increasing flight altitude (decreasing Reynolds number). At a given set of flow parameters, transient growth is stronger in the vicinity of the tip of the cone and in azimuthal locations away from both of the minor (centreline) and major (attachment line) axes of the cone. Linear optimal disturbances calculated at conditions of maximal transient growth are found to peak in the crossflow region of the elliptic cone. These structures are elongated along the streamwise spatial direction, while being periodic along the spanwise direction with periodicity lengths of the same order of magnitude as the well-known structures identified as crossflow vortices in both experiments and simulations.

Data reconstruction of rotating turbulent snapshots is investigated utilizing data-driven tools. This problem is crucial for numerous geophysical applications and fundamental aspects, given the concurrent effects of direct and inverse energy cascades. Additionally, benchmarking of various reconstruction techniques is essential to assess the trade-off between quantitative supremacy, implementation complexity and explicability. In this study, we use linear and nonlinear tools based on the proper orthogonal decomposition (POD) and generative adversarial network (GAN) for reconstructing rotating turbulence snapshots with spatial damages (inpainting). We focus on accurately reproducing both statistical properties and instantaneous velocity fields. Different gap sizes and gap geometries are investigated in order to assess the importance of coherency and multi-scale properties of the missing information. Surprisingly enough, concerning point-wise reconstruction, the nonlinear GAN does not outperform one of the linear POD techniques. On the other hand, the supremacy of the GAN approach is shown when the statistical multi-scale properties are compared. Similarly, extreme events in the gap region are better predicted when using GAN. The balance between point-wise error and statistical properties is controlled by the adversarial ratio, which determines the relative importance of the generator and the discriminator in the GAN training.

The impact of fluid drops on solid substrates is a cardinal fluid dynamics phenomenon intrinsically related to many fields. Although these impacting objects are very often non-spherical and non-Newtonian, previous studies have mainly focused on spherical Newtonian drops. As a result, both shape and rheological effects on the drop-spreading dynamics remain largely unexplored. In the present work we use a mixed approach combining experiments with multiphase three-dimensional numerical simulations to extend the work reported by Luu & Forterre (J. Fluid Mech., vol. 632, 2009, pp. 301–327) by highlighting the fundamental role of shape in the normal impact of viscoplastic drops. Such complex fluids are highly common in various industrial domains and ideally behave either like a rigid body or a shear-rate-dependent liquid, according to the stress solicitation. Spherical, prolate, cylindrical and prismatic drops are considered. The results show that, under negligible capillary effects, the impacting kinetic energy of the drop is dissipated through viscoplastic effects during the spreading process, giving rise to three flow regimes: (i) inertio-viscous, (ii) inertio-plastic, and (iii) mixed inertio-visco-plastic. These regimes are deeply affected by the drop initial aspect ratio, which in turn reveals the possibility of using drop shape to control spreading. The physical mechanisms driving the considered phenomenon are underlined by energy budget analyses and scaling laws. The results are summarised in a two-dimensional diagram linking the drop maximum spreading, minimum height and final shape with different spreading regimes through a single dimensionless parameter, here called the impact number.

An understanding of pressure propagation mechanisms is crucial in finding suitable conditions for the temporary storage, transmission and attenuation of a large pressure signal in a multi-plug gelled pipeline. The current work investigates the transient flow start in a multi-plug gelled pipeline, filled with a weakly compressible, thixotropic waxy gelled crude oil. A multi-plug gel can form either naturally or artificially. We solve time-dependent mass and momentum conservation equations for the gas phase and conservation equations together with a shear-history-dependent constitutive model for the gel phase to capture the transient phenomena. An advection equation traces the motion of the gel–gas interface using the volume of fluid method. The results of this work show that pressure propagation in the first gel plug compresses it. The compressed first gel plug further compresses the gas pocket, which delays pressure propagation in the downstream gel. The delay in the pressure propagation through the second gel plug creates a high-pressure gradient in the first gel plug. A high-pressure gradient in the first gel results in faster degradation of the first gel. Degraded gel offers a substantially lower resistance to flow, allowing a high-pressure gradient in the second gel. A steeper pressure gradient assists the breakage of the next gel plug and results in a sequential gel breakage. This sequential gel breakage allows flow restart in a long pipeline. The results also indicate that the compressibility of the gas pocket dominates the overall compressibility of the system, controlling both pressure propagation and flow-restart time.

