In the present study, the influence of a uniformly moving impinging shock on the resulting shock wave–turbulent boundary layer interaction is numerically investigated. The relative Mach number of the shock front travelling above a flat-plate model varied between 0 and 2.3, while the quasi-steady inflow conditions remained constant with a Mach number of 3. To quantitatively evaluate the effect of shock travelling speed, a well-known scaling method for interaction length in quasi-steady flows was applied as a reference after significant improvements in modelling the effects of Reynolds number and wall temperature using new and existing data. Moreover, previously obtained experimental results for a limited range of travelling speeds were employed to validate the obtained numerical results. Three ranges of shock travelling speeds with distinctly different properties were extracted and quantitatively described using a developed correlation-based approach built on the extended quasi-stationary scaling law. In the first range, the scaled interaction length reaches its maximum for the given interaction strength and can be directly described by the scaling law obtained for quasi-stationary interactions. In the second travelling-speed range, the dependence of the interaction length on the interaction strength is explicitly influenced by the shock movement. With increasing shock travelling speed, the scaled interaction length here decreases significantly faster than in the quasi-stationary reference case. The end of this speed range is reached when the absolute shock front speed has caught up with the maximum speed of sound in the interaction zone, and thus the interaction length has fallen to zero. This travelling-speed limit signifies the transition to the third range, where upstream influence is no longer possible.

We study the influence of fringing magnetic fields on turbulent thermal convection in a horizontally extended rectangular domain. The magnetic field is created in the gap between two semi-infinite planar magnetic poles, with the convection layer located near the edge of the gap. We employ direct numerical simulations in this set-up for fixed Rayleigh and small Prandtl numbers, but vary the fringe width by controlling the gap between the magnetic poles and the convection cell. The magnetic field generated by the magnets is strong enough to cease the flow in the high magnetic flux region of the convection cell. We observe that as the local vertical magnetic field strength increases, the large-scale structures become thinner and align themselves perpendicular to the longitudinal sidewalls. We determine the local Nusselt and Reynolds numbers as functions of the local Hartmann number (based on the vertical component of the magnetic field), and estimate the global heat and momentum transport. We show that the global heat transport decreases with increasing fringe width for strong magnetic fields but increases with increasing fringe width for weak magnetic fields. In the regions of large vertical magnetic fields, the convective motion becomes confined to the vicinity of the sidewalls. The amplitudes of these wall modes show a non-monotonic dependence on the fringe width.

In this study, for the first time, we consider longitudinal motion of the walls during peristalsis in a distensible tube and how this affects backward (or retrograde) flow, i.e. peristaltic reflux. Building on the analytical model developed by Shapiro et al. (J. Fluid Mech., vol. 37, no. 4, 1969, pp. 799–825) based on lubrication theory, we model peristalsis as a two-dimensional infinite sinusoidal wavetrain. We develop an objective function with high mechanical pumping efficiency and low reflux to find optimal peristalsis conditions. We show that optimal wall longitudinal motion contributes substantially to limiting reflux during peristalsis. The results suggest that the optimal form of wall longitudinal velocity is a linear function of the wall transverse coordinate, moving forward with the wave when the tube is distended and retracting when contracted. Our results are in general agreement with clinical observations of ureteral peristalsis.

