The paper contains a detailed study of the inertial instability of a barotropic Bickley jet on the $f$-plane in the continuously stratified primitive equations model, and a comparison of this essentially ageostrophic instability with the classical baroclinic one. Analytical and numerical investigation of the linear stability of the jet in the long-wave sector is performed for a range of Rossby and Burger numbers. The major results are that: (1) the standard symmetric inertial instability, appearing at high enough Rossby numbers, turns out to be the infinite-wavelength limit of an asymmetric inertial instability, this latter having the highest growth rate for a large range of vertical wavenumbers; (2) inertial instability coexists with the standard baroclinic instability, which becomes dominant at small Rossby numbers. Nonlinear saturation of the inertial instability of the jet with a superimposed random small-amplitude perturbation is then studied, using the Weather Research and Forecast model. It is shown that at first stages the inertial instability dominates. It is localized near the maximum of the anticyclonic shear and is associated with the highest attainable value of the vertical wavenumber. The saturation of the inertial instability leads to the homogenization of the geostrophic momentum in the unstable region. At later stages, another baroclinic instability develops, characterized by lower values of the vertical wavenumber. This instability saturates by forming large-scale vortices downstream. It is identified as the leading instability of a marginally inertially stable jet resulting from the initial one through homogenization of the geostrophic momentum. The rough scenario of the evolution of essentially ageostrophic jets is, thus, as follows: the inertial instability rapidly saturates and baroclinic instability takes over. It is shown that reorganization of the flow due to developing instabilities is an efficient source of inertia-gravity waves.

The paper reports a new lattice Boltzmann approach to simulating wetting–drying processes in shallow-water flows. The scheme is developed based on the Chapman–Enskog analysis and the Taylor expansion, which is consistent with the theory of the lattice Boltzmann method. All the forces, such as bed slope and bed friction, are taken into account naturally in determining the wet–dry interface, without the use of either the spurious assumption of a thin water film on a dry bed or the non-physical extrapolation of certain variables such as water depth or velocity. This offers a simple and general model for simulating wetting–drying processes in complex flows involving external forces. Its verification is carried out by modelling several one-dimensional (1D) and two-dimensional (2D) flows: (i) 1D sloshing over a parabolic container; (ii) a 1D tidal wave over three adverse bed slopes; (iii) a 1D solitary wave run up on a plane sloping beach; (iv) a tsunami run up on a plane beach; (v) a 2D stationary case with wet–dry boundaries; (vi) a 2D long-wave resonance over a parabolic basin; and (vii) a 2D solitary wave run up on a conical island. The numerical results agree well with analytical solutions, other numerical results and experimental data, demonstrating the effectiveness and accuracy of the new approach.

Deterministic lateral displacement (DLD) technology is a newly developed method which can separate microscale and nanoscale particles continuously and efficiently. In this paper, a direct numerical simulation method (i.e. a fictitious domain method) is used to simulate the motion of an elastic particle (modelled as homogeneously elastic body) in the DLD device. The effects of the particle deformability on the critical separation diameter are investigated. Our results indicate that there exists a critical deformability, below which the critical diameter decreases with increasing deformability, whereas beyond which the critical diameter increases with increasing deformability. The reasons are discussed via the consideration of the effects of the particle deformation and the lubrication force on the lateral position of the particle centre point. In addition, our results show that the increase in the gap distance between adjacent posts in both directions or in the longitudinal direction alone leads to the increase in the critical particle size with respect to the gap size, which can be explained by the lateral position of the separation streamline of the undisturbed flow.

