The interplay between convective, rotational and magnetic forces defines the dynamics within the electrically conducting regions of planets and stars. Yet their triadic effects are separated from one another in most studies, arguably due to the richness of each subset. In a single laboratory experiment, we apply a fixed heat flux, two different magnetic field strengths and one rotation rate, allowing us to chart a continuous path through Rayleigh–Bénard convection (RBC), two regimes of magnetoconvection, rotating convection and two regimes of rotating magnetoconvection, before finishing back at RBC. Dynamically rapid transitions are determined to exist between jump rope vortex states, thermoelectrically driven magnetoprecessional modes, mixed wall- and oscillatory-mode rotating convection and a novel magnetostrophic wall mode. Thus, our laboratory ‘pub crawl’ provides a coherent intercomparison of the broadly varying responses arising as a function of the magnetorotational forces imposed on a liquid-metal convection system.

In many geophysical and astrophysical flows, suppression of fluctuations along one direction of the flow drives a quasi-two-dimensional upscale flux of kinetic energy, leading to the formation of strong vortex condensates at the largest scales. Recent studies have shown that the transition towards this condensate state is hysteretic, giving rise to a limited bistable range in which both the condensate state as well as the regular three-dimensional state can exist at the same parameter values. In this work, we use direct numerical simulations of thin-layer flow to investigate whether this bistable range survives as the domain size and turbulence intensity are increased. By studying the time scales at which rare transitions occur from one state into the other, we find that the bistable range grows as the box size and/or Reynolds number $Re$ are increased, showing that the bistability is neither a finite-size nor a finite-$Re$ effect. We furthermore predict a cross-over from a bimodal regime at low box size, low $Re$ to a regime of pure hysteresis at high box size, high $Re$, in which any transition from one state to the other is prohibited at any finite time scale.

Moderate rotation and moderate horizontal confinement similarly enhance the heat transport in Rayleigh–Bénard convection (RBC). Here, we systematically investigate how these two types of flow stabilization together affect the heat transport. We conduct direct numerical simulations of confined-rotating RBC in a cylindrical set-up at Prandtl number $\textit {Pr}=4.38$, and various Rayleigh numbers $2\times 10^{8}\leqslant {\textit {Ra}}\leqslant 7\times 10^{9}$. Within the parameter space of rotation (given as inverse Rossby number $0\leqslant {\textit {Ro}}^{-1}\leqslant 40$) and confinement (given as height-to-diameter aspect ratio $2\leqslant \varGamma ^{-1}\leqslant 32$), we observe three heat transport maxima. At lower $ {\textit {Ra}}$, the combination of rotation and confinement can achieve larger heat transport than either rotation or confinement individually, whereas at higher $ {\textit {Ra}}$, confinement alone is most effective in enhancing the heat transport. Further, we identify two effects enhancing the heat transport: (i) the ratio of kinetic and thermal boundary layer thicknesses controlling the efficiency of Ekman pumping, and (ii) the formation of a stable domain-spanning flow for an efficient vertical transport of the heat through the bulk. Their interfering efficiencies generate the multiple heat transport maxima.

With particle image velocimetry (PIV), cross-correlation and optical flow methods have been mainly adopted to obtain the velocity field from particle images. In this study, a novel artificial intelligence (AI) architecture is proposed to predict an accurate flow field and drone rotor thrust from high-resolution particle images. As the ground truth, the flow fields past a high-speed drone rotor obtained from a fast Fourier transform-based cross-correlation algorithm were used along with the thrusts measured by a load cell. Two deep-learning models were developed, and for instantaneous flow-field prediction, a generative adversarial network (GAN) was employed for the first time. It is a spectral-norm-based residual conditional GAN translator that provides a stable adversarial training and high-quality flow generation. Its prediction accuracy is 97.21 % (coefficient of determination, or R2). Subsequently, a deep convolutional neural network was trained to predict the instantaneous rotor thrust from the flow field, and the model is the first AI architecture to predict the thrust. Based on an input of the generated flow field, the network had an R2 accuracy of 94.57 %. To understand the prediction pathways, the internal part of the model was investigated using a class activation map. The results showed that the model recognized the area receiving kinetic energy from the rotor and successfully made a prediction. The proposed architecture is accurate and nearly 600 times faster than the cross-correlation PIV method for real-world complex turbulent flows. In this study, the rotor thrust was calculated directly from the flow field using deep learning for the first time.