Compressible turbulent plane Couette flows are studied via direct numerical simulation for wall Reynolds numbers up to $Re_w=10\ 000$ and wall Mach numbers up to $M_w=5$. Various turbulence statistics are compared with their incompressible counterparts at comparable semilocal Reynolds numbers $Re^*_{\tau,c}$. The skin friction coefficient $C_f$, which decreases with $Re_w$, only weakly depends on $M_w$. On the other hand, the thermodynamic properties (mean temperature, density and others) strongly vary with $M_w$. Under proper scaling transformations, the mean velocity profiles for the compressible and incompressible cases collapse well and show a logarithmic region with the Kárman constant $\kappa =0.41$. Compared with wall units, the semilocal units yield a better collapse for the profiles of the Reynolds stresses. While the wall-normal and spanwise Reynolds stress components slightly decrease in the near-wall region, the inner peak of the streamwise component notably increases with increasing $M_w$ – indicating that flow becomes more anisotropic when compressible. In addition, the near-wall turbulence production decreases as $M_w$ increases – due to rapid wall-normal changes of viscosity caused by viscous heating. The streamwise and spanwise energy spectra show that the length scale of near-wall coherent structures does not vary with $M_w$ in semilocal units. Consistent with those in incompressible flows, the superstructures (the large-scale streamwise rollers) with a typical spanwise scale of $\lambda _z/h\approx 1.5{\rm \pi}$ become stronger with increasing $Re_w$. For the highest $Re_w$ studied, they contribute about $40\,\%$ of the Reynolds shear stress at the channel centre. Interestingly, flow visualization and correlation analysis show that the streamwise coherence of these structures degrades with increasing $M_w$. In addition, at comparable $Re^*_{\tau,c}$, the amplitude modulation of these structures on the near-wall small scales is quite similar between incompressible and compressible cases – but much stronger than that in plane Poiseuille flows.

Low Reynolds number turbulence in wall-bounded shear flows en route to laminar flow takes the form of spatially intermittent turbulent structures. In plane shear flows, these appear as a regular pattern of alternating turbulent and quasi-laminar flow. Both the physical and the spectral energy balance of a turbulent–laminar pattern in plane Couette flow are computed and compared to those of uniform turbulence. In the patterned state, the mean flow is strongly modulated and is fuelled by two mechanisms: primarily, the nonlinear self-interaction of the mean flow (via mean advection), and secondly, the extraction of energy from turbulent fluctuations (via negative spectral production, associated with an energy transfer from small to large scales). Negative production at large scales is also found in the uniformly turbulent state. Important features of the energy budgets are surveyed as a function of $Re$ through the transition between uniform turbulence and turbulent–laminar patterns.

Low Reynolds number turbulence in wall-bounded shear flows en route to laminar flow takes the form of oblique, spatially intermittent turbulent structures. In plane Couette flow, these emerge from uniform turbulence via a spatio-temporal intermittent process in which localised quasi-laminar gaps randomly nucleate and disappear. For slightly lower Reynolds numbers, spatially periodic and approximately stationary turbulent–laminar patterns predominate. The statistics of quasi-laminar regions, including the distributions of space and time scales and their Reynolds-number dependence, are analysed. A smooth, but marked transition is observed between uniform turbulence and flow with intermittent quasi-laminar gaps, whereas the transition from gaps to regular patterns is more gradual. Wavelength selection in these patterns is analysed via numerical simulations in oblique domains of various sizes. Via lifetime measurements in minimal domains, and a wavelet-based analysis of wavelength predominance in a large domain, we quantify the existence and nonlinear stability of a pattern as a function of wavelength and Reynolds number. We report that the preferred wavelength maximises the energy and dissipation of the large-scale flow along laminar–turbulent interfaces. This optimal behaviour is due primarily to the advective nature of the large-scale flow, with turbulent fluctuations playing only a secondary role.

We model linear, inviscid, internal tides generated by the interaction of a barotropic tide with one-dimensional topography. Starting from the body-forcing formulation of the hydrodynamic problem, we derive a coupled-mode system (CMS) using a local eigenfunction expansion of the stream function. For infinitesimal topography, we solve this CMS analytically, recovering the classical weak topography approximation (WTA) formula for the barotropic-to-baroclinic energy conversion rate. For arbitrary topographies, we solve this CMS numerically. The CMS enjoys faster convergence with respect to existing modal solutions and can be applied in the subcritical and supercritical regimes for both ridges and shelf profiles. We show that the non-uniform barotropic tide affects the baroclinic field locally over topographies with large slopes and we study the dependence of the radiated energy conversion rate on the criticality. We show that non-radiating or weakly radiating topographies are common in the subcritical regime. We also assess the region of validity of the WTA approximation for the commonly used Gaussian ridge and a compactly supported bump ridge studied here for the first time. Finally, we provide numerical evidence showing that in the strongly supercritical regime, the energy conversion rate for a ridge (respectively shelf) approaches the value obtained by the knife-edge (respectively step) topography.

