In hypersonic flight the shock wave and turbulent boundary layer interaction (STBLI) sharply increases wall heat transfer that intensifies the aerodynamic heating problems. In this work the STBLI is modelled by compression ramp flow with a Mach number of 5, a Reynolds number based on momentum thickness of 4652 and a wall to recovery temperature ratio of 0.5. The aerodynamic heat generation and transport mechanisms are investigated in the interaction based on theoretical analysis and direct numerical simulation (DNS) that agrees with previous studies. A prediction correlation of wall heat flux in STBLI is deduced theoretically and validated by some representative data including the present DNS, which improves the prediction accuracy and can be applied to a wider $Ma$ range compared with the canonical Q-P theory. The correlation indicates that the sharp increase of wall heat transfer in the STBLI can be explained by the boundary layer compression and the convection transport enhancement. Based on the DNS results, the aerodynamic heat generation and transport mechanisms are revealed in the separation, recirculation and reattachment zones in the STBLI. From this perspective, the peak heat flux can be further explained by the enhancement of near-wall turbulent energy dissipation, compression aerodynamic heat generation and the near-wall turbulent transport. The generation and transport of compression aerodynamic heat reveal the underlying mechanism of the strong correlation between the peak heat flux ratios and the pressure ratios in STBLIs.

We present a simulation-based study of the effect of a passing wave packet on underlying fully developed turbulence. We propose a novel wave-phase-resolved simulation method inspired by Helmholtz decomposition to directly couple the turbulence simulation with instantaneous wave orbital motions without wave-phase averaging. We also introduce a boundary condition treatment for the turbulence at the wave surface, which allows the turbulence simulation to be conducted in a rectangular domain while retaining the wave-phase effect. The results obtained from the proposed method reveal considerable variations in turbulence statistics, including the enstrophy and Reynolds normal stresses, during wave packet passage. Most changes occur rapidly when the narrow bandwidth around the wave packet core passes. Further analyses of the energy spectra indicate that the enhancement of turbulence occurs across a wide range of scales, with the near-surface small-scale motions experiencing the most significant intensification. Meanwhile, large-scale motions with scales comparable to the boundary layer depth are also enhanced. The mechanisms underlying the Reynolds normal stress variation at different length scales are related to the energy transfer from the wave orbital straining to turbulence through production, the pressure–strain effect, the pressure diffusion and the wave advection. By assessing the turbulence statistics and dynamics impacted by a wave packet in detail, this study provides an improved understanding of the response of a developed turbulent flow to a transient wave field. The proposed simulation method also proves to be a promising phase-resolved approach for efficiently modelling the wave effect on turbulence.

Radial unstable stratification is a potential source of turbulence in the cold regions of accretion disks. To investigate this thermal effect, here we focus on two-dimensional Rayleigh–Bénard convection in an annulus subject to radially dependent gravitational acceleration $g \propto 1/r$. Next to the Rayleigh number $Ra$ and Prandtl number $Pr$, the radius ratio $\eta$, defined as the ratio of inner and outer cylinder radii, is a crucial parameter governing the flow dynamics. Using direct numerical simulations for $Pr=1$ and $Ra$ in the range from $10^7$ to $10^{10}$, we explore how variations in $\eta$ influence the asymmetry in the flow field, particularly in the boundary layers. Our results show that in the studied parameter range, the flow is dominated by convective rolls and that the thermal boundary-layer (TBL) thickness ratio between the inner and outer boundaries varies as $\eta ^{1/2}$. This scaling is attributed to the equality of velocity scales in the inner ($u_i$) and outer ($u_o$) regions. We further derive that the temperature drops in the inner and outer TBLs scale as $1/(1+\eta ^{1/2})$ and $\eta ^{1/2}/(1+\eta ^{1/2})$, respectively. The scalings and the temperature drops are in perfect agreement with the numerical data.

The collapse of a vapour bubble over a material surface has been widely studied over the past few decades, but a comprehensive and quantitative analysis of the cavitation dynamics and its effects on solid materials at the mesoscale (nanometre up to micrometre), which would be of particular interest in applications exploiting cavitation power, is still lacking. In this work, we adopt a diffuse interface model to describe the microbubble dynamics, and a dynamic plasticity model for the solid. The former is particularly suited to studying the rich phenomenology characterising bubble collapse at the mesoscale, which comprises transitions to supercritical conditions, emission and propagation of shock waves, generation of liquid microjets and topological transitions, whereas the latter is used to characterise the permanent plastic deformation caused by the bubble collapse, and has been augmented to consider inertial effects, to assess whether or not an interaction between elastic and plastic waves may influence the resulting deformation. Results concerning the collapse of a microbubble at different liquid overpressures and initial standoff ratios are discussed, and the elastoplastic wave propagation in the solid, together with plastic deformation, is studied for different cases, depending on elastic and plastic material parameters.

