Frozen water might appear opaque since gas bubbles can get trapped in the ice during the freezing process. They nucleate and then grow near the advancing solidification front, due to the formation of a gas supersaturation region in its vicinity. A delicate interplay between the rate of mass transfer and the rate of freezing dictates the final shapes and sizes of the entrapped gas bubbles. In this work, we experimentally and numerically investigate the initial growth of such gas bubbles that nucleate and grow near the advancing ice front. We show that the initial growth of these bubbles is governed by diffusion and is enhanced due to a combination of the presence of the background gas concentration gradient and the motion of the approaching front. Additionally, we recast the problem into that of mass transfer to a moving spherical object in a homogeneous concentration field, finding good agreement between our experimental data and the existing scaling relations for that latter problem. Lastly, we address how fluid flow around the bubble might further affect this growth and qualitatively explore this through numerical simulations.

The dewetting of thin nanofilms is significantly affected by thermal fluctuations, liquid–solid slip and disjoining pressure, which can be described by lubrication equations augmented by appropriately scaled noise terms, known as stochastic lubrication equations. Here molecular dynamics simulations along with a newly proposed slip-generating method are adopted to study the instability of nanofilms with arbitrary slip. These simulations show that strong-slip dewetting is distinct from weak-slip dewetting by faster growth of perturbations and fewer droplets after dewetting, which cannot be predicted by the existing stochastic lubrication equation. A new stochastic lubrication equation considering the strong-slip boundary condition is thus derived using a long-wave approximation to the equations of fluctuating hydrodynamics. The linear stability analysis of this equation, i.e. surface spectrum, agrees well with molecular simulations. Interestingly, strong slip can break down the usual Stokes limits adopted in weak-slip dewetting and bring the inertia into effect. The evolution of the standard deviation of the film height $W^2(t)={\overline {h^2}-{\bar {h}}^2}$ at the initial stage of the strong-slip dewetting is found to be $W\sim t^{1/4}$ in contrast to $W\sim t^{1/8}$ for the weak-slip dewetting.

We explore the drawing of a shear-thinning or shear-thickening thread with an axisymmetric hole that evolves due to axial drawing, inertia and surface tension effects. The stress is assumed to be proportional to the shear rate raised to the $n$th power. The presence of non-Newtonian rheology and surface tension forces acting on the hole introduces radial pressure gradients that make the derivation of long-wavelength equations significantly more challenging than either a Newtonian thread with a hole or shear-thinning and shear-thickening threads without a hole. In the case of weak surface tension, we determine the steady-state profiles. Our results show that for negligible inertia the hole size at the exit becomes smaller as $n$ is decreased (i.e. strong shear-thinning effects) above a critical draw ratio, but surprisingly the opposite is true below this critical draw ratio. We determine an accurate estimate of the critical draw ratio and also discuss how inertia affects this process. We further show that the dynamics of hole closure is dominated by a different limit, and we determine the asymptotic forms of the hole closure process for shear-thinning and shear-thickening fluids with inertia. A linear instability analysis is conducted to predict the onset of draw resonance. We show that increased shear thinning, surface tension and inlet hole size all act to destabilise the flow. We also show that increasing shear-thinning effects reduce the critical Reynolds number required for unconditional stability. Our study provides valuable insights into the drawing process and its dependence on the physical effects.

The asymmetric instability in two streamwise orthogonal planes for three-dimensional flow-induced vibration (FIV) of an elastically mounted cube at a moderate Reynolds number of 300 is numerically investigated in this paper. The full-order computational fluid dynamics method, data-driven stability analysis via the eigensystem realization algorithm and the selective frequency damping method and total dynamic mode decomposition (TDMD) are applied here to explore this problem. Due to the unsteady non-axisymmetric wakefield formed for flow passing a stationary cube, the FIV response was found to exhibit separate structural stability and oscillations (including lock-in and galloping behaviour) in the two different streamwise orthogonal planes while the body is released. The initial kinetic energy accompanying the release of the cube could destabilize the above-mentioned structural stability. The observed FIV asymmetric instability is verified by the root trajectory of the structural mode obtained via data-driven stability analysis. The stability of the structural modes dominates regardless of whether the structural response oscillates significantly in various (reduced) velocity ranges. Further TDMD analysis on the wake structure, accompanied by the time–frequency spectrum of time-history structural displacements, suggested that the present FIV unit with galloping behaviour is dominated by the combination of the shifted base-flow mode, structure modes and several harmonics of the wake mode.