Hypersonic flow over a two-dimensional compression corner is investigated using computational fluid dynamics and global resolvent analysis in this study, which is a continuation of the work done by Hao et al. (J. Fluid Mech., vol. 919, 2021, p. A4). The same baseline free-stream conditions with a Mach number of 7.7 and a unit Reynolds number of 4.2 × 106 m−1 are considered. The ramp angles range from 0° (equivalent to a flat plate) to 12° (slightly below the critical angle of global instability). During this process, the base flow evolves from no separation to incipient separation to large separation. The resolvent analysis reveals that the optimal response to upstream disturbances localised near the leading edge is in the form of steady streamwise streaks for all interaction strengths, which arise from transient growth in the flat-plate boundary layer due to the lift-up mechanism and significantly grow near the corner due to the Görtler instability. The most amplified spanwise wavelength decreases as the ramp angle is increased and scales with the incoming boundary-layer thickness.

Flow and turbulent structures generated by the interaction of forced incoming oscillatory flow with a circular, vertical cylinder placed in an open channel with a horizontal bed are investigated using eddy-resolving simulations. Validation simulations performed with a Keulegan–Carpenter (KC) number of 20 and multiple-mode forcing corresponding to the laboratory experiment of Sumer et al. (J. Fluid Mech., vol. 332, 1997, pp. 41–70) show that detached eddy simulation (DES) predicts more accurately the amplification of the bed shear stress beneath the horseshoe vortex system (upstream side of the cylinder) and the maximum magnitude of the bed shear stress at the downstream (wake) side of the cylinder compared with unsteady Reynolds-averaged Navier–Stokes simulations. High-Reynolds-number DES simulations are then conducted with 1.5 ≤ KC ≤ 30.8 and one-mode sinusoidal forcing of the streamwise velocity in the approaching flow to investigate the changes in the wake vortex-flow regimes, the coherence of the horseshoe vortices and the generation of other near-bed coherent structures in the wake during the oscillatory cycle. The flow is periodic, no horseshoe vortices form and no vortices are shed in the wake for KC = 1.5. By contrast, for KC ≥ 8 horseshoe vortices are present over part of the oscillatory cycle and up to three wake vortices are shed over each half-cycle as KC is increased to 30.8. For an intermediate range of KC numbers, one (KC = 15.4) or two (KC = 8) of the vortices forming at the back of the cylinder during each half-cycle are washed around it when the flow reverses. The main horseshoe vortex and other horizontal near-bed vortices have a large capacity to amplify the bed shear stresses when the incoming velocity magnitude is significantly less than its peak value. Assuming the depth-averaged velocity in the incoming (undisturbed) oscillatory flow is the same in simulations conducted with different KC numbers, the peak values of the sediment entrainment potential measured by the mean (cycle-averaged) volumetric flux of sediment entrained from the bed over one oscillatory cycle occur for 8 ≤ KC ≤ 15.4. For all KC numbers, the in-line force variation over the oscillatory cycle is fairly well approximated by the Morison equation. For KC = 1.5, the in-line force is only due to inertia effects. For KC = 30.8, the maximum and minimum values of the phase-averaged in-line force are approximatively in phase with those of the incoming flow velocity. For KC ≥ 15, the phase-averaged in-line force coefficients vary between 0.8 and 1.1 during most of the oscillatory cycle (e.g. when the incoming flow velocity is not close to zero). This is different from cases with KC ≤ 8 where the in-line force coefficient is equal to zero twice during the oscillatory cycle as the in-line force becomes equal to zero for non-zero values of the incoming velocity. The largest cycle-to-cycle variations of the in-line force coefficient and in-line force are observed around KC = 8. For KC = 8 and 15.4, the cylinder is subject to relatively large phase-averaged spanwise drag forces that are comparable to the peak phase-averaged streamwise drag forces. As KC is increased to 30.8, the phase-averaged spanwise drag force becomes zero over the whole oscillatory cycle but the cylinder is still subject to large instantaneous spanwise forces over part of the oscillatory cycle.

