We perform direct numerical simulations of centrifugal convection with an oscillating rotational velocity of small amplitude to study the effects of oscillatory boundary motion. The oscillation period is the main control parameter, with its range corresponding to a Womersley number in the range $1\lt Wo\lt 300$. Oscillating boundaries generate a circumferential shear flow, which significantly inhibits heat transfer, with maximum suppression $87\,\%$ observed in the present parameter space. Through analysis of the background flow, we find that as the oscillation period increases, the increasing penetration depth of the oscillation and weakening local shear strength result in non-monotonic changes in heat transfer. Under high-frequency oscillation, the characteristic length scale of the viscous layer induced by the oscillation is smaller than the convective length scale, and shear manifests primarily as a continuous suppression of the boundary layer. In contrast, under low-frequency oscillation, the shear flow covers the entire region but with weak strength. The suppression effect of such shear flow exhibits periodicity, leading to alternating phases of convection inhibition and convection generation. The present findings explore the physical mechanisms behind the suppression of convective heat transfer by oscillation, and offer a new strategy for controlling convection systems, with potential implications for both fundamental research and industrial applications.

A generalised multiparameter model for linear modal stability and sensitivity analysis is developed. The stability and sensitivity equations are derived from a generalised vector-form governing equation comprised of multiple dimensionless parameters that represent different physical forces affecting the system’s stability. By introducing adjoint variables and constructing the Lagrangian identity, a differential relationship between the eigenvalue of the perturbation mode and dimensionless parameters is determined and defined as the global sensitivity gradient. It provides the constraint that must be satisfied for changes in different dimensionless parameters along the isoeigenvalue curve, which aids in the fast computation of the neutral curve. Moreover, the global sensitivity gradient can directly and intuitively evaluate the competitive relationship among the influences of various parameters on system instability. Based on the global sensitivity gradient, an optimal stability control strategy for transitioning from an unstable state to a stable state is discussed. Additionally, the relative sensitivity function is also introduced to investigate the influence of relative parameter variations on instability. To demonstrate the effectiveness of this method, three applications are presented: two-dimensional flow around a circular cylinder with a single dimensionless parameter Re; three-dimensional axisymmetric magnetohydrodynamic (MHD) flow around a sphere with two parameters Re and $N$; and two-dimensional MHD mixed convection with three parameters Re, ${\textit{Gr}}$ and $\textit{Ha}$.

Power minimisation in branched fluidic networks has gained significant attention in biology and engineering. The optimal network is defined by channel radii that minimise the sum of viscous dissipation and the volumetric energetic cost of the fluid. For limit cases including laminar flows, high-Reynolds-number turbulence or smooth-channel approximations, optimal solutions are known. However, current methods do not allow optimisation for a large intermediate part of the parameter space which is typically encountered in realistic fluidic networks that exhibit turbulent flow. Here, we present a unifying optimisation approach based on the Darcy friction factor, which has been determined for a wide range of flow regimes and fluid models and is applicable to the entire parameter space: (i) laminar and turbulent flows, including networks that exhibit both flow types, (ii) non-Newtonian fluids (powerlaw, Bingham and Herschel–Bulkley) and (iii) networks with arbitrary wall roughness, including non-uniform relative roughness. The optimal channel radii are presented analytically and graphically. All existing limit cases are recovered, and a concise framework is presented for systematic optimisation of fluidic networks. Finally, the parameter $x$ in the optimisation relationship $Q\propto R^{x}$, with $Q$ the flow rate and $R$ the channel radius, was approximated as a function of the Reynolds number, revealing in which case the entire network can be optimised based on one optimal channel radius, and in which case all radii must be optimised individually. Our approach can be extended to a wide range of fluidic networks for which the friction factor is known, such as different channel curvatures, bubbly flows or specific wall slip conditions.

