The shoreline hazard posed by ocean long waves such as tsunamis and meteotsunamis critically depends on the fraction of energy transmitted across the shallow near-shore shelf. In linear setting, bathymetric inhomogeneities of length comparable to the incident wavelength act as a protective high-pass filter, reflecting long waves and allowing only shorter waves to pass through. Here, we show that, for weakly nonlinear waves, the transmitted energy flux fraction can significantly depend on the amplitude of the incoming wave. The basis of this mechanism is the formation of dispersive shock waves (DSWs), a salient feature of nonlinear evolution of long water waves, often observed in tidal bores and tsunami/meteotsunami evolution. Within the framework of the Boussinesq equations, we show that the DSWs efficiently transfer wave energy into the high wavenumber band, where reflection is negligible. This is phenomenologically similar to self-induced transparency in nonlinear optics: small amplitude long waves are reflected by the bathymetric inhomogeneity, while larger amplitude waves that develop DSWs blueshift into the transparency regime and pass through. We investigate this mechanism in a simplified setting that retains only the key processes of DSW disintegration and reflection, while the effects such as bottom dissipation and breaking are ignored. The results suggests that the phenomenon is a robust, order-one effect. In contrast, the increased transmission due to the growth of bound harmonics associated with the steepening of the wave is weak. The results of the simplified modelling are validated by simulations with the FUNWAVE-TVD Boussinesq model.

Rotating Rayleigh–Bénard convection denotes the convection between a warm plate and a cold plate in a rotating environment. It is a classic model for understanding convective vortices in the atmosphere and ocean. The influence of background rotation on fluid inertia breaks the symmetry between cyclones and anticyclones. Such a symmetry breaking could be represented by vorticity skewness, which still lacks a systematic theory. Rapidly rotating convection with stress-free boundaries and unit Prandtl number is a convenient starting point. The investigation starts from the convective onset stage, where the vortices grow stationarily. Asymptotic analysis shows that the volumetric vorticity skewness $S$ is produced by the interaction between the $n=0,1$ and $n=1,2$ vertical eigenmodes. The $n=0$ (barotropic) mode contributes positively to $S$ mainly by stretching the vertical relative vorticity, an ageostrophic effect. The $n=2$ mode makes a minor negative contribution to $S$ by preferentially intensifying the outflow over the inflow, a non-hydrostatic effect. The theory predicts $S$ to be proportional to the global Rossby number defined with the volumetric standard deviation of vorticity, ${Ro_g}$. The proportional factor does not depend on the Rayleigh and Ekman numbers, agreeing with direct numerical simulations. Then the system enters the equilibrium stage. The stretching of vertical vorticity still contributes to $S$ dominantly. At ${Ro_g}\gtrsim 0.5$, the emergent unsteady flow significantly suppresses the asymmetry between the inflow and outflow strength, and weakens its influence on $S$.

This work examines the control of cross-flow instabilities (CFIs) and laminar–turbulent transition on a swept wing, through the plasma-based base flow modification (BFM) technique. The effect of experimentally derived plasma body forces on the steady boundary layer base flow is explored through numerical simulations. Linear stability theory is subsequently used to predict the net BFM effect on CFIs. Based on these preliminary predictions, experiments are conducted in a low-turbulence wind tunnel where a spanwise-invariant plasma actuator is installed near the wing leading edge and operated at constant input voltage and frequency. Various flow parameters governing the plasma-based BFM technique are investigated, namely the Reynolds number, angle of attack and wavelength of excited stationary CFI modes. Stationary and travelling CFIs are quantified by planar particle image velocimetry while the transition topology and location are recorded by infrared thermography. The results confirm the stabilising effect of BFM on the swept-wing boundary layer. However, the plasma-based BFM is found to render the boundary layer more susceptible to travelling CFIs. In the presence of both net BFM effect and intrinsic plasma unsteady perturbations, the plasma-based BFM technique achieves transition delay with specific combinations of Reynolds number, angle of attack and wavelength of excited stationary CFI modes. The present findings provide insights into the fundamental principles of operating plasma actuators within the context of BFM control.