Full numerical simulations of the Navier–Stokes equations for four cases of vertically falling liquid films with three-dimensional surface waves have been performed. Flow conditions are based on several previous experimental studies where the streamwise and spanwise wavelengths were imposed, which we exploit by simulating periodic wave segments. The considered flows are laminar but approach conditions at which intermittent wave-induced turbulence has been observed elsewhere. Working liquids range from water to silicone oil and cover a large interval of the Kapitza number ($\textit {Ka}=18\mbox{--}3923$), which relates capillary to viscous forces. Simulations were performed on a supercomputer, using a finite-volume code and the volume of fluid and continuum surface force methods to account for the multiphase nature of the flow. Our results show that surface waves, consisting of large horseshoe-shaped wave humps concentrating most of the liquid and preceded by capillary ripples on a thin residual film, segregate the flow field into two regions: an inertia-dominated one in the large humps, where the local Reynolds number is up to five times larger than its mean value, and a visco-capillary region, where capillary and/or viscous forces dominate. In the inertial region, an intricate structure of different-scale vortices arises, which is more complicated than film thickness variations there suggest. Conversely, the flow in the visco-capillary region of large-$\textit {Ka} $ fluids is entirely governed by the local free-surface curvature through the action of capillary forces, which impose the pressure distribution in the liquid film. This results in flow separation zones underneath the capillary troughs and a spanwise cellular flow pattern in the region of capillary wave interference. In some cases, capillary waves bridge the large horseshoe humps in the spanwise direction, coupling the two aforementioned regions and leading the flow to oscillate between three- and two-dimensional wave patterns. This persists over long times, as we show by simulations with the low-dimensional model of Scheid et al. (J. Fluid Mech., vol. 562, 2006, pp. 183–222) after satisfactory comparison with our direct simulations at short times. The governing mechanism is connected to the bridging capillary waves, which drain liquid from the horseshoe humps, decreasing their amplitude and wave speed and causing them to retract in the streamwise direction. Overall, it is observed that spanwise flow structures (not accounted for in two-dimensional investigations) are particularly complex due to the absence of gravity in this direction.

We use a three-dimensional computational model to study the fluid transport and mixing due to the beating of an infinite array of cilia. In accord with recent experiments, we observe two distinct regions: a fluid transport region above the cilia and a fluid mixing region below the cilia tip. The metachronal wave due to phase differences between neighbouring cilia is known to enhance the fluid transport above the ciliary tip. In this work, we show that the metachronal wave also enhances the mixing rates in the sub-ciliary region, often simultaneously with the flow rate enhancement. Our results suggest that this simultaneous enhancement in transport and mixing is due to an enhancement in shear flow. As the flow above the cilia increases, the shear rate in the fluid increases and this shear enhances stretching, which is an essential ingredient for mixing. Estimates of the mixing time scale indicate that, compared to diffusion, the mixing due to the cilia beat may be significant and sometimes dominates chemical diffusion.

The instability of shallow-water waves on a moderate shear to Langmuir circulation is considered. In such instances, specifically at the shallow end of the inner coastal region, the shear can significantly affect the drift giving rise to profiles markedly different from the simple Stokes drift. Since drift and shear are instrumental in the instability to Langmuir circulation, of key interest is how that variation in turn affects onset to Langmuir circulation. Also of interest is the effect on onset of various boundary conditions. To that end the initial value problem describing the wave–mean flow interaction which accounts for the multiple time scales of the surface waves, evolving shear and evolving Langmuir circulation is crafted from scratch, and includes the wave-induced drift and a consistent set of free-surface boundary conditions. The problem necessitates that Navier–Stokes be employed side by side with a set of mean-field equations. Specifically, the former is used to evaluate events with the shortest time scale, that is the wave field, while the mean field set is averaged over that time scale. This averaged set, the CLg equations, follow from the generalized Lagrangian mean equations and for the case at hand take the same form as the well-known CL equations, albeit with different time and velocity scales. Results based upon the Stokes drift are used as a reference to which those based upon drift profiles corrected for shear are compared, noting that the latter are asymptotic to the former as the waves transition from shallow to deep. Two typical temporal flow fields are considered: shear-driven flow and pressure-driven flow. Relative to the reference case, shear-driven flow is found to be destabilizing while pressure driven are stabilizing to Langmuir circulation. In pressure-driven flows it is further found that multiple layers, as opposed to a single layer, of Langmuir circulation can form, with the most intense circulations at the ocean floor. Moreover, the layers can extend into a region of flow beyond that in which the instability applies, suggesting that Langmuir circulation excited by the instability can in turn drive, as a dynamic consequence, contiguous albeit less intense Langmuir circulation. Pressure-driven flows also admit two preferred spacings, one closely in accord with observation for small-aspect-ratio Langmuir circulation, the other well in excess of observed large-aspect-ratio Langmuir circulation.