The effects of initial conditions on the evolution of the Richtmyer–Meshkov instability (RMI) at early to intermediate times are analysed, using numerical simulations of an idealised version of recent shock tube experiments performed at the University of Arizona (Sewell et al., J. Fluid Mech., vol. 917, 2021, A41). The experimental results are bracketed by performing both implicit large-eddy simulations of the high-Reynolds-number limit as well as direct numerical simulations (DNS) at Reynolds numbers lower than those observed in the experiments. Various measures of the mixing layer width $h$, known to scale as ${\sim }t^\theta$ at late time, based on both the plane-averaged turbulent kinetic energy and volume fraction profiles are used to explore the effects of initial conditions on $\theta$ and are compared with the experimental results. The decay rate $n$ of the total fluctuating kinetic energy is also used to estimate $\theta$ based on a relationship that assumes self-similar growth of the mixing layer. The estimates for $\theta$ range between 0.44 and 0.52 for each of the broadband perturbations considered and are in good agreement with the experimental results. Decomposing the mixing layer width into separate bubble and spike heights $h_b$ and $h_s$ shows that, while the bubbles and spikes initially grow at different rates, their growth rates $\theta _b$ and $\theta _s$ have equalised by the end of the simulations. Overall, the results demonstrate important differences between broadband and narrowband surface perturbations, as well as persistent effects of finite bandwidth on the growth rate of mixing layers evolving from broadband perturbations. Good agreement is obtained with the experiments for the different quantities considered; however, the results also show that care must be taken when using measurements based on the velocity field to infer properties of the concentration field.

Results from direct numerical simulations of a vertical natural convection boundary layer (NCBL) with $Pr=0.71$ reveal that the turbulence development of such a thermally driven convective flow has two distinct stages: at relatively low Grashof number, the bulk flow is turbulent while the near-wall region is laminar-like or weakly turbulent; at sufficiently high Grashof number, the entire flow becomes turbulent in the sense of von Kármán (cf. Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56, for the ultimate turbulent regime). Investigations on the turbulence statistics show that the near-wall Reynolds shear stress is negligible in the weakly turbulent regime but will grow in magnitude as the flow transitions to the ultimate regime at higher Grashof number. Similar behaviour is also seen in the streamwise turbulence intensity, where it develops from a mono-peak profile into a dual-peak structure as the Grashof number increases. At higher Grashof number, the near-wall energetic site is shown to have an energy distribution similar to that of a canonical wall-bounded turbulence (e.g. Hutchins & Marusic, Phil. Trans. R. Soc. A, vol. 365, 2007, pp. 647–664), with a peak centred at fixed location and wavelength ($y^+=18$ and $\lambda ^+_x=1000$) in viscous coordinates. Investigation on the spanwise spectra also suggests that the turbulent near-wall streaks emerge only at sufficiently high Grashof number, with constant spacing $\lambda _z^+\approx 130$. The extent of the weakly turbulent regime is identified using the maximum velocity location $\delta_m$ and a laminar length scale $\delta_u$. The development of near-wall turbulence is also investigated by examining the turbulence kinetic energy budget. In the weakly turbulent regime, the near-wall turbulence is sustained predominantly by the pressure transport in addition to the shear production. At higher Grashof number, the flow becomes fully turbulent, and both turbulent transport and shear production become stronger, while the pressure transport is decreased. These results also reveal that the production–dissipation ratio $P/\varepsilon$ of the NCBL would follow a fundamentally different trend to the canonical wall-bounded flows, which further supports that the near-wall turbulence generation is affected by the bulk flow.