High angle of attack flows over swept three-dimensional wings based on the NACA 0015 profile are studied numerically at low Reynolds numbers. Linear stability analysis is used to compute instability and receptivity of the flow via the respective three-dimensional (triglobal) direct and adjoint eigenmodes. The magnitude of the adjoint eigenvectors is used to identify regions of maximum flow receptivity to momentum forcing. It is found that such regions are located above the primary three-dimensional separation line, their spanwise position varying with wing sweep. The wavemaker region corresponding to the leading global eigenmode is computed and found to lie inside the laminar separation bubble (LSB) at the spanwise location of peak recirculation. Increasing the Reynolds number leads to the wavemaker becoming more compact in the spanwise direction, and concentrated in the top and bottom shear layers of the LSB. As sweep is introduced, the wavemaker moves towards the wing tip, following the spanwise displacement of maximum recirculation. Flow modifications resulting from application of different types of forcing are studied by direct numerical simulation initialised with insights gained from stability analysis. Periodic forcing at the regions of maximum receptivity to momentum forcing results in greater departure from the baseline case compared to same (low, linear) amplitude forcing applied elsewhere, underlining the potential of linear stability analysis to identify optimal regions for actuator positioning.

The present study investigates streamwise ($\overline {u^2}$) energy-transfer mechanisms in the inner and outer regions of turbulent boundary layers (TBLs). Particular focus is placed on the $\overline {u^2}$ production, its inter-component and wall-normal transport as well as dissipation, all of which become statistically significant in the outer region with increasing friction Reynolds number ($Re_{\tau }$). These properties are analysed using published data sets of zero, weak and moderately strong adverse-pressure-gradient (APG) TBLs across a decade of $Re_{\tau }$, revealing similarity in energy-transfer pathways for all these TBLs. It is found that both the inner and outer peaks of $\overline {u^2}$ are always associated with local maxima in the $\overline {u^2}$ production and its inter-component transport, and the regions below/above each of these peaks are always dominated by wall-ward/away-from-wall transport of $\overline {u^2}$, thereby classifying the $\overline {u^2}$ profiles into four distinct regimes. This classification reveals existence of phenomenologically similar energy-transfer mechanisms in the ‘inner’ and ‘outer’ regions of moderately strong APG TBLs, which meet at an intermediate location coinciding with the minimum in $\overline {u^2}$ profiles. Conditional averaging suggests existence of similar phenomena even in low $Re_{\tau }$ canonical and/or weak APG TBLs, albeit with the outer-region mechanisms weaker than those in the inner region. This explains the absence of their $\overline {u^2}$ outer peak and the dominance of $\overline {u^2}$ wall-normal transport away from the wall, which potentially originates from the inner region. Given that the wall-ward/away-from-wall transport of $\overline {u^2}$ is governed by the $Q_4$(sweeps)/$Q_2$(ejections) quadrants of the Reynolds shear stress, it is argued that the emergence of the $\overline {u^2}$ outer peak corresponds with the statistical dominance of $Q_4$ events in the outer region. Besides unravelling the dynamical significance of $Q_2$ and $Q_4$ events in the outer region of TBLs, the present analysis also proposes new phenomenological arguments for testing on canonical wall-turbulence data at very high $Re_{\tau }$.

