In this paper, we numerically study the mechanism of the oscillatory flow dynamics associated with the tip vortex cavitation (TVC) over an elliptical hydrofoil section. Using our recently developed three-dimensional variational multiphase flow solver, we investigate the TVC phenomenon at Reynolds number $Re = 8.95 \times 10^5$ via dynamic subgrid-scale modelling and the homogeneous mixture theory. To begin, we examine the grid resolution requirements and introduce a length scale considering both the tip vortex strength and the core radius. This length scale is then employed to non-dimensionalize the spatial resolution in the tip vortex region, the results of which serve as a basis for estimation of the required mesh resolution in large eddy simulations of TVC. We next perform simulations to analyse the dynamical modes of tip vortex cavity oscillation at different cavitation numbers, and compare them with the semi-analytical solution. The breathing mode of cavity surface oscillation is extracted from the spatial-temporal evolution of the cavity's effective radius. The temporally averaged effective radius demonstrates that the columnar cavity experiences a growth region followed by decay as it progresses away from the tip. Further examination of the characteristics of local breathing mode oscillations in the growth and decay regions indicates the alteration of the cavity's oscillatory behaviour as it travels from the growth region to the decay region, with the oscillations within the growth region being characterized by lower frequencies. For representative cavitation numbers $\sigma \in [1.2,2.6]$, we find that pressure fluctuations exhibit a shift of the spectrum towards lower frequencies as the cavitation number decreases, similar to its influence on breathing mode oscillations. The results indicate the existence of correlations between the breathing mode oscillations and the pressure fluctuations. While the low-frequency pressure fluctuations are found to be correlated with the growth region, the breathing mode oscillations within the decay region are related to higher-frequency pressure fluctuations. The proposed mechanism can play an important role in developing mitigation strategies for TVC, which can reduce the underwater radiated noise by marine propellers.

We experimentally and numerically characterize rapidly rotating radiatively driven thermal convection, beyond the sole heat transport measurements reported by Bouillaut et al. (Proc. Natl Acad. Sci., vol. 118, 2021, e2105015118). Based on a suite of direct numerical simulations (DNS) and additional processing of the experimental data collected by Bouillaut et al. (Proc. Natl Acad. Sci., vol. 118, 2021, e2105015118), we report the simultaneous validation of the scaling predictions of the ‘geostrophic turbulence’ regime – the diffusivity-free or ‘ultimate’ regime of rapidly rotating convection – for the heat transport and the temperature fluctuations. Following such cross-validation between DNS and laboratory experiments, we further process the numerical data to validate the ‘geostrophic turbulence’ scaling predictions for the flow velocity and horizontal scale. Radiatively driven convection thus appears as a versatile set-up for the laboratory observation of the diffusivity-free regimes of various convective flows of geophysical and/or astrophysical interest.

We present a new derivation of the kinetic equation for weak, non-hydrostatic internal gravity wave turbulence. The equation is equivalent to the one obtained by Caillol & Zeitlin (Dyn. Atmos. Oceans, vol. 32, issue 2, 2000, pp. 81–112), but it takes a canonical form. We show that it conserves the energy without involving the resonance condition in frequency, and look for the isotropic part of the steady, scale-invariant solutions. We provide a parametrization of the resonant manifold of non-hydrostatic internal gravity wave triadic interactions. This allows us to simplify the collision integral, and to evaluate the transfer coefficients of all triadic interactions. In the hydrostatic limit, our equation is equivalent to the Hamiltonian description of Lvov & Tabak (Phys. Rev. Lett., vol. 87, issue 16, 2001, 168501).