This study conducts a numerical investigation into the three-dimensional film boiling of liquid under the influence of external magnetic fields. The numerical method incorporates a sharp phase-change model based on the volume-of-fluid approach to track the liquid–vapour interface. Additionally, a consistent and conservative scheme is employed to calculate the induced current densities and electromagnetic forces. We investigate the magnetohydrodynamic effects on film boiling, particularly examining the pattern transition of the vapour bubble and the evolution of heat transfer characteristics, exposed to either a vertical or horizontal magnetic field. In single-mode scenarios, film boiling under a vertical magnetic field displays an isotropic flow structure, forming a columnar vapour jet at higher magnetic field intensities. In contrast, horizontal magnetic fields result in anisotropic flow, creating a two-dimensional vapour sheet as the magnetic strength increases. In multi-mode scenarios, the patterns observed in single-mode film boiling persist, with the interaction of vapour bubbles introducing additional complexity to the magnetohydrodynamic flow. More importantly, our comprehensive analysis reveals how and why distinct boiling effects are generated by various orientations of magnetic fields, which induce directional electromagnetic forces to suppress flow vortices within the cross-sectional plane.

Quasi-Keplerian flow, a special regime of Taylor–Couette co-rotating flow, is of great astrophysical interest for studying angular momentum transport in accretion disks. The well-known magnetorotational instability (MRI) successfully explains the flow instability and generation of turbulence in certain accretion disks, but fails to account for these phenomena in protoplanetary disks where magnetic effects are negligible. Given the intrinsic decrease of the temperature in these disks, we examine the effect of radial thermal stratification on three-dimensional global disturbances in linearised quasi-Keplerian flows under radial gravitational acceleration mimicking stellar gravity. Our results show a thermo-hydrodynamic linear instability for both axisymmetric and non-axisymmetric modes across a broad parameter space of the thermally stratified quasi-Keplerian flow. Generally, a decreasing Richardson or Prandtl number stabilises the flow, while a reduced radius ratio destabilises it. This work also provides a quantitative characterisation of the instability. At low Prandtl numbers $Pr$, we observe a scaling relation of the linear critical Taylor number $Ta_c\propto Pr^{-6/5}$. Extrapolating the observed scaling to high $Ta$ and low $Pr$ may suggest the relevance of the instability to accretion disks. Moreover, even slight thermal stratification, characterised by a low Richardson number, can trigger the flow instability with a small axial wavelength. These findings are qualitatively consistent with the results from a traditional local stability analysis based on short wave approximations. Our study refines the thermally induced linearly unstable transition route in protoplanetary disks to explain angular momentum transport in dead zones where MRI is ineffective.

We study the effect of acceleration and deceleration on the stability of channel flows. To do so, we derive an exact solution for laminar profiles of channel flows with an arbitrary, time-varying wall motion and pressure gradient. This solution then allows us to investigate the stability of any unsteady channel flow. In particular, we restrict our investigation to the non-normal growth of perturbations about time-varying base flows with exponentially decaying acceleration and deceleration, with comparisons to growth about a constant base flow (i.e. the time-invariant simple shear or parabolic profile). We apply this acceleration and deceleration through the velocity of the walls and through the flow rate. For accelerating base flows, perturbations never grow larger than perturbations about a constant base flow, while decelerating flows show massive amplification of perturbations – at a Reynolds number of $500$, properly timed perturbations about the decelerating base flow grow $ {O}(10^5)$ times larger than perturbations grow about a constant base flow. This amplification increases as we raise the rate of deceleration and the Reynolds number. We find that this amplification arises due to a transition from spanwise perturbations leading to the largest amplification to streamwise perturbations leading to the largest amplification that only occurs in the decelerating base flow. By evolving the optimal perturbations through the linearized equations of motion, we reveal that the decelerating base flow achieves this massive amplification through the Orr mechanism, or the down-gradient Reynolds stress mechanism, which accelerating and constant base flows cannot maintain.

The present study aims to examine the temporal linear stability analysis of isothermal plane Couette flow over a porous layer using the two-domain approach. The flow in the porous layer is described by the unsteady Darcy–Brinkman equations, whereas it is characterised by the Navier–Stokes equations in the fluid layer. In contrast to the Darcy model, it is observed that the isothermal plane Couette flow becomes unstable for such a superposed system on the inclusion of the Brinkman term. From the stability analysis, the two-dimensional mode is found to be least stable, and two modes of instability, namely porous mode and mixed mode are obtained under the consideration of the Darcy–Brinkman model along with advection term (DBA model). For Darcy number $(\delta )=0.01$, depending on the value of the stress-jump coefficient, mixed mode controls the instability of the system at small values of depth ratio $(\hat {d})$, and it disappears for relatively high values of $\hat {d}$, where the porous mode dominates. In addition, it has been observed that when $\hat {d}=0.1$, the critical mode of instability is found to be mixed for $\delta >0.02$ and porous for $\delta \le 0.02$. The stress-jump coefficient destabilises the flow in terms of energy production through perturbed stresses at the interface. As observed in the case of isothermal plane Poiseuille flow studied by Chang, Chen & Straughan (J. Fluid Mech., vol. 564, 2006, pp. 287–303), here also depth ratio (Darcy number) stabilises (destabilises) the flow. However, this characteristic does not remain valid when the advection term is eliminated from the considered momentum equation. For a certain range of $\hat {d} (\delta )$, the destabilising (stabilising) characteristic of the respective parameters are encountered when the fluid mode of instability prevails.

Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore, the NNs often struggle to converge when the solution to the real equation is very complex. Inspired by large eddy simulation in computational fluid dynamics, we propose an improved method based on filtering. We analysed the causes of the difficulties in physics-informed machine learning, and proposed a surrogate constraint (filtered partial differential equation, FPDE) of the original physical equations to reduce the influence of noisy and sparse observation data. In the noise and sparsity experiment, the proposed FPDE models (which are optimized by FPDE constraints) have better robustness than the conventional PDE models. Experiments demonstrate that the FPDE model can obtain the same quality solution with 100 % higher noise and 12 % quantity of observation data of the baseline. Besides, two groups of real measurement data are used to show the FPDE improvements in real cases. The final results show that the FPDE still gives more physically reasonable solutions when facing the incomplete equation problem and the extremely sparse and high-noise conditions. The proposed FPDE constraint is helpful for merging real-world experimental data into physics-informed training, and it works effectively in two real-world experiments: simulating cell movement in scratches and blood velocity in vessels.

We show that rotating Rayleigh–Bénard convection, where a rotating fluid is heated from below, exhibits a non-Hermitian topological invariant. Recently, Favier & Knobloch (J. Fluid Mech., vol. 895, 2020, R1) hypothesized that the robust sidewall modes in rapidly rotating convection are topologically protected. By considering a Berry curvature defined in the complex wavenumber space, we reveal that the bulk states can be characterized by a non-zero integer Chern number, implying a potential topological origin of the edge modes based on the Atiyah–Patodi–Singer index theorem (Fukaya et al., Phys. Rev. D, vol. 96 2017, 125004; Yu et al., Nucl. Phys. B, vol. 916, 2017, pp. 550–566). The linearized eigenvalue problem is intrinsically non-Hermitian, therefore, the definition of Berry curvature generalizes that of the stably stratified problem. Moreover, the three-dimensional set-up naturally regularizes the eigenvector, avoiding the compactification problem in shallow water waves (Tauber et al., J. Fluid Mech., vol. 868, 2019, R2). Under the hydrostatic approximation, it recovers a two-dimensional analogue of the one which explains the topological origin of the equatorial Kelvin and Yanai waves (Delplace et al., Science, vol. 358, issue 6366, 2017, pp. 1075–1077). The non-zero Chern number relies only on rotation when the fluid is stratified, no matter whether it is stable or unstable. However, the neutrally stratified system does not support a topological invariant. In addition, we define a winding number to visualize the topological nature of the fluid. Our results represent a step forward for the topologically protected states in convection, but the bulk-boundary correspondence requires a further direct analysis for proof, and the robustness of the edge states under varying boundary conditions remains a question to be answered.

Geothermal gradients and heterogeneous permeability are commonly observed in natural geological formations for underground CO$_2$ sequestration. In this study, we conduct three-dimensional direct numerical simulations on the double-diffusive convection with both unstable temperature and concentration gradients in homogeneous and heterogeneous porous media. For homogeneous porous media, the root-mean-squared velocity increases linearly with density ratio defined as the buoyancy ratio by temperature and concentration differences. The flow structures show no remarkable changes when temperature Rayleigh number ${Ra}_T$ is less than its critical value, but alter from sheet-like to cellular structures as ${Ra}_T$ surpasses this threshold. The concentration wavenumber scales approximately as $k_{rS}\sim {Ra}_e^{0.47}$ with a defined effective Rayleigh number ${Ra}_e$. By using a scale analysis, the concentration flux exhibits a consistent linear relation with the total driving forces for all simulations. For heterogeneous porous media, where the Dykstra–Parsons coefficient $V_{DP}$ and correlation length $l_{r}$ determine the spatial distribution of the permeability field, the flow is strengthened in places with higher permeability. The velocity and concentration flux are less affected by $l_{r}$ than that by $V_{DP}$. For small correlation length, the flow structures coarsen and their characteristic width generally increases with increasing heterogeneity. For large correlation length, small structures emerge in the regions with large permeability, which can be attributed to the intensified local Rayleigh number triggering more vigorous convection there. The variations of concentration flux with $l_{r}$ and $V_{DP}$ can be explained by the portion of area covered by high concentration with large vertical velocity near the boundaries.