Previous clinical, in vitro experimental and in silico simulation studies have shown the complex dynamics of flow through prosthetic heart valves. In the case of bileaflet mechanical heart valves (BMHVs), complex flow phenomena are observed due to the presence of two rigid leaflets. A numerical method for this type of study must be able to accurately simulate pulsatile flow through BMHVs with the inclusion of leaflet motion and high-Reynolds-number flow modelling. Consequently, this study aims at validating a numerical method that captures the flow dynamics for pulsatile flow through a BMHV. A $23~ \mbox{mm}$ St. Jude Medical (SJM) Regent™ valve is selected for use in both the experiments and numerical simulations. The entropic lattice-Boltzmann method is used to simulate pulsatile flow through the valve with the inclusion of reverse leakage flow, while prescribing the flowrate and leaflet motion from experimental data. The numerical simulations are compared against experimental digital particle image velocimetry (DPIV) results from a previous study for validation. The numerical method is shown to match well with the experimental results quantitatively as well as qualitatively. Simulations are performed with efficient parallel processing at very high spatiotemporal resolution that can capture the finest details in the pulsatile BMHV flow field. This study validates the lattice-Boltzmann method as suitable for simulating pulsatile, high-Reynolds-number flows through prosthetic devices for use in future research.

A numerical investigation of the mean wall shear stress properties on a spatially developing turbulent boundary layer over a smooth flat plate was carried out by means of a zonal detached eddy simulation (ZDES) technique for the Reynolds number range $3060\leq Re_{\theta }\leq 13\, 650$. Some asymptotic trends of global parameters are suggested. Consistently with previous findings, the calculation confirms the occurrence of very large-scale motions approximately $5\delta $ to $6 \delta $ long which are meandering with a lateral amplitude of $0.3 \delta $ and which maintain a footprint in the near-wall region. It is shown that these large scales carry a significant amount of Reynolds shear stress and their influence on the skin friction, denoted $C_{f,2}$, is revisited through the FIK identity by Fukagata, Iwamoto & Kasagi (Phys. Fluids, vol. 14, 2002, p. L73). It is argued that $C_{f,2}$ is the relevant parameter to characterize the high-Reynolds-number turbulent skin friction since the term describing the spatial heterogeneity of the boundary layer also characterizes the total shear stress variations across the boundary layer. The behaviour of the latter term seems to follow some remarkable self-similarity trends towards high Reynolds numbers. A spectral analysis of the weighted Reynolds stress with respect to the distance to the wall and to the wavelength is provided for the first time to our knowledge and allows us to analyse the influence of the largest scales on the skin friction. It is shown that structures with a streamwise wavelength $\lambda _x >\delta $ contribute to more than $60\, \%$ of $C_{f,2}$, and that those larger than $\lambda _x >2\delta $ still represent approximately $45\, \%$ of $C_{f,2}$.

Vorticity transport is analysed within the leading-edge vortex generated on a rectangular flat plate of aspect ratio 4 undergoing a starting rotation motion in a quiescent fluid. Two analyses are conducted on the inboard half of the blade to better understand the vorticity transport mechanisms responsible for maintaining the quasi-equilibrium state of the leading-edge vortex. An initial global analysis between the $25$ and $50\, \%$ spanwise positions suggests that, although spanwise velocity is significant, spanwise convection of vorticity is insufficient to balance the flux of vorticity from the leading-edge shear layer. Subsequent detailed analyses of vorticity transport in planar control volumes at the $25$ and $50\, \%$ spanwise positions verify this conclusion and demonstrate that vorticity annihilation due to interaction between the leading-edge vortex and the opposite-sign layer on the plate surface is an important, often dominant, mechanism for regulation of leading-edge-vortex circulation. Thus, it provides an important condition for maintenance of an attached leading-edge vortex on the inboard portion of the blade.