This paper investigates the shock-induced instability of the interfaces between gases and dense granular media with finite length via the coarse-grained compressible computational fluid dynamics–discrete parcel method. Despite generating a typical spike-bubble structure reminiscent of the Richtmyer–Meshkov instability (RMI), the shock-driven granular instability (SDGI) is governed by fundamentally different mechanisms. Unlike the RMI arising from baroclinic vorticity deposition on the interface, the SDGI is closely associated with the interfacial and bulk granular dynamics, which evolve with the transient coupling between particles and gases. Consequently, the SDGI follows a growth law distinctly different from that of the RMI, namely a semilinear slow regime followed by an exponentially expedited regime and a quadratic asymptotic regime. We further establish the instability criteria of the SDGI for granular media with infinite and finite lengths, which do not exist in the RMI. A scaling growth law of the SDGI for dense granular media with finite length is derived by normalizing the time with the rarefaction propagation time, which successfully collapses the data from cases with varying shock strength, particle column length and particle volume fraction and ought to hold for granular media with varying particle parameters. The effect of the initial perturbation magnitude can be properly considered in the scaling growth law by incorporating it into the length normalization.

Grounding lines exist where land-based glacial ice flows on to a body of water. Accurately modelling grounding-line migration at the ice–ocean interface is essential for estimating future ice-sheet mass change. On the interior of ice sheets, the shores of subglacial lakes are also grounding lines. Grounding-line positions are sensitive to water volume changes such as sea-level rise or subglacial-lake drainage. Here, we introduce numerical methods for simulating grounding-line dynamics in the marine ice sheet and subglacial-lake settings. Variational inequalities arise from contact conditions that relate normal stress, water pressure and velocity at the base. Existence and uniqueness of solutions to these problems are established using a minimisation argument. A penalty method is used to replace the variational inequalities with variational equations that are solved using a finite-element method. We illustrate the grounding-line response to tidal cycles in the marine ice-sheet problem and filling–draining cycles in the subglacial-lake problem. We introduce two computational benchmarks where the known lake volume change is used to measure the accuracy of the numerical method.

New insight into the contribution of the microscale vortex evolution to convection heat transfer in porous media is presented in this paper. The objective is to determine how the microscale vortices influence convection heat transfer in turbulent flow inside porous media. The microscale temperature distribution is analysed using flow visualization in two dimensions using streamlines and in three dimensions using the Q-criterion. The pertinent observations are supplemented with a comparison of surface skin friction and heat transfer using: (i) surface skin-friction lines and (ii) the joint probability density function of the pressure and skin-friction coefficients, along with the Nusselt number. The microscale flow phenomena observed are corroborated with the features of the frequency spectra of the drag coefficient and macroscale Nusselt number. The large eddy simulation technique is used in this study to investigate the flow field inside a periodic porous medium. The Reynolds numbers of the flow are 300 and 500. The porous medium consists of solid obstacles in the shape of square and circular cylinders. Two distinct flow regimes are represented by using the porosities of 0.50 and 0.87. The results show that the surface Nusselt number distribution is dependent on whether the micro-vortices are attached to or detached from the surface of the obstacle. The spectra of the macroscale Nusselt number and the pressure drag are similar, signifying a correlation between the dynamics of heat transfer and the microscale turbulent structures. Both vortex shedding and secondary flow instabilities are observed that significantly influence the Nusselt number. The fundamental insight gained in this paper can inform the development of more robust macroscale models of convection heat transfer in turbulent flow in porous media.