Melting and solidification in periodically time-modulated thermal convection are relevant for numerous natural and engineering systems, for example, glacial melting under periodic sun radiation and latent thermal energy storage under periodically pulsating heating. It is highly relevant for the estimation of melt rate and melt efficiency management. However, even the dynamics of a solid–liquid interface shape subjected to a simple sinusoidal heating has not yet been investigated in detail. In this paper, we offer a better understanding of the modulation frequency dependence of the melting and solidification front. We numerically investigate periodic melting and solidification in turbulent convective flow with the solid above and the melted liquid below, and sinusoidal heating at the bottom plate with the mean temperature equal to the melting temperature. We investigate how the periodic heating can prevent the full solidification, and the resulting flow structures and the quasi-equilibrium interface height. We further study the dependence on the heating modulation frequency. As the frequency decreases, we found two distinct regimes, which are ‘partially solid’ and ‘fully solid’. In the fully solid regime, the liquid freezes completely, and the effect of the modulation is limited. In the partially solid regime, the solid partially melts, and a steady or unsteady solid–liquid interface forms depending on the frequency. The interface height can be derived based on the energy balance through the interface. In the partially solid regime, the interface height oscillates periodically, following the frequency of modulation. Here, we propose a perturbation approach that can predict the dependency of the oscillation amplitude on the modulation frequency.

We investigated the effects of two-dimensional sharp-edged rectangular bumps on Tollmien–Schlichting (TS) wave evolution using direct numerical simulation. The bump height, $h$, ranged from 5 % to 40 % of the local displacement thickness, $\delta ^*$. Behind the bump, a recirculating flow region could be formed whose length increased nonlinearly with $h$. The bump height effect on the TS wave, which was the dominant, scaled super-exponentially with $h$. We also showed a substantial effect of the $\delta ^*$-based Reynolds number, ${\textit {Re}} _{\delta ^*}$. Firstly, the bump wake extended with ${\textit {Re}} _{\delta ^*}$, promoting larger TS wave growth rates. The second effect is related to proximity to the upper branch of the instability loop, accounting for the influence of the TS frequency, as well. It dictates the bump impact increases as it gets closer to transition, either by the bump moving downstream or the transition moving upstream. For a 40 % high bump, for example, changing the ${\textit {Re}} _{\delta ^*}$ at the bump location from 1500 to 2000 increased $\Delta N$ by a factor of 2 ($\Delta N$ represents a measure of a surface irregularity effect on the smooth plate N-factor). We also found that $(\Delta N)_{max}$ increases linearly with ${\textit {Re}} _{hh}$. Results in the subsonic regime showed that the bump impact attenuates with Mach number up to 0.7 but above it, stabilisation is surpassed by the destabilising effect caused by the recirculation lengthening. This is mostly associated with the bump wake that extends with the pressure gradient which increases substantially towards the sonic speed. This is enhanced if the surface is adiabatic rather than isothermal.

We investigate a turbulent boundary layer (TBL) under uniform pressure force variations, focusing on understanding its response to local pressure force, local pressure force variation (local disequilibrating effect) and upstream history. The flow starts as a zero-pressure-gradient (ZPG) TBL, followed by a uniform increase in the ratio of pressure force to turbulent force in the outer region and concludes with a uniform decrease of the same magnitude. This last zone includes a subzone with a diminishing adverse pressure gradient (APG), followed by an increasing favourable pressure gradient (FPG). In both subzones, the impact remains the same: mean momentum gain and turbulence reduction. In the outer region, the mean flow responds to force balance changes with a considerable delay. The accumulated flow history leads to a FPG TBL at the domain's end with a momentum defect comparable to APG TBLs. Below $y^+=10$, the mean flow responds almost instantaneously to pressure force changes. In the overlap layer, velocity profiles deviate from the conventional logarithmic law of ZPG TBL. Outer-layer turbulence decays more slowly than it increases initially, the latter turbulence increase persisting even after the pressure force begins to decrease. As a result of the slow turbulence decay, the FPG TBL at the domain's end exhibits unusually high outer turbulence levels. Near the wall, turbulence responds with a delay to pressure force changes, partly due to the influence of large-scale turbulence. All these significant cumulative effects of continuous pressure force variation indicate that parameters based solely on local variables cannot fully describe the physics of non-equilibrium TBLs.

