In this paper, we explore the hydrodynamics of spheroidal active particles in viscosity gradients. This work provides a more accurate modelling approach, in comparison to spherical particles, for anisotropic organisms such as Paramecium swimming through inhomogeneous environments, but more fundamentally examines the influence of particle shape on viscotaxis. We find that spheroidal squirmers generally exhibit dynamics consistent with their spherical analogues, irrespective of the classification of swimmers as pushers, pullers or neutral swimmers. However, the slenderness of the spheroids tends to reduce the impact of viscosity gradients on their dynamics; when a swimmer becomes more slender, the viscosity difference across its body is reduced, which leads to slower reorientation. We also derive the mobility tensor for passive spheroids in viscosity gradients, generalizing previous results for spheres and slender bodies. This work enhances our understanding of how shape factors into the dynamics of passive and active particles in viscosity gradients, and offers new perspectives that could aid the control of both natural and synthetic swimmers in complex fluid environments.

The growth with fetch of young wind waves under steady wind forcing that is commonly attributed to shear flow instability results in a spatially inhomogeneous wave field with a spectrum evolving along the tank. The present laboratory study accounts for multiple co-existing statistically stationary random frequency harmonics. Single-point synchronous measurements of the instantaneous surface elevation and of its along-wind slope component are performed by optical methods at numerous locations. Assuming exponential spatial growth, the phase shift between the surface elevation and surface slope at each frequency is related to the spatial growth rate of each harmonic. The validity of the assumption that the wave energy varies exponentially with fetch is examined in a separate set of experiments; the instantaneous surface elevation at various wind-forcing conditions is measured at multiple locations along the tank. The spatial variation of the energy of individual frequency harmonics is determined. It is found that, below the local peak frequency, the energy of each harmonic grows exponentially, while the evolution of waves at frequencies approaching and exceeding the local peak is strongly affected by sheltering by the dominant wave, as well as by nonlinear bound waves. The outcomes of two independent methods of determination of spatial growth rates at a range of young wave frequencies are compared. The accumulated data also enable quantitative analysis of the sheltering phenomenon. The essential difference between the spatial and the temporal wind-wave evolution cases is discussed.

The presence of a dispersed phase can significantly modulate the drag in turbulent systems. We derived a conserved quantity that characterizes the radial transport of azimuthal momentum in the fluid–fluid two-phase Taylor–Couette turbulence. This quantity consists of contributions from advection, diffusion and two-phase interface, which are closely related to density, viscosity and interfacial tension, respectively. We found from interface-resolved direct numerical simulations that the presence of the two-phase interface consistently produces a positive contribution to the momentum transport and leads to drag enhancement, while decreasing the density and viscosity ratios of the dispersed phase to the continuous phase reduces the contribution of local advection and diffusion terms to the momentum transport, respectively, resulting in drag reduction. Therefore, we concluded that the decreased density ratio and the decreased viscosity ratio work together to compete with the presence of a two-phase interface for achieving drag modulation in fluid–fluid two-phase turbulence.

Numerical simulations have been conducted to examine the structure of diffusive-convection staircases in the presence of vortical-mode-induced turbulent forcing. By modulating the input power $P$ and the background density ratio $R_\rho$, we have identified three distinct types of staircase structures in these simulations: namely staircases maintained in the system driven by double-diffusion, by turbulence or by a combination of both double-diffusion and turbulence. While we showed that staircases maintained in the double-diffusion-dominated system are accurately characterised by the existing model originally proposed by Linden & Shirtcliffe (J. Fluid Mech., vol. 87, no. 3, 1978, pp. 417–432), we introduced new physical models to describe the staircase structures maintained in the turbulence-dominated system and the system driven by both turbulence and double-diffusion. Our integrated model reveals that turbulence fundamentally governs the entire life cycle of the diffusive-convection staircases, encompassing their formation, maintenance and eventual disruption in the Arctic Ocean's thermohaline staircases. While our previous work of Ma & Peltier (J. Fluid Mech., vol. 931, 2022b) demonstrated that turbulence could initiate the formation of Arctic staircases, these staircases are sustained by both turbulence and double-diffusion acting together after formation has occurred. Strong turbulence may disrupt staircase structures; however, the presence of weak turbulence could lead to unstable stratification within mixed layers of the staircases, as well as enhancing vertical heat and salt fluxes. Turbulence can even sustain a stable staircase structure factor when $R_\rho$ is relatively large, following a similar mechanism to the density staircases observed in laboratory experiments. Consequently, previous parameterisations (e.g. Kelley, J. Geophys. Res.: Oceans, vol. 95, no. C3, 1990, pp. 3365–3371) on the vertical heat flux across the diffusive-convection staircases may provide a significant underestimation of the heat transport by ignoring the influences of turbulence.