A cylindrical vesicle under tension can undergo a pearling instability, characterized by the growth of a sinusoidal perturbation which evolves towards a collection of quasi-spherical bulbs connected by thin tethers, like pearls on a necklace. This is reminiscent of the well-known Rayleigh–Plateau instability, where surface tension drives the amplification of sinusoidal perturbations of a cylinder of fluid. We calculate the growth rate of perturbations for a cylindrical vesicle under tension, considering the effect of both inner and outer fluids, with different viscosities. We show that this situation differs strongly from the classical Rayleigh–Plateau case in the sense that, first, the tension must be above a critical value for the instability to develop and, second, even in the strong tension limit, the surface preservation constraint imposed by the presence of the membrane leads to a different asymptotic behaviour. The results differ from previous studies on pearling due to the consideration of variations of tension, which are shown to enhance the pearling instability growth rate, and lower the wavenumber of the fastest growing mode.

A new damping mechanism for vertically-sheared inertial motions is described involving an inertia–gravity wave that oscillates at half the inertial frequency, $f$, and that grows at the expense of inertial shear. This parametric subharmonic instability forms in baroclinic, geostrophic currents where thermal wind shear, by reducing the potential vorticity of the fluid, allows inertia–gravity waves with frequencies less than $f$. A stability analysis and numerical simulations are used to study the instability criterion, energetics, and finite-amplitude behaviour of the instability. For a flow with uniform shear and stratification, parametric subharmonic instability develops when the Richardson number of the geostrophic current nears $Ri_{PSI}=4/3+\gamma \cos \phi $, where $\gamma $ is the ratio of the inertial to thermal wind shear magnitude and $\phi $ is the angle between the inertial and thermal wind shears at the initial time. Inertial shear enters the instability criterion because it can also modify the potential vorticity and hence the minimum frequency of inertia–gravity waves. When this criterion is met, inertia–gravity waves with a frequency $f/2$ and with flow parallel to isopycnals amplify, extracting kinetic energy from the inertial shear through shear production. The solutions of the numerical simulations are consistent with these predictions and additionally show that finite-amplitude parametric subharmonic instability both damps inertial shear and is itself damped by secondary shear instabilities. In this way, parametric subharmonic instability opens a pathway to turbulence where kinetic energy in inertial shear is transferred to small scales and dissipated.

We report results from an experimental study of cavity formation during the impact of superhydrophobic spheres onto water. Using a simple splash-guard mechanism, we block the spray emerging during initial contact from closing thus eliminating the phenomenon known as ‘surface seal’, which typically occurs at Froude numbers $\mathit{Fr}= V_{0}^{2}/(gR_{0}) = O(100)$. As such, we are able to observe the evolution of a smooth cavity in a more extended parameter space than has been achieved in previous studies. Furthermore, by systematically varying the tank size and sphere diameter, we examine the influence of increasing wall effects on these guarded impact cavities and note the formation of surface undulations with wavelength $\lambda =O(10)~ \mathrm{cm}$ and acoustic waves $\lambda _{a}=O(D_{0})$ along the cavity interface, which produce multiple pinch-off points. Acoustic waves are initiated by pressure perturbations, which themselves are generated by the primary cavity pinch-off. Using high-speed particle image velocimetry (PIV) techniques we study the bulk fluid flow for the most constrained geometry and show the larger undulations ($\lambda =O (10~ \mathrm{cm}$)) have a fixed nature with respect to the lab frame. We show that previously deduced scalings for the normalized (primary) pinch-off location (ratio of pinch-off depth to sphere depth at pinch-off time), $H_{p}/H = 1/2$, and pinch-off time, $\tau \propto (R_{0}/g)^{1/2}$, do not hold for these extended cavities in the presence of strong wall effects (sphere-to-tank diameter ratio), $\epsilon = D_{0}/D_{tank} \gtrsim 1/16$. Instead, we find multiple distinct regimes for values of $H_{p}/H$ as the observed undulations are induced above the first pinch-off point as the impact speed increases. We also report observations of ‘kinked’ pinch-off points and the suppression of downward facing jets in the presence of wall effects. Surprisingly, upward facing jets emanating from first cavity pinch-off points evolve into a ‘flat’ structure at high impact speeds, both in the presence and absence of wall effects.