Internal shear layers generated by the longitudinal libration of the inner core in a spherical shell rotating at a rate $\varOmega ^*$ are analysed asymptotically and numerically. The forcing frequency is chosen as $\sqrt {2}\varOmega ^*$ such that the layers issued from the inner core at the critical latitude in the form of concentrated conical beams draw a simple rectangular pattern in meridional cross-sections. The asymptotic structure of the internal shear layers is described by extending the self-similar solution known for open domains to closed domains where reflections on the boundaries occur. The periodic ray path ensures that the beams remain localised around it. Asymptotic solutions for both the main beam along the critical line and the weaker secondary beam perpendicular to it are obtained. The asymptotic predictions are compared with direct numerical results obtained for Ekman numbers as low as $E=10^{-10}$. The agreement between the asymptotic predictions and numerical results improves as the Ekman number decreases. The asymptotic scalings in $E^{1/12}$ and $E^{1/4}$ for the amplitudes of the main and secondary beams, respectively, are recovered numerically. Since the self-similar solution is singular on the axis, a new local asymptotic solution is derived close to the axis and is also validated numerically. This study demonstrates that, in the limit of vanishing Ekman numbers and for particular frequencies, the main features of the flow generated by a librating inner core are obtained by propagating through the spherical shell the self-similar solution generated by the singularity at the critical latitude on the inner core.

The impact of flexible rectangular aluminum plates on a quiescent water surface is studied experimentally. The plates are mounted via pinned supports at the leading and trailing edges to an instrument carriage that drives the plates at constant velocity and various angles relative to horizontal into the water surface. Time-resolved measurements of the hydrodynamic normal force ($F_n$) and transverse moment ($M_{to}$), the spray root position ($\xi _r$) and the plate deflection ($\delta$) are collected during plate impacts at 25 experimental conditions for each plate. These conditions comprise a matrix of impact Froude numbers ${Fr} = V_n(gL)^{-0.5}$, plate stiffness ratios $R_D= \rho _w V_n^2 L^3D^{-1}$ and submergence time ratios $R_T= T_sT_{1w}^{-1}$. It is found that $R_D$ is the primary dimensionless ratio controlling the role of flexibility during the impact. At conditions with low $R_D$, maximum plate deflections on the order of $1$ mm occur and the records of the dimensionless form of $F_n$, $M_{to}$, $\xi _r$ and $\delta _c$ are nearly identical when plotted vs $tT_s^{-1}$. In these cases, the impact occurs over time scales substantially greater than the plate's natural period, and a quasi-static response ensues with the maximum deflection occurring approximately midway through the impact. For conditions with higher $R_D$ ($\gtrsim 1.0$), the above-mentioned dimensionless quantities depend strongly on $R_D$. These response features indicate a dynamic plate response and a two-way fluid–structure interaction in which the deformation of the plate causes significant changes in the hydrodynamic force and moment.