Identifying the governing parameters of self-sustained oscillation is crucial for the diagnosis, prediction and control of thermoacoustic instabilities. In this paper, we propose and validate a novel method for computing the parameters of thermoacoustic oscillation in a stochastic environment, which exploits a physics-informed neural network (PINN). Specifically, we introduce a negative log-likelihood loss function that integrates the stochastic samples and the solution of the Fokker–Planck equation. The proposed framework is validated using the numerically generated signal and the experimental data obtained from an annular combustor, both before and after the supercritical Hopf bifurcation. The results of PINN-based system identification show good agreement with the actual system parameters and the original stochastic signal, with improved accuracy compared to established methods. To the best of our knowledge, this study constitutes the first demonstration of the PINN-inverse approach that uses the noise-induced dynamics of thermoacoustic systems, opening up new pathways for diagnosing and predicting the thermoacoustic behaviour of various combustion systems.

The dynamics of turbulent flows past lateral cavities is relevant for multiple environmental applications. In rivers and coastal environments, these lateral recirculating regions constitute surface storage zones, where large-scale turbulent coherent structures control the transport and fate of contaminants. Mass transport in these flows is typically represented by one-dimensional first-order equations that predict the evolution of the spatially integrated concentration between the cavity and the main channel. These models, however, cannot represent the long-term evolution of the concentration or incorporate memory effects induced by turbulence. In this investigation, we carry out large-eddy simulations (LES) of the open-channel flow with a lateral square cavity of Mignot et al. (Phys. Fluids, vol. 28, issue 4, 2016, 045104). The model is coupled with an advection–diffusion equation and a Lagrangian particle model to investigate the transport mechanisms in the cavity and across the interface. From the simulations we provide quantitative comparisons of the physical processes from both perspectives, and investigate the effects of turbulent coherent structures on residence times and trajectories from finite-time Lyapunov exponents. From the Lagrangian results, we identify general spatial distributions of time scales in the cavity associated with the dynamics of coherent structures, providing new insights into the mechanisms that drive the global transport. We also show that an upscaled model informed by LES and based on a fractional derivative captures the evolution of concentration, and the exchange between the cavity and the main channel, providing accurate predictions of mass transport and reproducing the temporal dependence observed at larger scales.

Floquet stability analysis and direct simulations of a circular cylinder undergoing vortex-induced vibration (VIV) are presented. Simulation predictions are examined for the reduced velocity range over which there is a strong and periodic resonant response: $U_r \in [4.0, 8.0]$, focusing on a mass ratio of $m^* = 2.546$ matching a number of previous investigations. Over most of this range, the dominant wake modes present are analogous to modes A, B and QP (quasi-periodic) observed in a stationary circular cylinder wake. However, at $U_r = 4.5$, the dominant modes are B, QP and a subharmonic mode (SH), whereas at $U_r = 4.0$, the two-dimensional base state switches to a $P+S$ wake. The critical Reynolds number for two- to three-dimensional transition is observed to decrease with an increase of $U_r$, in line with a decreasing response amplitude. Over this range, the minimum ${\textit {Re}}$ for which the wake remains two-dimensional is 202, which occurs at $U_r = 7.5$, but this increases to ${\textit {Re}}_{cr} = 300$ at $U_r = 4.5$, noting the critical Reynolds number for a stationary circular cylinder is ${\textit {Re}}_{cr}=189$. The corresponding critical spanwise wavelengths for $U_r = 4.5$ and 8 are $1.4D$ (mode B) and $4.0D$ (mode A), respectively. Simulations indicate that even at $Re=300$, flow three-dimensionality increases the amplitude of the lower branch considerably. The investigation establishes the role of oscillation amplitude and reduced velocity in three-dimensional transition for elastically mounted systems.