In this study, we analyse ‘magneto-Stokes’ flow, a fundamental magnetohydrodynamic (MHD) flow that shares the cylindrical-annular geometry of the Taylor–Couette cell but uses applied electromagnetic forces to circulate a free-surface layer of electrolyte at low Reynolds numbers. The first complete, analytical solution for time-dependent magneto-Stokes flow is presented and validated with coupled laboratory and numerical experiments. Three regimes are distinguished (shallow-layer, transitional and deep-layer flow regimes), and their influence on the efficiency of microscale mixing is clarified. The solution in the shallow-layer limit belongs to a newly identified class of MHD potential flows, and thus induces mixing without the aid of axial vorticity. We show that these shallow-layer magneto-Stokes flows can still augment mixing in distinct Taylor dispersion and advection-dominated mixing regimes. The existence of enhanced mixing across all three distinguished flow regimes is predicted by asymptotic scaling laws and supported by three-dimensional numerical simulations. Mixing enhancement is initiated with the least electromagnetic forcing in channels with order-unity depth-to-gap-width ratios. If the strength of the electromagnetic forcing is not a constraint, then shallow-layer flows can still yield the shortest mixing times in the advection-dominated limit. Our robust description of momentum evolution and mixing of passive tracers makes the annular magneto-Stokes system fit for use as an MHD reference flow.

Lozano-Duran et al. (J. Fluid Mech., vol. 914, 2021, p. A8) have recently identified the ability of streamwise-averaged turbulent streak fields ${\mathcal {U}}(y,z,t)\hat {\boldsymbol {x}}$ in minimal channels to produce short-term transient growth as the key linear mechanism needed to sustain turbulence at $Re_{\tau }=180$. Here, in an attempt to extend this result to larger domains and higher $Re_{\tau }$, we model this streak transient growth as a two-stage linear process by first selecting the dominant streak structure expected to emerge over the eddy turnover time on the turbulent mean profile $U(y)\hat {\boldsymbol {x}}$, and then examining the secondary growth on this (frozen) streak field ${\mathcal {U}}(y,z)\hat {\boldsymbol {x}}$. Choosing the mean streak amplitude and eddy turnover time consistent with simulations captures the growth thresholds found by Lozano-Duran et al. (2021) for sustained turbulence. In a larger domain at $Re_{\tau }=180$, the most energetic near-wall streaks observed in simulations are close to the predicted optimal streaks. This most energetic streak spacing, approaches the optimal streak at $Re_{\tau }=550$ where the secondary growth possible on each also comes together. A key prediction from the model is that the threshold transient growth required to sustain turbulence decreases with increasing $Re_{\tau }$. More fundamentally, the work of Lozano-Duran et al. (2021) and our results suggest a subtle but significant revision of Malkus's (J. Fluid Mech., vol. 1, 1956, pp. 521–539) classic hypothesis concerning realisable turbulent mean profiles. The key property for a realisable turbulent mean profile could be the ability to generate sufficient short-term transient growth rather than dependence on its (long-term) linear stability characteristics, which was Malkus's original idea.

The recent work of Siegelman & Young (Proc. Natl Acad. Sci. USA, vol. 120, issue 44, 2023, e2308018120) revealed two extreme states reached by the evolution of unforced and weakly damped two-dimensional turbulence above random rough topography, separated by a critical kinetic energy $E_\#$. The low- and high-energy solutions correspond to topographically locked and roaming vortices, surrounded by non-uniform and homogeneous background potential vorticity (PV), respectively. However, we found that these phenomena are restricted to the particular intermediate length scale where the energy was initially injected into the system. Through simulations initialized by injecting the energy at larger and smaller length scales, we found that the long-term state of topographic turbulence is also dependent on the initial length scale and thus the initial enstrophy. If the initial length scale is comparable to the domain size, the long-term flow field resembles the minimum-enstrophy state proposed by Bretherton & Haidvogel (J. Fluid Mech., vol. 78, issue 1, 1976, pp. 129–154), with very few topographically locked vortices; the long-term enstrophy is quite close to the minimum value, especially when the energy is no larger than $E_\#$. As the initial length scale becomes smaller, more vortices nucleate and become more mobile; the long-term enstrophy increasingly deviates from the minimum value. Simultaneously, the background PV tends to homogenization, even if the energy is below $E_\#$. These results complement the phenomenology of topographic turbulence documented by Siegelman & Young, by showing that the minimum-enstrophy and background PV homogenization states can be adequately approached by large- and small-scale initial fields, respectively, with relatively arbitrary energy.