The problem of hydroelastic wave diffraction by a surface-piercing vertical circular cylinder mounted on the bottom of an ice-covered channel is considered. The ice sheet is modelled as an elastic thin plate with homogeneous properties, while the linearized velocity potential theory is adopted to describe the motion of the fluid. The solution starts from the Green function satisfying all other boundary conditions apart from that on the body surface. This is obtained through applying a Fourier transform in the longitudinal direction of the channel and adopting an eigenfunction expansion in the vertical direction. The boundary conditions on the side walls and ice edges are imposed through an orthogonal product. Through the Green function, the velocity potential due to a surface-piercing structure with arbitrary shape can be expressed through a source distribution formula derived in this work, in which only integrals over the body surface and its interaction line with the ice sheet need to be retained. For a vertical circular cylinder, the unknown source distribution can be expanded further into a Fourier series in the circumferential direction, and then the analytical solution of the velocity potential can be obtained further. Extensive results and discussions are provided for the hydrodynamic forces and vertical shear forces on the cylinder, as well as the deflection and strain of the ice sheet. In particular, the behaviour of the solution near one of the natural frequencies of the channel is investigated in detail.

Thin, roughly horizontal low-permeability layers are a common form of large-scale heterogeneity in geological porous formations. In this paper, the dynamics of a buoyancy-driven plume in a two-dimensional layered porous medium is studied theoretically, with the aid of high-resolution numerical simulations. The medium is uniform apart from a thin, horizontal layer of a much lower permeability, located a dimensionless distance $L\gg 1$ below the dense plume source. If the dimensionless thickness $2\unicode[STIX]{x1D700}L$ and permeability $\unicode[STIX]{x1D6F1}$ of the low-permeability layer are small, the effect of the layer is found to be well parameterized by its impedance $\unicode[STIX]{x1D6FA}=2\unicode[STIX]{x1D700}L/\unicode[STIX]{x1D6F1}$. Five different regimes of flow are identified and characterized. For $\unicode[STIX]{x1D6FA}\ll L^{1/3}$, the layer has no effect on the plume, but as $\unicode[STIX]{x1D6FA}$ is increased the plume widens and spreads over the layer as a gravity current. For still larger $\unicode[STIX]{x1D6FA}$, the flow becomes destabilized by convective instabilities both below and above the layer, until, for $\unicode[STIX]{x1D6FA}\gg L$, the spread of the plume is dominated by convective mixing and buoyancy is transported across the layer by diffusion alone. Analytical models for the spread of the plume over the layer in the various different regimes are presented.

A turbulent circular disk wake database (Chongsiripinyo & Sarkar, J. Fluid Mech., vol. 885, 2020) at Reynolds number $Re = U_\infty D/\nu = 5 \times 10^{4}$ is interrogated to identify the presence of large-scale streaks – coherent elongated regions of streamwise velocity. The unprecedented streamwise length – until $x/D \approx 120$ – of the simulation enables investigation of the near and far wakes. The near wake is dominated by the vortex shedding (VS) mode residing at azimuthal wavenumber $m=1$ and Strouhal number $St = 0.135$. After filtering out the VS structure, conclusive evidence of large-scale streaks with frequency $St \rightarrow 0$, equivalently streamwise wavenumber $k_x \rightarrow 0$ in the wake, becomes apparent in visualizations and spectra. These streaky structures are found throughout the simulation domain beyond $x/D \approx 10$. Conditionally averaged streamwise vorticity fields reveal that the lift-up mechanism is active in the near as well as the far wake, and that ejections contribute more than sweeps to events of intense $-u'_xu'_r$. Spectral proper orthogonal decomposition is employed to extract the energy and the spatiotemporal features of the large-scale streaks. The streak energy is concentrated in the $m=2$ azimuthal mode over the entire domain. Finally, bispectral mode decomposition is conducted to reveal strong interaction between $m=1$ and $St = \pm 0.135$ modes to give the $m=2$, $St \rightarrow 0$ streak mode. Our results indicate that the self-interaction of the VS mode generates the $m=2$, $St \rightarrow 0$ streamwise vortices, which leads to streak formation through the lift-up process. To the authors’ knowledge, this is the first study that reports and characterizes large-scale low-frequency streaks and the associated lift-up mechanism in a turbulent wake.