This article presents a data-driven model based on modal decomposition, applied to approximate the low-order statistics of the spatially averaged wall-shear stress in a turbulent channel flow over a porous wall with two anisotropic permeabilities, producing drag increase or reduction when compared with the case of an isotropic porous wall. The model is comparable to a neural network architecture using a linear map to a classification. To create this model, we use high-order dynamic mode decomposition (DMD) to identify the structures describing the main flow dynamics, and then test different linear combinations of these modes to estimate the time evolution of the stress at the porous interface. The coefficients of the model are obtained by training the model against the results of direct numerical simulations over different time intervals. Depending on the number and the way of combining the DMD modes, the reduced-order models presented can reconstruct the wall-shear stress with relative error smaller than 0.01 % and reproduce its statistical variations for at least 1500 time units with relative error in the standard deviation or the mean smaller than 5 %. The model has also been tested to approximate the statistics of the wall-shear stress over the whole wall, showing that the regeneration of the flow structures can be reproduced by the nonlinear interaction of modes. Finally, considering the DMD modes as communities in a neural network, we examine the influence of the mode-to-mode interaction on the nonlinear flow dynamics, which explains the performance of the different models.

The instability of the interface between a dielectric and a conducting liquid, excited by a spatially homogeneous interface-normal time-periodic electric field, is studied based on experiments and theory. Special attention is paid to the spatial structure of the excited Faraday waves. The dominant modes of the instability are extracted using high-speed imaging in combination with an algorithm evaluating light refraction at the liquid–liquid interface. The influence of the liquid viscosities on the critical voltage corresponding to the onset of instability and on the dominant wavelength is studied. Overall, good agreement with theoretical predictions that are based on viscous fluids in an infinite domain is demonstrated. Depending on the relative influence of the domain boundary, the patterns exhibit either discrete modes corresponding to surface harmonics or boundary-independent patterns. The agreement between experiments and theory confirms that the electrostatically forced Faraday instability is sufficiently well understood, which may pave the way to control electrostatically driven instabilities. Last but not least, the analogies to classical Faraday instabilities may enable new approaches to study effects that have so far only been observed for mechanical forcing.

Parameterizing mesoscale eddies in ocean circulation models remains an open problem due to the ambiguity with separating the eddies from large-scale flow, so that their interplay is consistent with the resolving skill of the employed non-eddy-resolving model. One way to address the issue is by using recently formulated dynamically filtered eddies. These eddies are obtained as the field errors of fitting some given reference ocean circulation into the employed coarse-grid ocean model. The main strengths are (i) no explicit spatio-temporal filter is needed for separating the large-scale and eddy flow components, (ii) the eddies are dynamically translated into the error-correcting forcing that perfectly augments the coarse-grid model towards reproducing the reference circulation. We uncovered physical properties of the eddies by interpreting involved nonlinear eddy/large-scale interactions via the classical flux-gradient relation. We described the eddies in terms of their full, space–time dependent transport tensor, which was made unique by constraining it to be the same for the potential vorticity, momentum and buoyancy fluxes. Both diffusive and advective parts of the transport tensor were found to be significant. The diffusive tensor component is characterised by polar eigenvalues and is further decomposed into isotropic and filamentation components. The latter component completely dominates, therefore, it should be taken into account by eddy parameterizations, which is not yet the case. We also showed that spatial inhomogeneities of the transport tensor components are important. Comparing these properties with those obtained for more common, locally filtered eddies revealed that they are distinctly different.

We study the stability of steady convection rolls in two-dimensional Rayleigh–Bénard convection with free-slip boundaries and horizontal periodicity over 12 orders of magnitude in the Prandtl number $(10^{-6} \leq Pr \leq 10^6)$ and 6 orders of magnitude in the Rayleigh number $(8{\rm \pi} ^4 < Ra \leq 10^8)$. The analysis is facilitated by partitioning our modal expansion into so-called even and odd modes. With aspect ratio $\varGamma = 2$, we observe that zonal modes (with horizontal wavenumber equal to zero) can emerge only once the steady convection roll state consisting of even modes only becomes unstable to odd perturbations. We determine the stability boundary in the $(Pr,Ra)$ plane and observe remarkably intricate features corresponding to qualitative changes in the solution, as well as three regions where the steady convection rolls lose and subsequently regain stability as the Rayleigh number is increased. We study the asymptotic limit $Pr \to 0$ and find that the steady convection rolls become unstable almost instantaneously, eventually leading to nonlinear relaxation osculations and bursts, which we can explain with a weakly nonlinear analysis. In the complementary large-$Pr$ limit, we observe that the zonal modes at the instability switch off abruptly at a large, but finite, Prandtl number.