We propose a data-driven methodology to learn a low-dimensional manifold of controlled flows. The starting point is resolving snapshot flow data for a representative ensemble of actuations. Key enablers for the actuation manifold are isometric mapping as encoder, and a combination of a neural network and a $k$-nearest-neighbour interpolation as decoder. This methodology is tested for the fluidic pinball, a cluster of three parallel cylinders perpendicular to the oncoming uniform flow. The centres of these cylinders are the vertices of an equilateral triangle pointing upstream. The flow is manipulated by constant rotation of the cylinders, i.e. described by three actuation parameters. The Reynolds number based on a cylinder diameter is chosen to be $30$. The unforced flow yields statistically symmetric periodic shedding represented by a one-dimensional limit cycle. The proposed methodology yields a five-dimensional manifold describing a wide range of dynamics with small representation error. Interestingly, the manifold coordinates automatically unveil physically meaningful parameters. Two of them describe the downstream periodic vortex shedding. The other three describe the near-field actuation, i.e. the strength of boat-tailing, the Magnus effect and forward stagnation point. The manifold is shown to be a key enabler for control-oriented flow estimation.

Elastoinertial turbulence (EIT) is a chaotic flow resulting from the interplay between inertia and viscoelasticity in wall-bounded shear flows. Understanding EIT is important because it is thought to set a limit on the effectiveness of turbulent drag reduction in polymer solutions. Here, we analyse simulations of two-dimensional EIT in channel flow using spectral proper orthogonal decomposition (SPOD), discovering a family of travelling wave structures that capture the sheetlike stress fluctuations that characterise EIT. The frequency-dependence of the leading SPOD mode contains distinct peaks and the mode structures corresponding to these peaks exhibit well-defined travelling structures. The structure of the dominant travelling mode exhibits shift–reflect symmetry similar to the viscoelasticity-modified Tollmien–Schlichting (TS) wave, where the velocity fluctuation in the travelling mode is characterised by large-scale regular structures spanning the channel and the polymer stress field is characterised by thin, inclined sheets of high polymer stress localised at the critical layers near the channel walls. The travelling structures corresponding to the higher-frequency modes have a very similar structure, but are nested in a region roughly bounded by the critical layer positions of the next-lower-frequency mode. A simple theory based on the idea that the critical layers of mode $\kappa$ form the ‘walls’ for the structure of mode $\kappa +1$ yields quantitative agreement with the observed wave speeds and critical layer positions, indicating self-similarity between the structures. The physical idea behind this theory is that the sheetlike localised stress fluctuations in the critical layer prevent velocity fluctuations from penetrating them.

The flow of a nematic liquid crystal in a Hele-Shaw cell with an electrically controlled viscous obstruction is investigated using both a theoretical model and physical experiments. The viscous obstruction is created by temporarily electrically altering the viscosity of the nematic in a region of the cell across which an electric field is applied. The theoretical model is validated experimentally for a circular cylindrical obstruction, demonstrating user-controlled flow manipulation of an anisotropic liquid within a heterogeneous single-phase microfluidic device.

This study uses high-fidelity simulations (direct numerical simulation or large-eddy simulation) and experimental datasets to analyse the effect of non-equilibrium streamwise mean pressure gradients (adverse or favourable), including attached and separated flows, on the statistics of boundary-layer wall-pressure fluctuations. The datasets collected span a wide range of Reynolds numbers ($Re_\theta$ from 300 to 23 400) and pressure gradients (Clauser parameter from $-0.5$ to 200). The datasets are used to identify an optimal set of variables to scale the wall-pressure spectrum: edge velocity, boundary layer thickness and the peak magnitude of Reynolds shear stress. Using the present datasets, existing semi-empirical models of the wall-pressure spectrum are shown unable to capture effects of strong, non-equilibrium adverse pressure gradients, due to inappropriate scaling of the wall pressure using the wall shear stress, calibration with limited types of flows and dependency on model parameters based on the friction velocity, which reduces to zero at the detachment point. To address these shortcomings, a generalized wall-pressure spectral model is developed with parameters that characterize the extent of the logarithmic layer and the strength of the wake. Derived from the local mean streamwise velocity profile, these two parameters inherently carry the effect of the Reynolds number, as well as those of the non-equilibrium pressure gradient and its history. Comparison with existing models shows that the proposed model behaves well and is more accurate in strong-pressure-gradient flows and in separated-flow regions.

Drop collision with a solid particle is a ubiquitous phenomenon in a wide range of applications, including rain, spray coating, cooling or cleaning, particle encapsulation, inkjet printing, and additive manufacturing. Understanding the dynamics of drop collision is essential for optimizing these processes. In this study, we present a comprehensive experimental and analytical investigation of non-axisymmetric as well as axisymmetric drop impact on a solid particle. We use a high-speed video system to visualize the drop profile during the impact, and measure the drop height and spreading diameter for different liquid viscosities, ratios of the target to drop diameters, offsets, and various other impact parameters. We then develop a theoretical model for drop spreading on a solid spherical particle that relies on the formulation of a remote asymptotic solution for the inviscid flows, generated by non-axisymmetric drop impact. Next, the viscous effects in a thin viscous boundary layer are considered, which allows the formulation of an expression for the residual lamella thickness and maximum spreading. The theoretically predicted evolution of the lamella thickness, the residual film thickness, and the maximum spreading angle agree well with the experimental data presented in this work and the literature. Finally, we present a novel approach for in situ measurement of liquid viscosity, drop impact viscometry, at high shear rates via a single drop impact experiment, with potential application in industries where non-Newtonian drops play a major role, such as pesticide spraying, paint droplet spreading, blood drop impact and fuel injectors.