Standing acoustic waves have been known to generate Eulerian time-mean ‘streaming’ flows at least since the seminal investigation of Lord Rayleigh in the 1880s. Nevertheless, a recent body of numerical and experimental evidence has shown that inhomogeneities in the ambient density distribution lead to much faster flows than arise in classical Rayleigh streaming. The emergence of these unusually strong flows creates new opportunities to enhance heat transfer in systems in which convective cooling cannot otherwise be easily achieved. To assess this possibility, a theoretical study of acoustic streaming in an ideal gas confined in a rectangular channel with top and bottom walls maintained at fixed but differing temperatures is performed. A two time scale system of equations is utilized to efficiently capture the coupling between the fast acoustic waves and the slowly evolving streaming flow, enabling strongly nonlinear regimes to be accessed. A large suite of numerical simulations is carried out to probe the streaming dynamics, to highlight the critical role played by baroclinically generated wave vorticity and to quantify the additional heat flux induced by the standing acoustic wave. Proper treatment of the two-way coupling between the waves and mean flow is found to be essential for convergence to a self-consistent steady state, and the variation of the resulting acoustically enhanced steady-state heat flux with both the amplitude of the acoustic wave and the $O(1)$ aspect ratio of the channel is documented. For certain parameters, heat fluxes almost two orders of magnitude larger than those realizable by conduction alone can be attained.

Recent numerical calculations have revealed the existence of fast jets in inviscid fluids when a pressure maximum exists close to a free boundary. This paper describes two-dimensional and axisymmetric configurations for which asymptotic analysis suggests that such jets can become infinitely long in finite time.

The volume filtering of the governing equations of a particle-laden flow allows for simulating the fluid phase as a continuum, and accounting for the momentum exchange between the fluid and the particles by adding a source term in the fluid momentum equations. The volume filtering of the Navier–Stokes equations allows consideration of the effect that particles have on the fluid without further assumptions, but closures arise of which the implications are not fully understood. It is common to either neglect these closures or model them using assumptions of which the implications are unclear. In the present paper, we carefully study every closure in the volume-filtered fluid momentum equation and investigate their impact on the momentum and energy transfer dependent on the filtering characteristics. We provide an analytical expression for the viscous closure that arises because the filter and spatial derivative in the viscous term do not commute. An analytical expression for the regularization of the particle momentum source of a single sphere in the Stokes regime is derived. Furthermore, we propose a model for the subfilter stress tensor, which originates from filtering the advective term. The model for the subfilter stress tensor is shown to agree well with the subfilter stress tensor for small filter widths relative to the size of the particle. We show that, in contrast to common practice, the subfilter stress tensor requires modelling and should not be neglected. For filter widths comparable to the particle size, we find that the commonly applied Gaussian regularization of the particle momentum source is a poor approximation of the spatial distribution of the particle momentum source, but for larger filter widths, the spatial distribution approaches a Gaussian. Furthermore, we propose a modified advective term in the volume-filtered momentum equation that consistently circumvents the common stability issues observed at locally small fluid volume fractions. Finally, we propose a generally applicable form of the volume-filtered momentum equation and its closures based on clear and well-founded assumptions. Based on the new findings, guidelines for point-particle simulations and the filter width with respect to the particle size and fluid mesh spacing are proposed.

The spatial evolution of various statistical parameters of fetch-limited waves generated by steadily blowing wind over mean water flow in a wind-wave flume is investigated experimentally. Measurements are performed in both along- and against-wind current conditions, and compared with measurements in the absence of current. A rake of capacitance-type wave gauges is used to measure surface elevation for a wide range of wind and water current velocities; additionally, an optical wave gauge is used to measure the directional properties of the wind-wave field in the presence of a mean water current at multiple locations. The variation with fetch of essential wave parameters such as characteristic wave energy, dominant frequency, power spectra and temporal coherence, as well as higher-order statistical moments that characterize wave shape, is presented for co- and counter-wind water currents, and compared with the no-current condition. The findings in the presence of mean water flow are interpreted in the framework of the viscous shear flow instability model of Geva & Shemer (Phys. Rev. Lett., vol. 128, 2022, 124501).