The study investigates the impact of a vertically layered bathymetry, consisting of submerged vertical plates, on a ship wake through theoretical analysis and experimental realization. For subwavelength distances between the plates, the analysis relies on a homogenized model that provides an effective, anisotropic, dispersion relation for the propagation of water waves. Our findings reveal that a highly asymmetric wake can be achieved, with the degree of asymmetry contingent upon the ship propagation direction in relation to the plate orientation. This anisotropy is characterized with respect to water depth and to ship length using the dimensionless depth and hull Froude numbers. Laboratory experiments align closely with theoretical predictions, confirming that the asymmetry of the wake can indeed be managed through manipulation of bathymetric conditions.

Direct numerical simulation (DNS) of a turbulent boundary layer over the Gaussian (Boeing) bump is performed. This boundary layer exhibits a series of adverse and favourable pressure gradients and convex and concave curvature effects before separating. These effects on turbulent boundary layers are characterised and compared with a lower-Reynolds-number flow over the same geometry. The momentum budgets are analysed in the streamline-aligned coordinate system upstream of the separation region. These momentum budgets allow the simplification of equations to facilitate an integral analysis. Integral-analysis-based approximations for Reynolds stresses in the inner and outer regions of the boundary layer are also formulated. The shear and wall-normal Reynolds stress profiles normalised by these approximations exhibit a better collapse compared with friction velocity and Zagarola–Smits normalisations in the strong favourable pressure gradient region and in the mild adverse pressure region that precedes it in this flow. Simplification of these Reynolds stress approximations along with results from the DNS are used to obtain semi-empirical approximations that are able to provide stress closure in terms of wall solution fields for the turbulent boundary layer under consideration.

This paper investigates the effect of curvature on curved detonation and its reflections. Specifically, the study focuses on two aspects: the effect of curvature on the postwave parameters and their gradients, and the stabilization of Mach reflection. Relationships are established between the curvature and the gradients of the postwave parameters, thus providing a basis for examining detonation reflections and obtaining a comprehensive understanding of curved detonation. In particular, these relationships offer a valuable analytical tool to predict the postwave gradients, as well as providing a fresh perspective to understand the transformation from Mach reflection to regular reflection in curved detonation. The validity of these relationships is confirmed by comparison with simulation results. Two mechanisms by which curvature influences the stationarity of Mach reflection are identified. An increase in wave angle and interference between wave systems leading to the generation and integration of subsonic zones are the reasons for the non-stationarity of the Mach reflection in curved detonation. Besides, the effect mechanisms of choked flow which is considered to be the root cause are analysed in detail. On the basis of a theoretical model, the development of a quantitative criterion for the stability of detonation reflection is proposed, and its validity is confirmed by simulations. This criterion is used in a comprehensive investigation of the primary factors affecting the stability of detonation wave reflections, providing insights that will be of great value for the further development of detonation engines.