The spatiotemporal dynamics of a turbulent boundary layer subjected to an unsteady pressure gradient are studied. A dynamic sequence of favourable to adverse pressure gradients (FAPGs) is imposed by deforming a section of the wind tunnel ceiling, transitioning the pressure gradient from zero to a strong FAPG within 0.07 s. At the end of the transient, the acceleration parameter is $K$ = $6 \times 10^{-6}$ in the favourable pressure gradient (FPG) region and $K$ = $-4.8 \times 10^{-6}$ in the adverse pressure gradient (APG) region. The resulting unsteady response of the boundary layer is compared with equivalent steady pressure gradient cases in terms of turbulent statistics and coherent structures. While the steady FAPG effects, as shown by Parthasarathy & Saxton-Fox (2023), caused upstream stabilisation in the FPG, a milder APG response downstream, and the formation of an internal layer, the unsteady case presented in this paper shows a reduced stabilisation in the FPG region, a stronger APG response and a weaker internal layer. This altered response is hypothesised to stem from the different spatiotemporal pressure gradient histories experienced by turbulent structures when the pressure gradient changes at a time scale comparable to their convection.

This paper investigates the weakly nonlinear isotropic bidirectional Benney–Luke (BL) equation, which is used to describe oceanic surface and internal waves in shallow water, with a particular focus on soliton dynamics. Using the Whitham modulation theory, we derive the modulation equations associated with the BL equation that describe the evolution of soliton amplitude and slope. By analysing rarefaction waves and shock waves within these modulation equations, we derive the Riemann invariants and modified Rankine–Hugoniot conditions. These expressions help characterise the Mach expansion and Mach reflection phenomena of bent and reverse bent solitons. We also derive analytical formulae for the critical angle and the Mach stem amplitude, showing that as the soliton speed is in the vicinity of unity, the results from the BL equation align closely with those of the Kadomtsev–Petviashvili (KP) equation. Corresponding numerical results are obtained and show excellent agreement with theoretical predictions. Furthermore, as a far-field approximation for the forced BL equation – which models wave and flow interactions with local topography – the modulation equations yield a slowly varying similarity solution. This solution indicates that the precursor wavefronts created by topography moving at subcritical or critical speeds take the shape of a circular arc, in contrast to the parabolic wavefronts observed in the forced KP equation.

The recently proposed near-wall turbulence predictive model quantifies the degree of the superposition and the amplitude modulation exerted by large-scale coherent structures on small scales in the linear and nonlinear terms of the formula, respectively, and achieves the prediction of streamwise velocity in the inner region. However, the multiscale effect and the time shift confirmed in the amplitude modulation have not yet been simultaneously taken into account in the model, which could limit the prediction accuracy especially at high Reynolds numbers. In this study, the role of the nonlinear term in the model is clarified based on high-quality flow data obtained in atmospheric surface layers: it redistributes the energy of the universal signal in the time domain and determines the accuracy of the predictive odd moments. An analysis of the multiscale effect and the time shifts in the nonlinear term is subsequently conducted, followed by a demonstration of the refinement in the quality of the universal signal after separately incorporating them into the model. The amplitude modulation is revealed when the two factors are simultaneously considered, and profiles of the scales that dominate the modulation and time shifts with height is provided. Thus, the nonlinear term of the existing model is modified, proposing an polished scheme that can quantify the nonlinear modulation terms more accurately.

This paper presents a peridynamics-based computational approach for modelling coupled fluid flow and heat transfer problems. A new thermo-hydrodynamic peridynamics model is formulated with the semi-Lagrangian scheme and non-local operators. To enhance accuracy and numerical stability, a multi-horizon scheme is developed to introduce distinct horizons for the flow field and thermal field. The multi-horizon scheme helps to capture the convective zone and complex thermal flow pattern while effectively mitigating possible oscillations in temperature. We validate the computational approach using benchmarks and numerical examples including heat conduction, natural convection in a closed cavity, and Rayleigh–Bénard convection cells. The results demonstrate that the proposed method can accurately capture typical thermal flow behaviours and complex convective patterns. This work offers a new foundation for future development of a unified peridynamics framework for robust, comprehensive multi-physics analysis of thermal fluid–solid interaction problems with complex evolving discontinuities in solids.