Multifidelity models (MFMs) can be used to construct predictive models for flow quantities of interest (QoIs) over the space of uncertain/design parameters, with the purpose of uncertainty quantification, data fusion and optimization. For numerical simulation of turbulence, there is a hierarchy of methodologies ranked by accuracy and cost, where each methodology may have several numerical/modelling parameters that control the predictive accuracy and robustness of its resulting outputs. Compatible with these specifications, the present hierarchical MFM strategy allows for simultaneous calibration of the fidelity-specific parameters in a Bayesian framework as developed by Goh et al. (Technometrics, vol. 55, no. 4, 2013, pp. 501–512). The purpose of the MFM is to provide an improved prediction, mainly interpolation over the range covered by training data, by combining lower- and higher-fidelity data in an optimal way for any number of fidelity levels; even providing confidence intervals for the resulting QoI. The capabilities of the MFM are first demonstrated on an illustrative toy problem, and it is then applied to three realistic cases relevant to engineering turbulent flows. The latter include the prediction of friction at different Reynolds numbers in turbulent channel flow, the prediction of aerodynamic coefficients for a range of angles of attack of a standard airfoil and the uncertainty propagation and sensitivity analysis of the separation bubble in the turbulent flow over periodic hills subject to geometrical uncertainties. In all cases, based on only a few high-fidelity data samples, the MFM leads to accurate predictions of the QoIs. The result of the uncertainty quantification and sensitivity analyses are also found to be accurate compared with the ground truth in each case.

It is generally believed that the temperature and the velocity fields are highly coupled in compressible wall-bounded turbulence. In the present study, we employ a linear model, i.e. the two-dimensional spectral linear stochastic estimation (SLSE), to study this coupling from the perspective of the multi-scale energy-containing eddies. Particular attention is paid to the relevant statistical characteristics of the temperature field. The connections of the two fields are found to be varied with the wall-normal position in the boundary layer. In a nutshell, their entanglement is strongest in the near-wall region, and only the extreme thermal events cannot be captured by SLSE. In the logarithmic region, only the scales that correspond to the attached eddies and the very large-scale motions (VLSMs) are firmly coupled. The near-wall footprints of the former are organized in an additive manner and fulfil the predictions of the celebrated attached-eddy model. In the outer region, the two fields are linearly coupled only at the scales corresponding to VLSMs. These findings are demonstrated to be insensitive to the Mach number effects and ascribed to the similarity between the momentum and the heat transfer in compressible wall turbulence. It is also shown that it is the Reynolds number rather than Mach number that acts as a key similarity parameter in constructing their coupling. The framework built in the present study may pave a way for investigating the multi-physics coupling in turbulence, and reinforcing our analysing and modelling capability to the interrelated problems.

We report direct numerical simulations of the flow around a spanwise-flexible wing in forward flight. The simulations were performed at $Re=1000$ for wings of aspect ratio 2 and 4 undergoing a heaving and pitching motion at Strouhal number $St_c\approx 0.5$. We have varied the effective stiffness of the wing $\varPi _1$ while keeping the effective inertia constant, $\varPi _0=0.1$. It has been found that there is an optimal aerodynamic performance of the wing linked to a damped resonance phenomenon, that occurs when the imposed frequency of oscillation approaches the first natural frequency of the structure in the fluid, $\omega _{n,f}/\omega \approx 1$. In that situation, the time-averaged thrust is maximum, increasing by factor 2 with respect to the rigid case with an increase in propulsive efficiency of approximately 15 %. This enhanced aerodynamic performance results from the combination of larger effective angles of attack of the outboard wing sections and a delayed development of the leading edge vortex. With increasing flexibility beyond the resonant frequency, the aerodynamic performance drops significantly, in terms of both thrust production and propulsive efficiency. The cause of this drop lies in the increasing phase lag between the deflection of the wing and the heaving/pitching motion, which results in weaker leading edge vortices, negative effective angles of attack in the outboard sections of the wing, and drag generation in the first half of the stroke. Our results also show that flexible wings with the same $\omega _{n,f}/\omega$ but different aspect ratio have the same aerodynamic performance, emphasizing the importance of the structural properties of the wing for its aerodynamic performance.