This work deals with the linear surface waves generated by a vessel advancing at a constant forward speed. These waves, known as ship waves, appear stationary to an observer on the vessel. Rather than exploring the well-studied stationary ship waves, this work delves into the physical properties of ship waves measured at Earth-fixed locations. While it might have been expected that analysing these waves in an Earth-fixed coordinate system would be a straightforward transformation from existing analytical theories in a moving coordinate system, the reality proves to be quite different. The properties of waves measured at fixed locations due to a passing ship turn out to be complex and non-trivial. They exhibit unique characteristics, being notably unsteady and short crested, despite appearing stationary to an observer on the generating vessel. The analytical expressions for the physical properties of these unsteady waves are made available in this work, including the amplitude, frequency, wavenumber, direction of propagation, phase velocity and group velocity. Based on these newly derived expressions and two-point measurements, an inverse method has been presented for determining the advancing speed and the course of motion of the moving ship responsible for the wave generation. The results from this study can be used in a wide range of applications, such as interpreting data from point measurements and assessing the roles of ship waves in transporting ocean particles.

Numerical analysis of a steady monatomic gas flow about the point of the regular reflection of a strong oblique shock wave from the symmetry plane is conducted with the Navier–Stokes–Fourier (NSF) equations, the regularized Grad 13-moment (R13) equations and the direct simulation Monte Carlo (DSMC) method. In contrast to the inviscid solution to this problem completely defined by the Rankine–Hugoniot (RH) relations, all three models predict a complicated flow structure with strong thermal non-equilibrium and a long wake with flow parameters not predicted by the RH relations. The temperature $T_y$ related to thermal motion of molecules in the direction normal to the symmetry plane has a maximum inside the reflection zone while in a planar shock wave the maximum is observed for the $T_x$ temperature. The R13 equations predict these features much better than the NSF equations and are in good agreement with the benchmark DSMC results. An analysis of the flow with the conservation equations was conducted in order to evaluate the effects of various processes on a fluid element moving along the symmetry plane. In contrast to the shock wave where effects of viscosity and heat conduction are one-dimensional with zeroth net contribution to the fluid-element energy across the shock, the flow across the zone of the shock reflection is dominated by two-dimensional effects with positive net contribution of viscosity and negative contribution of heat conduction to the fluid-element energy. These effects are believed to be the main source of the wake with parameters deviating from the RH values.

Nonlinear machine learning for turbulent flows can exhibit robust performance even outside the range of training data. This is achieved when machine-learning models can accommodate scale-invariant characteristics of turbulent flow structures. This study presents a data-driven approach to reveal scale-invariant vortical structures across Reynolds numbers that provide insights for supporting nonlinear machine-learning-based studies of turbulent flows. To uncover conditions for which nonlinear models are likely to perform well, we use a Buckingham-Pi-based sparse nonlinear scaling to find the influence of the Pi groups on the turbulent flow data. We consider nonlinear scalings of the invariants of the velocity gradient tensor for an example of three-dimensional decaying isotropic turbulence. The present scaling not only enables the identification of vortical structures that are interpolatory and extrapolatory for the given flow field data but also captures non-equilibrium effects of the energy cascade. As a demonstration, the present findings are applied to machine-learning-based super-resolution analysis of three-dimensional isotropic turbulence. We show that machine-learning models reconstruct vortical structures well in the interpolatory space with reduced performance in the extrapolatory space revealed by the nonlinearly scaled invariants. The present approach enables us to depart from labelling turbulent flow data with a single parameter of Reynolds number and comprehensively examine the flow field to support training and testing of nonlinear machine-learning techniques.

Evaporation of multicomponent droplets is important, albeit complex, in a wide range of applications, and requires a careful investigation. We investigate experimentally and numerically the evaporation characteristics of spherical, ethanol–water droplets with different initial concentration ratios in the acoustic levitation field. Imaging techniques and infrared thermometry are used for acquiring volume and surface temperature variations of droplets, reflecting their mass and heat transfer characteristics. Numerical simulations are conducted using modified parameters based on a theoretical model to consider the effect of the acoustic field. The calculation results show good agreement with the experimental data. The concentration and temperature distribution within the droplet is further investigated based on the numerical results.