Miscible Rayleigh–Taylor (RT) turbulence exhibits a wide range of length scales in both the velocity and density fields, leading to complex deformations of isoscalar surfaces and enhanced mixing due to nonlinear interactions among different scales. Through high-resolution numerical simulations and a coarse-graining analysis, we demonstrate that the variance of the heavy fluid concentration, initially maximised by the unstable stratification, progressively cascades from larger to smaller scales, eventually dissipates at the smallest scale. The transfer of scalar variance, $\Pi ^Y$, primarily governed by the filtered strain rate tensor, is effectively captured by a nonlinear model that links $\Pi ^Y$ to the isoscalar surface stretching. On the other hand, the backscatter of scalar variance transfer, represented by the negative component of $\Pi ^Y$, is influenced by the filtered vorticity field. Furthermore, we examine the directional anisotropy of scalar transfer in RT turbulence, enhancing the accuracy of the nonlinear model by separating the horizontal mean of the mass fraction from its fluctuating part.

The dispersion behaviour of solutes in flow is crucial to the design of chemical separation systems and microfluidics devices. These systems often rely on coupled electroosmotic and pressure-driven flows to transport and separate chemical species, making the transient dispersive behaviour of solutes highly relevant. However, previous studies of Taylor dispersion in coupled electroosmotic and pressure-driven flows focused on the long-term dispersive behaviour and the associated analyses cannot capture the transient behaviour of solute. Further, the radial distribution of solute has not been analysed. In the current study, we analyse the Taylor dispersion for coupled electroosmotic and pressure-driven flows across all time regimes, assuming a low zeta potential (electric potential at the shear plane), the Debye–Hückel approximation and a finite electric double layer thickness. We first derive analytical expressions for the effective dispersion coefficient in the long-time regime. We also derive an unsteady, two-dimensional (radial and axial) solute concentration field applicable in the latter regime. We next apply Aris’ method of moments to characterise the unsteady propagation of the mean axial position and the unsteady growth of the variance of the solute zone in all time regimes. We benchmark our predictions with Brownian dynamics simulations across a wide and relevant dynamical regime, including various time scales. Lastly, we derive expressions for the optimal relative magnitudes of electroosmotic versus pressure-driven flow and the optimum Péclet number to minimise dispersion across all time scales. These findings offer valuable insights for the design of chemical separation systems, including the optimisation of capillary electrophoresis devices and electrokinetic microchannels and nanochannels.

This study presents an automatic differentiation (AD)-based optimisation framework for flow control in compressible turbulent channel flows. Using a differentiable solver, JAX-Fluids, we designed fully differentiable boundary conditions that allow for the precise calculation of gradients with respect to boundary control variables. This facilitates the efficient optimisation of flow control methods. The framework’s adaptability and effectiveness are demonstrated using two boundary conditions: opposition control and tunable permeable walls. Various optimisation targets are evaluated, including wall friction and turbulent kinetic energy (TKE), across different time horizons. In each optimisation, there were around $4\times 10^4$ control variables and $3\times 10^{9}$ state variables in a single episode. Results indicate that TKE targeted opposition control achieves a more stable and significant reduction in drag, with effective suppression of turbulence throughout the channel. In contrast, strategies that focus directly on minimising wall friction were found to be less effective, exhibiting instability and increased turbulence in the outer region. The tunable permeable walls also show potential to achieve stable drag reduction through a ‘flux-inducing’ mechanism. This study demonstrates the advantages of AD-based optimisation in complex flow control scenarios and provides physical insight into the choice of the quantity of interest for improved optimisation performance.