The transient shear-induced particle migration of frictional non-Brownian suspensions is studied using particle-resolved simulations. The numerical method – the fictitious domain method – is well suited to heterogeneous flows thanks to a frame-invariant formulation of the subgrid (lubrication) corrections that does not involve the ambient flow (Orsi et al., J. Comput. Phys., vol. 474, 2023, 111823). The paper aims to give an accurate quantitative picture of the mass and momentum balance during the flow. The various assumptions and local constitutive laws that together form the suspension balance model (SBM) are thoroughly examined. To this purpose, the various quantities of interest are locally averaged in space and time, and their profile across the channel is extensively studied, with specific attention to the time evolution of the different contributions, either hydrodynamic in nature or from contact interactions, to the shear and normal stresses. The latter, together with the velocity gradient in the wall-normal direction and the volume fraction profile, yield the local constitutive laws, which are compared with their counterpart obtained in homogeneous shear flow. A fair agreement is observed except in a layering area at the boundaries and at the very centre of the channel. In addition, the main assumption of the SBM, i.e. the local relation between the hydrodynamic force on the particles and the particle flux, is meticulously investigated. The hydrodynamic force is found to be mainly a drag, except in the lower range of the probed volume fractions, where a non-drag contribution is observed.

Microvortex generators (MVGs) are a promising solution to control shock wave/turbulent boundary layer interactions (SBLIs), especially in supersonic inlets. In this study, we examine the effects of a microramp vortex generator on an SBLI generated by an oblique shock wave and a turbulent boundary layer using direct numerical simulations (DNSs). Two cases, with and without the presence of a microramp, are compared in terms of their mean and unsteady flow features at free-stream Mach number equal to 2 and friction Reynolds number at the inviscid shock impingement equal to 600. The long integration period allows us to assess how microramps affect the typical low-frequency unsteadiness observed in SBLIs, and the data generated may serve as a reference for simulations of lower fidelity or reduced order models. The analysis shows that the three-dimensional microramp wake alters the interaction region dramatically, inducing a significant spanwise modulation and topology change of the separation. For example, tornado-like structures redistribute the flow in both the spanwise and wall-normal directions inside the recirculation region. The increase in momentum close to the wall by the ramp vortices effectively delays the onset of the separation and, thus, the separation length, but at the same time leads to a significant increase in the intensity of the wall-pressure fluctuations. We then characterise the mutual interaction between the arch-like vortices around the ramp wake and the SBLI. The specific spanwise vorticity shows that these vortices follow the edge of the separation and their intensity, apart from mean compressibility effects, is not affected by the shocks. The shocks, instead, are deformed in shape by the periodic impingement of the vortices, although the spectral analysis did not reveal any significant trace of their shedding frequency in the separation region. These Kelvin–Helmholtz vortices, however, may be relevant in the closure of the separation bubble. Fourier analysis also shows a constant increase, in both value and magnitude, in the low-frequency peak all along the span, suggesting that the motion of the separation shock remains coherent while being disturbed by the arch-like vortices and oscillating at a higher frequency in absolute terms.

In a horizontally heated melting system, where a solid substance is subject to melting by a warmer liquid beneath, the presence of solute in the liquid introduces a complex interplay between temperature and concentration dynamics. Employing a recently developed sharp interface method (Xue et al., J. Comput. Phys., vol. 491, 2023), we conduct direct numerical simulations to investigate the transient behaviour of the system across a broad range of Rayleigh numbers and solute concentrations. Our observations reveal distinct flow regimes: at low concentrations, the system resembles a temperature-driven melting problem, characterized by vortex rolls beneath the melting interface. As the solute concentration increases, a stably stratified layer emerges beneath the interface, leading to the transition from thermal convection to penetrative convection, which resembles those flow characteristics observed in the double-diffusive convection. This shift results from the competition between the stabilizing effect induced by solute concentration gradient and the destabilizing effect caused by temperature gradient. Otherwise in the diffusion regime, characterized by very high solute concentrations, the flow becomes static due to the complete suppression of convection by the stably stratified layer. This regime further exhibits two distinct patterns: ‘melting’ and ‘dissolution’. Beyond characterizing diverse flow patterns, our study conducts a quantitative analysis, examining heat/mass transfer, melting rates, and the evolution of temperature and concentration at the interface. These insights contribute to a better understanding of the intricate interplay between temperature and solute concentration during phase change, with implications for accurately estimating melting rates in binary fluid systems.