The stability of streamwise corner flow is investigated by means of direct numerical simulation at subcritical Reynolds numbers. The flow is harmonically forced, and global modes are extracted through a spectral decomposition. Spatial amplification in the near-corner region is observed even though the flow is shown to be subcritical in terms of spatial linear theory. This apparent discrepancy is resolved by extending the local analysis to include non-modal effects. It is demonstrated that the amplification is a result of the interaction between two coexistent spatial transient growth processes that can be associated with different parts of the linear stability spectrum. A detailed investigation of the underlying mechanisms shows that the transient amplification behaviour is caused by pseudo-resonance between the inviscid corner mode, and different sets of viscous modes. By comparison with studies of other locally inflectional flows, it is found that viscid–inviscid pseudo-resonance might be a general phenomenon leading to selective noise amplification.

We consider a homogeneous fluid of viscosity $\nu $ confined within an oblate spheroidal cavity of arbitrary eccentricity $\mathcal{E}$ marked by the equatorial radius $d$ and the polar radius $d \sqrt{1-\mathcal{E}^2}$ with $0<\mathcal{E}<1$. The spheroidal container rotates rapidly with an angular velocity ${\boldsymbol{\Omega}}_0 $ about its symmetry axis and precesses slowly with an angular velocity ${\boldsymbol{\Omega}}_p$ about an axis that is fixed in space. It is through both topographical and viscous effects that the spheroidal container and the viscous fluid are coupled together, driving precessing flow against viscous dissipation. The precessionally driven flow is characterized by three dimensionless parameters: the shape parameter $\mathcal{E}$, the Ekman number ${\mathit{Ek}}=\nu /(d^2 \delimiter "026A30C {\boldsymbol{\Omega}}_0\delimiter "026A30C )$ and the Poincaré number ${\mathit{Po}}=\pm \delimiter "026A30C {\boldsymbol{\Omega}}_p\delimiter "026A30C / \delimiter "026A30C \boldsymbol{\Omega}_0\delimiter "026A30C $. We derive a time-dependent asymptotic solution for the weakly precessing flow in the mantle frame of reference satisfying the no-slip boundary condition and valid for a spheroidal cavity of arbitrary eccentricity at ${\mathit{Ek}}\ll 1$. No prior assumptions about the spatial–temporal structure of the precessing flow are made in the asymptotic analysis. We also carry out direct numerical simulation for both the weakly and the strongly precessing flow in the same frame of reference using a finite-element method that is particularly suitable for non-spherical geometry. A satisfactory agreement between the asymptotic solution and direct numerical simulation is achieved for sufficiently small Ekman and Poincaré numbers. When the nonlinear effect is weak with $\delimiter "026A30C {\mathit{Po}}\delimiter "026A30C \ll 1$, the precessing flow in an oblate spheroid is characterized by an azimuthally travelling wave without having a mean azimuthal flow. Stronger nonlinear effects with increasing $\delimiter "026A30C {\mathit{Po}}\delimiter "026A30C $ produce a large-amplitude, time-independent mean azimuthal flow that is always westward in the mantle frame of reference. Implications of the precessionally driven flow for the westward motion observed in the Earth’s fluid core are also discussed.