The interaction between deformable surfaces and oscillatory driving is known to produce complex secondary time-averaged flows due to inertial and elastic nonlinearities. Here, we revisit the problem of oscillatory flow in a cylindrical tube with a deformable wall, and analyse it under a long-wave theory for small deformations, but for arbitrary Womersley numbers. We find that the oscillatory pressure does not vary linearly along the length of a deformable channel, but instead decays exponentially with spatial oscillations. We show that this decay occurs over an elasto-visco-inertial length scale that depends on the material properties of the fluid and the elastic walls, the geometry of the system, and the frequency of the oscillatory flow, but is independent of the amplitude of deformation. Inertial and geometric nonlinearities associated with the elastic deformation of the channel drive a time-averaged secondary flow. We quantify the flow using numerical solutions of the perturbation theory, and gain insight by developing analytic approximations. The theory identifies a complex non-monotonic dependence of the time-averaged flux on the elastic compliance and inertia, including a reversal of the flow. Finally, we show that our analytic theory is in excellent quantitative agreement with the three-dimensional direct numerical simulations of Pande et al. (Phys. Rev. Fluids, vol. 8, no. 12, 2023, 124102).

When subjected to external stress exceeding their yield stress ($\sigma _{Y}$), yield stress fluids (YSFs) undergo transition from solid to liquid. While the flow dynamics of capillary flows – including wetting, coating, spreading, and wicking – can be predicted accurately for fluids without yield stress, only a few asymptotic solutions have been validated against experiments for YSFs. In this study, we explore experimentally and theoretically the entire dynamics and solidifying process during capillary imbibition of YSFs, representing the fundamental aspect of capillarity-driven flow. We observe that during the gradual deceleration of capillary rise, YSFs exhibit apparent flow below $\sigma _{Y}$. This unexpected behaviour is linked to wall slip, manifested as plug flow in particle image velocimetry analyses. We introduce a model with numerical solutions, grounded in the rheological properties of YSFs and slip mechanisms, to accurately describe this liquid–solid transitional behaviour.

Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over-predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is presented which corrects this and is shown to conserve energy. New theoretical predictions are supported by numerical results which use averaging of simulations of wave scattering over finite sections of random bathymetry for which transfer matrix eigenvalues are used to accurately measure decay. The model of wave propagation used in this paper is derived from a linearised long-wavelength assumption whereby depth averaging leads to time harmonic waves being represented as solutions to a simple ordinary differential equation. In this paper it is shown how this can be adapted to incorporate a model of a continuous covering of the surface by fragmented floating ice. Attenuation of waves through broken ice of random thickness is then analysed in a similar manner as bed variations have been previously. General features of the predicted attenuation are discussed in relation to existing theoretical models for attenuation due to multiple scattering through random ice environments and to field data, particularly in the model's ability to capture a ‘rollover effect’ at higher frequencies.

This research investigates the wake–foil interactions between two oscillating foils in a tandem configuration undergoing energy harvesting kinematics. Oscillating foils have been shown to extract hydrokinetic energy from free-stream flows through a combination of periodic heave and pitch motions, at relatively higher amplitudes and lower reduced frequency than thrust generating foils. When placed in tandem, the wake–foil interactions can govern the energy harvesting efficiency of the system due to a reduced relative flow velocity in combination with a structured and coherent wake of vortices shed from the high amplitude flapping of upstream foils. This work utilizes simulations of two tandem foils to parameterize and model the energy harvesting performance as a function of array configuration and foil kinematics. Once the wake of the leading foil has been fully parameterized, the placement, phase angle and kinematic stroke of the second foil is utilized to estimate the time-dependent power curve. The algorithm predicts the power of the second foil through the mean and unsteady wake characteristics, including the direct impingement of a vortex with the trailing foil.