Rayleigh–Bénard convection in a rotating spherical shell provides a simplified model for convective dynamics of planetary and stellar interiors. Over the past decades, the problem has been studied extensively via numerical simulations, but most previous simulations set the Prandtl number $Pr$ to unity. In this study we build more than 200 numerical models of rotating convection in a spherical shell over a wide range of $Pr$ ($10^{-2}\le Pr \le 10^2$). By increasing the Rayleigh number $Ra$, we characterise four different flow regimes, starting from the linear onset to multiple modes, then transitioning to the geostrophic turbulence and eventually approaching the weakly rotating regime. In the multiple modes regime, we show evidence of triadic resonances in numerical models with different $Pr$, which may provide a generic mechanism for the transition from laminar to turbulence in rotating convection. We analyse scaling behaviours of the heat transfer and convective flow speeds in numerical simulations, paying particular attention to the $Pr$ dependence. We find that the so-called diffusion-free scaling for the heat transfer cannot reconcile all numerical models with different $Pr$ in the geostrophic turbulence regime. However, the characteristic flow speeds at different $Pr$ roughly follow a unified scaling that can be described by visco-Archimedean–Coriolis force balances, though the scaling tends to approach the Coriolis-inertial-Archimedean force balance at low $Pr$. We also show that transition behaviours from rotating to non-rotating convection depend on $Pr$. The transition criteria based on heat transfer and flow morphology would be rather different when $Pr>1$, but the two criteria are consistent for cases with $Pr\le 1$. Both scaling behaviours and transition behaviours suggest that the heat transfer is controlled by the boundary layers while the convective flow speeds are mainly determined by the force balance in the bulk for cases with $Pr>1$, which is in line with recent experimental results with moderate to high $Pr$. For cases with $Pr \le 1$, both the heat transfer and convective velocities are approaching the inviscid dynamics in the bulk. We also briefly analysed the magnitude and scaling of zonal flows at different $Pr$, showing that the zonal flow amplitude rapidly increases as $Pr$ decreases.

In this note, we study the effect of viscosity gradients on the energy dissipated by the motion of microswimmers and the associated efficiency of that motion. Using spheroidal squirmer model swimmers in weak linearly varying viscosity fields, we find that efficiency depends on whether they generate propulsion from the back (pushers) or the front (pullers). Pushers are faster and more efficient when moving down gradients, but slower and less efficient moving up viscosity gradients, and the opposite is true for pullers. However, both pushers and pullers display negative viscotaxis, therefore pushers dynamically tend to the most efficient orientation, while pullers tend to the least. We also evaluate the effect of shape on power expenditure and efficiency when swimming in viscosity gradients, and find that in general, the change in both due to gradients decreases monotonically with increasing slenderness. This work shows how shape and gait play an important role in determining dynamics and efficiency in inhomogeneous environments, and demonstrating that both efficiency minimizing and maximizing stable dynamical states are possible.

In the present work, the tangential (swirl) velocity component is superimposed at the intake of a narrow fluidic cylindrical pipe to achieve the desired mixing of inelastic non-Newtonian fluids/solutes at the outlet. We discuss an analytical method for obtaining the swirl velocity profile, considering the nonlinear viscous effects for both shear-thinning and shear-thickening fluids, represented by the power-law model. We numerically solve the species transport equation, coupled with the analytically derived swirl velocity, using our in-house developed code for the concentration distribution in the flow field. The results show that the inlet swirl and an increase in the shear-thinning fluid property improve advection-dominated mixing. Additionally, higher Reynolds numbers significantly enhance advection's dominance, as more rotation leads to the generation of vortices, resulting in an engulfment flow (chaotic convection) based mixing. We demonstrate that considering the increase in the shear-thinning fluid property with swirl intake reduces the amount of mixing time required in the convective regime.