We perform a comprehensive linear non-modal stability analysis of the Rayleigh–Bénard convection with and without a Poiseuille/Couette flow in Oldroyd-B fluids. In the absence of shear flow, unlike the Newtonian case in which the perturbation energy decays monotonically with time, the interaction between temperature gradient and polymeric stresses can surprisingly cause a transient growth up to 104. This transient growth is maximized at the Hopf bifurcation when the stationary instability dominant in the weakly elastic regime transitions to the oscillatory instability dominant in the strongly elastic regime. In the presence of a Poiseuille/Couette flow, the streamwise-uniform disturbances may achieve the greatest energy amplification, and similar to the pure bounded shear flows, Gmax ∝ Re2 and tmax ∝ Re, where Gmax is the maximum energy growth, tmax the time to attain Gmax, Re the Reynolds number. It is noteworthy that there exist two peaks during the transient energy growth at high-Re cases. Different from the first one which is less affected by the temperature gradient and elasticity, the second peak, at which the disturbance energy is the largest, is simultaneously determined by the temperature gradient, elasticity and shear intensity. Specifically, the polymeric stresses field absorbs energy from the temperature field and base flow, which is partially transferred into the perturbed hydrodynamic field eventually, driving the transient amplification of the perturbed wall-normal vorticity.

Feigenbaum universality is shown to occur in subcritical shear flows. Our testing ground is the counter-rotation regime of the Taylor–Couette flow, where numerical calculations are performed within a small periodic domain. The accurate computation of up to the seventh period-doubling bifurcation, assisted by a purposely defined Poincaré section, has enabled us to reproduce the two Feigenbaum universal constants with unprecedented accuracy in a fluid flow problem. We have further devised a method to predict the bifurcation diagram up to the accumulation point of the cascade based on the detailed inspection of just the first few period-doubling bifurcations. Remarkably, the method is applicable beyond the accumulation point, with predictions remaining valid, in a statistical sense, for the chaotic dynamics that follows.

The influence of parametric forcing on a viscoelastic fluid layer, in both gravitationally stable and unstable configurations, is investigated via linear stability analysis. When such a layer is vertically oscillated beyond a threshold amplitude, large interface deflections are caused by Faraday instability. Viscosity and elasticity affect the damping rate of momentary disturbances with arbitrary wavelength, thereby altering the threshold and temporal response of this instability. In gravitationally stable configurations, calculations show that increased elasticity can either stabilize or destabilize the viscoelastic system. In weakly elastic liquids, higher elasticity increases damping, raising the threshold for Faraday instability, whereas the opposite is observed in strongly elastic liquids. While oscillatory instability occurs in Newtonian fluids for all gravity levels, we find that parametric forcing below a critical frequency will cause a monotonic instability for viscoelastic systems at microgravity. Importantly, in gravitationally unstable configurations, parametric forcing above this frequency stabilizes viscoelastic fluids, until the occurrence of a second critical frequency. This result contrasts with the case of Newtonian liquids, where under the same conditions, forcing stabilizes a system for all frequencies below a single critical frequency. Analytical expressions are obtained under the assumption of long wavelength disturbances predicting the damping rate of momentary disturbances as well as the range of parameters that lead to a monotonic response under parametric forcing.

We explore the instability and oscillation dynamics of barrel-shaped droplets on cylindrical fibres, contributing to a deeper understanding of fibre–droplet interactions critical to both natural systems and industrial applications. Unlike sessile droplets on flat surfaces, droplets on fibres exhibit unique behaviours due to the curvature of the fibre, such as transitions from axisymmetric (barrel) to non-axisymmetric (clamshell) shapes governed by droplet volume, contact angle and fibre radius. Using a linear inviscid theory, we compute the frequency spectrum of barrel-shaped droplets and identify stability thresholds for the barrel-to-clamshell transition by examining the first rocking mode, with a focus on the role of contact line conditions. This analysis resolves experimental anomalies concerning the stability of half-barrel-shaped droplets on hydrophobic fibres. Our findings also reveals diverse frequency spectra: droplets on thin fibres exhibit Rayleigh–Lamb-like spectral features, while those on thicker fibres show reduced sensitivity to azimuthal wavenumber. Interestingly, the instability of sectoral modes on thick fibres resembles the Rayleigh–Plateau instability of static rivulets, with fibre curvature slightly reducing growth rates at small axial wavenumbers but increasing them at larger ones.