One major challenge for a continuum model to describe nanoscale confined fluid flows is the lack of a boundary condition that can capture molecular-scale slip behaviours. In this work, we propose a molecular-kinetic boundary condition to model the fluid–surface and fluid–fluid molecular interactions using the Lennard–Jones type potentials, and add a mean-field force to the momentum equation. This new boundary condition is then applied to investigate the nanoscale Couette and Poiseuille flows using the generalised hydrodynamic model developed by Guo et al. (Phys. Fluids, volume 18, issue 6, 2006a, 067107). The accuracy of our model is validated by molecular dynamics simulations and other models for a broad range of parameters including density, shear rate, wettability and channel width. Our simulation results reveal some unexpected and unintuitive slip behaviours at the nanoscale, including the epitaxial layering structure of fluids and the slip length minimum. The slip length minimum, which is analogous to the Knudsen minimum, can be explained by competing fluid–solid and fluid–fluid molecular interactions as density varies. A new scaling law is proposed for the slip length to account for not only the competing effect between the fluid–solid and fluid–fluid molecular interactions, but also many other physical mechanisms including the competition between the fluid internal potential energy and kinetic energy, and the confinement effect. While the slip length is nearly constant at the low shear rates, it increases rapidly at the high shear rates due to friction reduction. These molecular-scale slip behaviours are caused by energy corrugations at the fluid–solid interface where strong fluid–solid and fluid–fluid molecular interactions interplay.

We investigate the effects of the turbulent dynamic range on active scalar mixing in stably stratified turbulence by adapting the theoretical passive scalar modelling arguments of Beguier, Dekeyser & Launder (1978) (Phys. Fluids, vol. 21 (3), pp. 307–310) and demonstrating their usefulness through consideration of the results of direct numerical simulations of statistically stationary homogeneous stratified and sheared turbulence. By analysis of inertial and inertial–convective subrange scalings, we show that the relationship between the active scalar and turbulence time scales is predicted by the ratio of the Kolmogorov and Obukhov–Corrsin constants, provided mean flow parameters permit the two subrange scalings to be appropriate approximations. We use the resulting relationship between time scales to parameterise an appropriate turbulent mixing coefficient $\varGamma \equiv \chi /\epsilon$, defined here as the ratio of available potential energy ($E_p$) and turbulent kinetic energy ($E_k$) dissipation rates. With the analysis presented here, we show that $\varGamma$ can be estimated by $E_p,E_k$ and a universal constant provided an appropriate Reynolds number is sufficiently high. This large Reynolds number regime appears here to occur at $ {{Re_b}} \equiv \epsilon / \nu N^{2} \gtrapprox 300$ where $\nu$ is the kinematic viscosity and $N$ is the characteristic buoyancy frequency. We propose a model framework for irreversible diapycnal mixing with robust theoretical parametrisation and asymptotic behaviour in this high-$ {{Re_b}}$ limit.

In the present study, a set of physics-informed and data-driven approaches are examined towards the development of an accurate reduced-order model for a turbulent plane Couette flow. Based on the utilisation of the proper orthogonal decomposition (POD), a particular focus is given to the development of a reduced-order model where the number of POD modes are not large enough to cover the full dynamics of the given turbulent state, the situation directly relevant to the reduced-order modelling for turbulent flows. Starting from the conventional Galerkin projection approach ignoring the truncation error, three approaches enhanced by both physics and data are examined: (1) sparse regression of the POD-Galerkin dynamics; (2) Galerkin projection with an empirical eddy-viscosity model; (3) Galerkin projection with an optimal eddy viscosity obtained from a newly proposed sparse regression – an idea applying the sparse identification of nonlinear dynamics framework to an eddy-viscosity model. The sparse regression of the POD-Galerkin dynamics does not perform well, as the number of POD modes for the given chaotic dynamics appears to be too small. While the unsatisfactory performance of the Galerkin projection model with an empirical eddy viscosity is observed, the newly proposed approach, which combines the concept of an optimal eddy-viscosity closure with a sparse regression, more accurately approximates the chaotic dynamics than the other reduced-order models considered. This is demonstrated with the mean and time scales of the POD mode amplitudes as well as the first- and second-order turbulence statistics.