In this paper I consider the self-excited rotation of an elliptical cylinder towed in a viscous fluid as a canonical model of nonlinear fluid–structure interactions with possible applications in the design of sensors and energy extraction devices. First, the self-excited ellipse system is shown to be analogous to the forced bistable oscillators studied in classic chaos theory. A single variable, the distance between the pivot and the centroid, governs the system bifurcation into bistability. Next, fully coupled computational fluid dynamics simulations of the motion of the cylinder demonstrate limit cycle, period doubling, intermittently chaotic and fully chaotic dynamics as the distance is further adjusted. The viscous wake behind the cylinder is presented for the limit-cycle cases and new types of stable wakes are characterized for each. In contrast, a chaotic case demonstrates an independence of the wake and structural states. The rotational kinetic energy is quantified and correlated to the vortex shedding and the trajectory periodicity. Chaotic and high-period system responses are found to persist when structural damping is applied and for Reynolds numbers as low as 200.

A detailed laboratory investigation of the mechanical and low-solubility gas coupling between wind and water has been undertaken using a suite of microphysical measurement techniques. Under a variety of wind conditions and in the presence and absence of mechanically generated short waves, approximately fetch-independent surface conditions have been achieved over short laboratory fetches of several metres. The mechanical coupling of the surface is found to be consistent with Banner (J. Fluid Mech. vol. 211, 1990, pp. 463–495) and Banner & Peirson (J. Fluid Mech. vol. 364, 1998, pp. 115–145). Bulk observations of re-aeration are consistent with previous laboratory studies. The surface kinematical behaviour is in accordance with the observations of Peirson & Banner (J. Fluid Mech. vol. 479, 2003, pp. 1–38). Also, their predictions of a strong enhancement of low-solubility gas flux at the onset of microscale breaking is confirmed and direct observations show a concomitant onset of very thin aqueous diffusion sublayers. It is found that the development of strong parasitic capillary waves towards the incipient breaking limit does not noticeably enhance constituent transfer. Across the broad range of conditions investigated during this study, the local instantaneous constituent transfer rate remains approximately log-normally distributed with an approximately constant standard deviation of $0.62\pm 0.15({\mathrm{log}}_e(\mathrm{m}~ {\mathrm{s}}^{-1}))$. Although wind-forced water surfaces are shown to be punctuated by intense tangential stresses and local surface convergence, localized surface convergence does not appear to be the single critical factor determining exchange rate. Larger-scale orbital wave straining is found to be a significant constituent transfer process in contrast to Witting (J. Fluid Mech. vol. 50, 1971, pp. 321–334) findings for heat fluxes, but the measured effects are consistent with his model. By comparing transfer rates in the presence and absence of microscale breaking, low-solubility gas transfer was decomposed into its turbulent/capillary ripple, gravity-wave-related and microscale breaking contributions. It was found that an efficiency factor of approximately $17\, \%$ needs to be applied to Peirson & Banner’s model, which is extended to field conditions. Although bulk thermal effects were observed and thermal diffusion layers are presumed thicker than their mass diffusion counterparts, significant thermal influences were not observed in the results.

This paper describes an investigation of the acoustic properties of a rigid plate with a periodic pattern of holes, in a compressible, ideal, inviscid fluid in the absence of mean flow. Leppington & Levine (J. Fluid Mech., vol. 61, 1973, pp. 109–127) obtained an approximation of the reflection and transmission coefficients of a plane wave incident on an infinitely thin plate with a rectangular array of perforations, assuming that a characteristic size of the perforations is negligible relative to that of the unit cell of the grating, itself assumed to be negligible relative to the wavelength. One part of the present study is of methodological interest. It establishes that it is possible to extend their approach to thick plates with a skew grating of perforations, thus confirming recent results of Bendali et al. (SIAM J. Appl. Math., vol. 73 (1), 2013, pp. 438–459), but in a much simpler way without using complex matched asymptotic expansions of the full wave or to a grating of multipoles. As is well-known, effective compliances for the plate can then be derived from the corresponding approximations of the reflection and transmission coefficients. These compliances are expressed in terms of the Rayleigh conductivity of an isolated perforation. Consequently, in one other part of the present study, the methodology recently introduced by Laurens et al. (ESAIM, Math. Model. Numer. Anal., vol. 47 (6), 2013, pp. 1691–1712) to obtain sharp bounds for the Rayleigh conductivity has been extended to include the case for which the openings of the perforations on the upper and lower sides of the plate are elliptical in shape. This not only enables the determination of these bounds and of the associated reflection and transmission coefficients for actual plates with tilted perforations but also yields single expressions covering all usual cases of perforations: straight or tilted with a circular or an elliptical cross-section.