We present new experiments of particle-laden turbulent fountains in a uniform horizontal crossflow, $u_a$, with momentum flux, $M_0$, and buoyancy flux, $B_0$. We use the ratio, $P$, of the crossflow speed to the characteristic fountain speed, $M_0^{-1/4}|B_0|^{1/2}$, and the ratio $U$, of the Stokes fall speed of the particles, $v_s$, to the characteristic fountain speed, to characterise the dynamics of a particle fountain in a crossflow. We find that the dynamics of these particle fountains can be categorised into three distinct regimes. In regime I when the fall speed of the particles is small in comparison with the characteristic fountain speed ($U\ll 1$), the particles remain well-coupled to the fountain fluid and the flow essentially behaves as a single-phase fountain in a crossflow. In the transitional regime II ($0.1< U<1$), when the fall speed of particles is comparable to the characteristic fountain speed, we observe some particles separating from the fountain fluid during the descent of the flow which leaves some fluid neutrally buoyant. As $U>1$ (regime III), we observe particles separating from the fountain as it rises from the source. We measure the average dispersal distance of the particles and the speed of the descending particles as a function of $U$ and $P$ and compare these results with models of a single-phase fountain in a crossflow. We build a regime diagram to describe the effect of $U$ and $P$ on the flow dynamics and consider our work in the context of deep-submarine volcanic eruptions.

Inspired by geological structures formed by magmatic intrusions that deform the Earth's crust, we investigate the elastohydrodynamic growth of a viscoplastic blister under an elastic sheet resting on a prewetted substrate. By combining experiments, scaling analysis and numerical simulations, we reveal new regimes for the elastoviscoplastic growth dynamics of the blister. The blister height and its apparent radius grow as $h(0,t) \sim t^{5/9}$ and $R(t) \sim t^{2/9}$ if the fluid pressure is set by bending of the sheet, and as $h(0,t) \sim t^{5/13}$ and $R(t) \sim t^{4/13}$ if the fluid pressure is set by stretching of the sheet. A plug-like flow inside the blister dictates its dynamics, whereas the blister takes a self-similar shape given by a balance of the fluid's yield stress and the pressure gradient induced by the deformation of the elastic sheet.

The perturbation response of small-scale shear layers in turbulence is investigated with direct numerical simulations (DNS). The analysis of shear layers in isotropic turbulence suggests that the typical layer thickness is about four times the Kolmogorov scale $\eta$. Response for sinusoidal perturbations is investigated for an isolated shear layer, which models a mean flow around the shear layers in turbulence. The vortex formation in the shear layer is optimally promoted by the perturbation whose wavelength divided by the layer thickness is about 7. These results indicate that the small-scale shear instability in turbulence is efficiently promoted by velocity fluctuations with a wavelength of about $30\eta$. Furthermore, DNS are carried out for decaying turbulence initialised by the artificially modified velocity field of isotropic turbulence. The vortex formation from shear layers is accelerated under the influence of external perturbations with the efficient wavelength to promote the instability. When velocity fluctuations with this wavelength are eliminated by a band-cut filter, the shear layers tend to persist for a long time without producing vortices. These behaviours affect the number of vortices in turbulence, which increases and decreases when velocity perturbations with the unstable wavelength of the instability are artificially amplified and damped, respectively. The increase in the number of vortices results in the enhancement of kinetic energy dissipation, enstrophy production and strain self-amplification. These results indicate that the perturbation response of shear layers is important in the small-scale dynamics of turbulence as well as the modulation of small-scale turbulent motions by external disturbance.