Using fluctuating hydrodynamics we investigate the effect of thermal fluctuations in the dissipation range of homogeneous isotropic turbulence. Simulations confirm theoretical predictions that the energy spectrum is dominated by these fluctuations at length scales comparable to the Kolmogorov length. We also find that the extreme intermittency in the far-dissipation range predicted by Kraichnan is replaced by Gaussian thermal equipartition.

The velocity field of stationary, turbulent, twin round jets has been found to scale with an intrinsic velocity $U_0$ and length $L_0$, both depending linearly on inflow plane parameters – jet velocity $U_j$, diameter $d$ and distance between jets $S$. Flow fields were obtained from large-eddy simulations at these conditions in two experiments: (1) at Reynolds number ${Re}=230\,000$ based on $U_j$ and $d$, and $S/d=5$; and (2) at ${Re} = 25\,000$, $S/d = 2, 4, 8$. Each jet develops independently and then merges into a single jet with an elliptic cross-section. Downstream, the jet becomes circular after a mild overshoot. Close quantitative agreement with experiment was obtained in all cases. As the merged jets develop, fluctuation levels over a central half-width are nearly uniform and scale with the local maximum mean velocity. In all cases, the mean streamwise velocity along the centreline of the configuration, $U_c$, rises to a peak $U_0$ at a distance $L_0$ from the inflow plane. The velocity $U_0$ decreases and $L_0$ increases with $S$. For all nozzle spacings, a similar development was observed: $U_c/U_0$ is a function of distance $x/L_0$ only, and is essentially independent of $S/d$ and ${Re}$. Further, these intrinsic and input quantities are connected by simple relations: $U_0 = U_j/(1.02S/d + 0.44)$ and $L_0/d = 5.58S/d - 1.16$. The far field development of the merged jet can also be scaled with $U_0$ and $S$, analogous to round jet scaling with $U_j$ and $d$. Thus all twin round jets may be described by these new intrinsic scales.

We report on the presence of the boundary zonal flow in rotating Rayleigh–Bénard convection evidenced by two-dimensional particle image velocimetry. Experiments were conducted in a cylindrical cell of aspect ratio $\varGamma =D/H=1$ between its diameter ($D$) and height ($H$). As the working fluid, we used various mixtures of water and glycerol, leading to Prandtl numbers in the range $6.6 \lesssim \textit {Pr} \lesssim 76$. The horizontal velocity components were measured at a horizontal cross-section at half height. The Rayleigh numbers were in the range $10^8 \leq \textit {Ra} \leq 3\times 10^9$. The effect of rotation is quantified by the Ekman number, which was in the range $1.5\times 10^{-5}\leq \textit {Ek} \leq 1.2\times 10^{-3}$ in our experiment. With our results we show the first direct measurements of the boundary zonal flow (BZF) that develops near the sidewall and was discovered recently in numerical simulations as well as in sparse and localized temperature measurements. We analyse the thickness $\delta _0$ of the BZF as well as its maximal velocity as a function of Pr, Ra and Ek, and compare these results with previous results from direct numerical simulations.

We show that in the linear approximation there are three classes of reflectionless wave propagation on a surface of shallow water in the channel with spatially varying depth, width and current speed. Two of these classes have been described in our previous paper (Churilov & Stepanyants, J. Fluid Mech., vol. 931, 2022, A15), and the third one was discovered recently and is described here. The general analysis of the problem shows that, within the approach used in both of our papers, these three classes apparently exhaust all possible cases of exact solutions of the problem considered. We show that the reflectionless flow can be global for certain conditions, i.e. it can exist on the entire $x$-axis. There are also reflectionless flows which exist only on limited intervals of the $x$-axis.