As most mathematically justifiable Lagrangian coherent structure detection methods rely on spatial derivatives, their applicability to sparse trajectory data has been limited. For experimental fluid dynamicists and natural scientists working with Lagrangian trajectory data via passive tracers in unsteady flows (e.g. Lagrangian particle tracking or ocean buoys), obtaining material measures of fluid rotation or stretching is an active topic of research. To facilitate frame-indifferent investigations in unsteady and sparsely sampled flows, we present a novel approach to quantify fluid stretching and rotation via relative Lagrangian velocities. This technique provides a formal objective extension of quasi-objective metrics to unsteady flows by accounting for mean flow behaviour. For extremely sparse experimental data, fluid structures may be significantly undersampled and the mean flow behaviour becomes difficult to quantify. We provide a means to maintain the accuracy of our novel sparse flow diagnostics in extremely sparse sampling scenarios, such as ocean buoy data and Lagrangian particle tracking. We use data from multiple numerical and experimental flows to show that our methods can identify structures beyond existing limits of sparse, frame-indifferent diagnostics and exhibit improved interpretability over common frame-dependent diagnostics.

We study the dynamics of thermal and momentum boundary regions in three-dimensional direct numerical simulations of Rayleigh–Bénard convection for the Rayleigh-number range $10^5\leq Ra \leq 10^{11}$ and $Pr=0.7$. Using a Cartesian slab with horizontal periodic boundary conditions and an aspect ratio of 4, we obtain statistical homogeneity in the horizontal $x$- and $y$-directions, thus approximating best an extended convection layer relevant for most geo- and astrophysical flow applications. We observe upon canonical use of combined long-time and area averages, with averaging periods of at least 100 free-fall times, that a global coherent mean flow is practically absent and that the magnitude of the velocity fluctuations is larger than the mean by up to 2 orders of magnitude. The velocity field close to the wall is a collection of differently oriented local shear-dominated flow patches interspersed by extensive shear-free incoherent regions which can be as large as the whole cross-section, unlike for a closed cylindrical convection cell of aspect ratio of the order 1. The incoherent regions occupy a 60 % area fraction for all Rayleigh numbers investigated here. Rather than resulting in a pronounced mean flow with small fluctuations about such a mean, as found in small-aspect-ratio convection, the velocity field is dominated by strong fluctuations of all three components around a non-existent or weak mean. We discuss the consequences of these observations for convection layers with larger aspect ratios, including boundary layer instabilities and the resulting turbulent heat transport.

Linear stability analysis currently fails to predict turbulence transition in canonical viscous flows. We show that two alternative models of the boundary condition for incipient perturbations at solid walls produce linear instabilities that could be sufficient to explain turbulence transition. In many cases, the near-wall behaviour of the discovered instabilities is empirically indistinguishable from the classical no-slip condition. The ability of these alternative boundary conditions to predict linear instabilities that are consistent with turbulence transition suggests that the no-slip condition may be an overly simplified model of fluid–solid interface physics, particularly as a description of the flow perturbations that lead to turbulence transition in wall-bounded flows.

Direct numerical simulation (DNS) of rotating pipe flows up to $Re_\tau \approx 3000$ is carried out to investigate drag reduction effects associated with axial rotation, extending previous studies carried out at a modest Reynolds number (Orlandi & Fatica, J. Fluid Mech., vol. 343, 1997, pp. 43–72; Orlandi & Ebstein, Intl J. Heat Fluid Flow, vol. 21, 2000, pp. 499–505). The results show that the drag reduction, which we theoretically show to be equivalent to net power saving assuming no mechanical losses, monotonically increases as either the Reynolds number or the rotation number increases, proportionally to the inner-scaled rotational speed. Net drag reduction up to approximately $70\,\%$ is observed, while being far from flow relaminarisation. Scaling laws for the mean axial and azimuthal velocity are proposed, from which a predictive formula for the friction factor is derived. The formula can correctly represent the dependency of the friction factor on the Reynolds and rotation numbers, maintaining good accuracy for low-to-moderate rotation numbers. Examination of the turbulent structures highlights the role of rotation in widening and elongating the small-scale streaks, with subsequent suppression of sweeps and ejections. In the core part of the flow, clear weakening of large-scale turbulent motions is observed at high Reynolds numbers, with subsequent suppression of the outer-layer peak in the pre-multiplied spectra. The Fukagata–Iwamoto–Kasagi decomposition indicates that, consistent with a theoretically derived formula, the outer layer yields the largest contribution to drag reduction at increasingly high Reynolds numbers. In contrast, both the inner and the outer layers contribute to drag reduction as the rotation number increases.