We investigate the intermittency of the coupling behaviour in screeching twin round supersonic jets at low Mach numbers across a range of nozzle spacings. Application of proper orthogonal decomposition combined with time-frequency wavelet analysis and spectral proper orthogonal decomposition shows that intermittency can manifest in twin jets as either a competition between the two symmetries, or the jets uncoupling and recoupling. The time scales on which symmetry switching occurs can vary strongly, ranging from $O(10^2)$ to $O(10^3)$ screech cycles. A transition from one symmetry to another is accompanied by a slight change in the screech frequency ranging from 0.30 % to 0.63 %. It was observed that complete uncoupling occurred only at the largest nozzle spacing of $s/D=6$ and at Mach numbers close to modal staging. When the jets are uncoupled they screech at slightly different frequencies, with a disparity of approximately 0.6 %. The coupling is particularly intermittent in the transition from the A1 to A2 branch, where the A2 mode is first observed, and tends toward steady coupling with increasing Mach number.

Cryogenic carbon capture (CCC) can preferentially desublimate $\text {CO}_2$ out of the flue gas. A widespread application of CCC requires a comprehensive understanding of $\text {CO}_2$ desublimation properties. This is, however, highly challenging due to the multiphysics behind it. This study proposes a lattice Boltzmann (LB) model to study $\text {CO}_2$ desublimation on a cooled cylinder surface during CCC. In two-dimensional (2-D) simulations, various $\text {CO}_2$ desublimation and capture behaviours are produced in response to different operation conditions, namely, gas velocity (Péclet number $\textit {Pe}$) and cylinder temperature (subcooling degree $\Delta T_{sub}$). As $\textit {Pe}$ increases or $\Delta T_{sub}$ decreases, the desublimation rate gradually becomes insufficient compared with the $\text {CO}_2$ supply via convection/diffusion. Correspondingly, the desublimated solid $\text {CO}_2$ layer (SCL) transforms from a loose (i.e. cluster-like, dendritic or incomplete) structure to a dense one. Four desublimation regimes are thus classified as diffusion-controlled, joint-controlled, convection-controlled and desublimation-controlled regimes. The joint-controlled regime shows quantitatively a desirable $\text {CO}_2$ capture performance: fast desublimation rate, high capture capacity, and full cylinder utilization. Regime distributions are summarized on a $\textit {Pe}$–$\Delta T_{sub}$ space to determine operation parameters for the joint-controlled regime. Moreover, three-dimensional simulations demonstrate four similar desublimation regimes, verifying the reliability of 2-D results. Under regimes with loose SCLs, however, the desublimation process shows an improved $\text {CO}_2$ capture performance in three dimensions. This is attributed to the enhanced availability of gas–solid interface and flow paths. This work develops a reliable LB model to study $\text {CO}_2$ desublimation, which can facilitate applications of CCC for mitigating climate change.

We consider a special type of hydraulic jumps (internal bores) which, in the vertically bounded system of two immiscible fluids with slightly different densities, conserve not only the mass and impulse but also the circulation and energy. This is possible only at specific combinations of the upstream and downstream states. Two such combinations are identified with arbitrary upstream and downstream interface heights. The first has a cross-symmetry between the interface height and shear on both sides of the jump. This symmetry, which is due to the invariance of the two-layer shallow-water system with swapping the interface height and shear, ensures the automatic conservation of the impulse and energy as well as the continuity of characteristic velocities across the jump. The speed at which such jumps propagate is defined uniquely by the conservation of the mass and circulation. The other possibility is a marginally stable shear flow that can have fully conservative jumps with discontinuous characteristic velocities. Both types of conservative jumps are shown to represent a long-wave approximation to the so-called solibores that appear as smooth permanent-shape solutions in a weakly non-hydrostatic model. A new analytical solution for solibores is obtained and found to agree very well with the previous DNS results for partial-depth lock release flow. The finding that certain large-amplitude hydraulic jumps can be fully conservative, while most are not such even in the inviscid approximation, points towards the wave dispersion as a primary mechanism behind the lossy nature of internal bores.