The shock-induced evolution of a gas layer with two fast/slow interfaces is investigated theoretically and experimentally. Specifically, the gas layer is located between a lighter gas and a heavier gas, forming a light/medium/heavy (LMH) configuration. Linear stability analysis is utilised to derive a new analytical model to quantify the Richtmyer–Meshkov instability (RMI) on the two interfaces of such an A/B/C-type fluid layer. Three quasi-one-dimensional (1-D) LMH fluid layers with different initial layer thicknesses are generated to study the wave patterns and interface motions. A general 1-D theory is established to describe the motions of the shock/rarefaction waves reverberating inside the fluid layer and the displacements of the two interfaces. Six quasi-2-D LMH fluid layers with diverse initial layer-thickness and amplitude combinations are created to explore the hydrodynamic instabilities of the two interfaces. It is found that the interface coupling significantly influences the interface evolution, even resulting in an abnormal phase reversal of a shocked fast/slow interface if the two interfaces are anti-phase and the initial layer is very thin. The specific conditions for the abnormal phase reversal and the instability freeze out are deduced. Moreover, the additional RMI (or Rayleigh–Taylor stabilisation) imposed by the shock (or rarefaction waves) reverberating inside an LMH fluid layer on the first (or second) interface is quantified. It is proved that the reverberating waves inside an LMH fluid layer stabilise the two interfaces. Finally, a nonlinear model is obtained by incorporating the nonlinearity effect into the linear model, which well describes the perturbation growths of the two interfaces in a later regime.

In this paper, we develop an asymptotic theory for steadily travelling gravity–capillary waves under the small-surface tension limit. In an accompanying work (Shelton et al., J. Fluid Mech., vol. 922, 2021) it was demonstrated that solutions associated with a perturbation about a leading-order gravity wave (a Stokes wave) contain surface-tension-driven parasitic ripples with an exponentially small amplitude. Thus, a naive Poincaré expansion is insufficient for their description. Here, we develop specialised methodologies in exponential asymptotics for derivation of the parasitic ripples on periodic domains. The ripples are shown to arise in conjunction with Stokes lines and the Stokes phenomenon. The resultant analysis associates the production of parasitic ripples to the complex-valued singularities associated with the crest of a steep Stokes wave. A solvability condition is derived, showing that solutions of this type do not exist at certain values of the Bond number. The asymptotic results are compared with full numerical solutions and show excellent agreement. The work provides corrections and insight of a seminal theory on parasitic capillary waves first proposed by Longuet-Higgins (J. Fluid Mech., vol. 16, issue 1, 1963, pp. 138–159).

The presence of a solid boundary can cause a substantial increase in added mass due to a solid body movement in the fluid. If the body is very close to the boundary, the added mass increases at an even greater rate. The added mass can be of considerable importance in many dams and hydropower, water/ocean, civil and mechanical engineering problems; furthermore, it has an important effect on the dynamics of the vibrating body in the fluid. The principal aim of this paper is to define a novel model to properly evaluate the near-bottom effects of the added mass and to investigate the instantaneous pressure field due to a body movement that changes the thickness of a compressible thin fluid film close to a solid boundary. The body movement can be due to the application of an external force according to Newton's law. This phenomenon is studied theoretically in this paper, and a hydrodynamic model able to compute the instantaneous pressure field in the thin fluid film is drawn out. The fluid film thickness variation, producing compression and decompression waves, tends to reduce the mean body displacement due to external forces, but it generates both high-frequency fluctuations in body force and in body displacements. For the first time, this novel study provides the near-bottom added mass and justifies the strong body accelerations measured in the laboratory experiments that have not been evidenced in the theoretical studies in the known literature.