We examine the form, properties, stability and evolution of simply-connected vortex-patch relative quasi-equilibria in the single-layer $f$-plane shallow-water model of geophysical fluid dynamics. We examine the effects of the size, shape and strength of vortices in this system, represented by three distinct parameters completely describing the families of the quasi-equilibria. Namely, these are the ratio $\gamma = L/L_D$ between the horizontal size of the vortices and the Rossby deformation length; the aspect ratio $\lambda $ between the minor to major axes of the vortex; and a potential vorticity (PV)-based Rossby number $\mathit{Ro}= q^{\prime }/f$, the ratio of the PV anomaly $q^{\prime }$ within the vortex to the Coriolis frequency $f$. By defining an appropriate steadiness parameter, we find that the quasi-equilibria remain steady for long times, enabling us to determine the boundary of stability $\lambda _c=\lambda _c(\gamma ,\mathit{Ro})$, for $0.25 \leq \gamma \leq 6$ and $\delimiter "026A30C \mathit{Ro}\delimiter "026A30C \leq 1$. By calling two states which share $\gamma ,\delimiter "026A30C \mathit{Ro}\delimiter "026A30C $ and $\lambda $ ‘equivalent’, we find a clear asymmetry in the stability of cyclonic ($\mathit{Ro}> 0$) and anticyclonic ($\mathit{Ro}<0$) equilibria, with cyclones being able to sustain greater deformations than anticyclones before experiencing an instability. We find that ageostrophic motions stabilise cyclones and destabilise anticyclones. Both types of vortices undergo the same main types of unstable evolution, albeit in different ranges of the parameter space, (a) vacillations for large-$\gamma $, large-$\mathit{Ro}$ states, (b) filamentation for small-$\gamma $ states and (c) vortex splitting, asymmetric for intermediate-$\gamma $ and symmetric for large-$\gamma $ states.

This investigation deals with the study of the mean structure of a mildly unstable non-ideal detonation wave. The analysis is based on the integration of one-dimensional reactive Euler equations with friction forces using a third-order Runge–Kutta scheme and a fifth-order weighted essentially non-oscillatory (WENO5) spatial discretization. A one-step Arrhenius reaction mechanism is used for modelling the chemical reaction. When the frictional forces are active, the limit cycle based on the post-shock pressure reveals an enhanced pulsating behaviour of the downstream subsonic reaction zone compared to the ideal case. The results show that the detonation-velocity deficit increases as the mean reaction zone becomes thicker compared to the generalized ZND model. A new master equation, based on the Favre-averaged quantities, is derived and analysed along with new sonicity and thermicity conditions. The analysis of the species, momentum and energy balances reveals that the presence of mechanical fluctuations within the reaction zone constitutes another source of energy withdrawal, meaning that the detonation deviates from its laminar structure. Furthermore, the compressibility of the flow is analysed and the relationships between the fluctuations of temperature, velocity and reactive scalar are discussed in terms of strong Reynolds analogies.

Topologically non-trivial configurations of stratified fluid domains are shown to generate selection mechanisms for conserved quantities. This is illustrated within the special case of a two-fluid system when the density of one of the fluids limits to zero, such as in the case of air and water. An explicit example is provided, demonstrating how the connection properties of the air domain affect total horizontal momentum conservation, despite the apparent translational invariance of the system. The correspondence between this symmetry and the selection process is also studied within the framework of variational principles for stratified ideal fluids.