We show how a complete mathematical model of a physical process can be learned directly from data via a hybrid approach combining three simple and general ingredients: physical assumptions of smoothness, locality and symmetry, a weak formulation of differential equations and sparse regression. To illustrate this, we extract a complete system of governing equations of fluid dynamics – the Navier–Stokes equation, the continuity equation and the boundary conditions – as well as the pressure-Poisson and energy equations, from numerical data describing a highly turbulent channel flow in three dimensions. Whether they represent known or unknown physics, relations discovered using this approach take the familiar form of partial differential equations, which are easily interpretable and readily provide information about the relative importance of different physical effects. The proposed approach offers insight into the quality of the data, serving as a useful diagnostic tool. It is also remarkably robust, yielding accurate results for very high noise levels, and should thus be well suited for analysis of experimental data.

Cross-stream migration of a deformable fluid particle is investigated computationally in a pressure-driven channel flow of a viscoelastic fluid via interface-resolved simulations. Flow equations are solved fully coupled with the Giesekus model equations using an Eulerian–Lagrangian method and extensive simulations are performed for a wide range of flow parameters to reveal the effects of particle deformability, fluid elasticity, shear thinning and fluid inertia on the particle migration dynamics. Migration rate of a deformable particle is found to be much higher than that of a solid particle under similar flow conditions mainly due to the free-slip condition on its surface. It is observed that the direction of particle migration can be altered by varying shear thinning of the ambient fluid. With a strong shear thinning, the particle migrates towards the wall while it migrates towards the channel centre in a purely elastic fluid without shear thinning. An onset of elastic flow instability is observed beyond a critical Weissenberg number, which in turn causes a path instability even for a nearly spherical particle. An inertial path instability is also observed once particle deformation exceeds a critical value. Shear thinning is found to be suppressing the path instability in a viscoelastic fluid with a high polymer concentration whereas it reverses its role and promotes path instability in a dilute polymer solution. It is found that migration of a deformable particle towards the wall induces a secondary flow with a velocity that is approximately an order of magnitude higher than the one induced by a solid particle under similar flow conditions.

This study explores the application of a wall-attached ferrofluid film to decrease skin-friction drag in turbulent channel flow. We conduct experiments using water as a working fluid in a turbulent channel flow set-up, where one wall is coated with a ferrofluid layer held in place by external permanent magnets. Depending on the flow conditions, the interface between the two fluids is observed to form unstable travelling waves. While ferrofluid coating has been previously employed in laminar and moderately turbulent flows (Reynolds number $Re<4000$) to reduce drag by creating a slip condition at the fluid interface, its effectiveness in fully developed turbulent conditions, particularly when the interface exhibits instability, remains uncertain. Our primary objective is to assess the effectiveness of ferrofluid coating in reducing turbulent drag with particular focus on scenarios when the ferrofluid layer forms unstable waves. To achieve this, we measure flow velocity using two-dimensional particle tracking velocimetry (2D-PTV), and the interface contour between the fluids is determined using an interface tracking algorithm. Our results reveal the significant potential of ferrofluid coating for drag reduction, even in scenarios where the interface between the surrounding fluid and ferrofluid exhibits instability, with observed drag reduction rates up to 95 %. In particular, waves with an amplitude significantly smaller than a viscous length scale positively contribute to drag reduction, while larger waves are detrimental, because of induced turbulent fluctuations. However, for the latter case, slip outcompetes the extra turbulence so that drag is still reduced.