The dynamics of thin, non-circular droplets evaporating in the diffusion-limited regime is examined. The challenging non-rectilinear mixed boundary problem this poses is solved using a novel asymptotic approach and an asymptotic expansion for the evaporative flux from the free surface of the droplet is found. While theoretically valid only for droplets that are close to circular, it is demonstrated that the methodology can successfully be applied to droplets with a wide variety of footprint shapes, including polygons and highly non-convex domains. As our solution for the flux fundamentally represents a novel result in potential theory, the applications are numerous, as the mixed boundary value problem arises in fields as diverse as electrostatics and contact mechanics. Here, we demonstrate the practicality of our result by considering the analytically tractable case of deposition of solute from large droplets in detail, including a matched asymptotic analysis to resolve the pressure, streamlines and deposition up to second order.

A droplet charged above the Rayleigh limit is unstable. In the resulting dynamical process, referred to as a Coulomb explosion, smaller droplets with higher charge-to-mass ratios are ejected, reducing the charge of the parent droplet below the Rayleigh limit. Furthermore, if the droplet is sufficiently small, the electric field on its surface can promote ion field emission. Ion emission can lower the charge of a spherical droplet below its Rayleigh limit, keeping it stable, or reduce the charge of a deforming droplet, changing its dynamics and potentially preventing the Coulomb explosion. This article develops a continuum phase field electrohydrodynamic model to study the interplay between Coulomb explosions and ion emission, using charged nanodroplets of the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMI-Im) as a case study. In small droplets (diameter $D \lesssim 20$ nm for EMI-Im), the electric field is strong enough to emit ions in the early phase of the droplet's evolution, suppressing the Coulomb explosion. For $20 \lesssim D \lesssim 45$ nm, the electric field on the EMI-Im droplet may not promote significant ion emission; however, as the unstable droplet becomes ellipsoidal, ions are emitted from its vertices, ultimately suppressing the Coulomb explosion while shedding $20\unicode{x2013}40\,\%$ of the initial charge. For larger EMI-Im droplets, $45 \lesssim D \lesssim 100$ nm, the evolution typical of a Coulomb explosion is observed, accompanied by ion emission which is however insufficient to prevent the Coulomb explosion. Ion emission and the smaller progeny droplets account for $24\,\%$ and $16\,\%$ of the initial charge, respectively.

Helical rotating turbulence is a chiral and anisotropic flow. The energy and helicity transfers of helical rotating turbulence are studied in this paper. First, we discuss the antisymmetry and conservation of energy and helicity transfers. There are three expressions for helicity transfers due to the commutability of differential operators. The first expression is derived here. The second expression violates antisymmetry, and the third one introduces non-physical effects. The relations of these expressions are discussed in detail, including those about the sum of all triads and partial triads, as well as those about helical wave decomposition. Through direct numerical simulations, we find that helicity can reduce inverse energy cascades. The inhibition is mainly associated with transhelical energy fluxes and the interactions of two-dimensional modes. The inverse cascades of decomposed energy fluxes are related to the two-dimensionalization. For helicity, rotation does not affect the total helicity flux but generally suppresses the decomposed helicity fluxes. Positive homochiral and negative heterochiral helicity fluxes are associated with corresponding positive anisotropic transfers. Notably, the transhelical helicity fluxes increase the amplitudes of both positive and negative helicity, which is related to the chirality polarization.

This paper describes, from a theoretical point of view, the appearance and characteristics of granular roll waves in chute flow, and the maximal size these waves can attain for a given influx of material into the system. Granular roll waves are steady travelling wave solutions of the generalized Saint-Venant equations for flowing granular matter, appearing when the Froude number $Fr$ of the incoming flow exceeds a critical value, $Fr>Fr_{cr}$. We focus upon the phase space of the corresponding dynamical system, where the roll waves take the form of a stable limit cycle around an unstable fixed point; this limit cycle gives precise information on the size and periodicity of the roll wave. It is found that, for any given value of $Fr$, the limit cycle cannot become arbitrarily large because it is constrained by a homoclinic loop in phase space. Roll waves of larger amplitude can be generated by increasing the Froude number $Fr$.