Dynamic stall at low Reynolds numbers, $Re \sim O(10^4)$, exhibits complex flow physics with co-existing laminar, transitional and turbulent flow regions. Current state-of-the-art stall onset criteria use parameters that rely on flow properties integrated around the leading edge. These include the leading edge suction parameter or $LESP$ (Ramesh et al., J. Fluid Mech., vol. 751, 2014, pp. 500–538) and boundary enstrophy flux or $BEF$ (Sudharsan et al., J. Fluid Mech., vol. 935, 2022, A10), which have been found to be effective for predicting stall onset at moderate to high $Re$. However, low-$Re$ flows feature strong vortex-shedding events occurring across the entire airfoil surface, including regions away from the leading edge, altering the flow field and influencing the onset of stall. In the present work, the ability of these stall criteria to effectively capture and localize these vortex shedding events in space and time is investigated. High-resolution large-eddy simulations for an SD7003 airfoil undergoing a constant-rate, pitch-up motion at two $Re$ (10 000 and 60 000) and two pitch rates reveal a rich variety of unsteady flow phenomena, including instabilities, transition, vortex formation, merging and shedding, which are described in detail. While stall onset is reflected in both $LESP$ and $BEF$, local vortex-shedding events are identified only by the $BEF$. Therefore, $BEF$ can be used to identify both dynamic stall onset and local vortex-shedding events in space and time.

Three-dimensional non-rotating odd viscous liquids give rise to Taylor columns and support axisymmetric inertial-like waves (J. Fluid Mech., vol. 973, 2023, A30). When an odd viscous liquid is subjected to rigid-body rotation however, there arise in addition a plethora of other phenomena that need to be clarified. In this paper, we show that three-dimensional incompressible or two-dimensional compressible odd viscous liquids, rotating rigidly with angular velocity $\varOmega$, give rise to both oscillatory and evanescent inertial-like waves or a combination thereof (which we call of mixed type) that can be non-axisymmetric. By evanescent, we mean that along the radial direction, typically when moving away from a solid boundary, the velocity field decreases exponentially. These waves precess in a prograde or retrograde manner with respect to the rotating frame. The oscillatory and evanescent waves resemble respectively the body and wall-modes observed in (non-odd) rotating Rayleigh–Bénard convection (J. Fluid Mech., vol. 248, 1993, pp. 583–604). We show that the three types of waves (wall, body or mixed) can be classified with respect to pairs of planar wavenumbers $\kappa$ which are complex, real or a combination, respectively. Experimentally, by observing the precession rate of the patterns, it would be possible to determine the largely unknown values of the odd viscosity coefficients. This formulation recovers as special cases recent studies of equatorial or topological waves in two-dimensional odd viscous liquids which provided examples of the bulk–interface correspondence at frequencies $\omega <2\varOmega$. We finally point out that the two- and three-dimensional problems are formally equivalent. Their difference then lies in the way data propagate along characteristic rays in three dimensions, which we demonstrate by classifying the resulting Poincaré–Cartan equations.

Two-dimensional turbulence transfers its energy towards the lowest mode in the domain, but domain geometry exerts a powerful control. On the sphere, with its three axes of rotational symmetry, angular momentum conservation prevents energy from entering the three lowest modes – those corresponding to the spherical harmonics $Y_1^0$ and $Y_1^{\pm 1}$ – because the amplitudes of these three modes are proportional to the three conserved components of the angular momentum vector. Non-spherical ellipsoids partly or completely break the rotational symmetry corresponding to angular momentum conservation. The flow on spheroids, which have only one axis of rotational symmetry, conserves only a single component of angular momentum. If the axis of symmetry is taken to be the $z$-axis, then only the $z$-component of angular momentum is conserved. Energy can flow into the other two lowest modes. The general triaxial ellipsoid breaks all rotational symmetries, thus angular momentum is not conserved, and energy can flow into any mode. We describe numerical experiments that confirm these predictions.

In this work we investigate the spatio-temporal nature of various coherent modes present in a wind turbine wake using a combination of new particle image velocimetry experiments and data from Biswas & Buxton (J. Fluid Mech., vol. 979, 2024, A34). A multiscale triple decomposition of the acquired velocity field is sought to extract the coherent modes and, thereafter, the energy exchanges to and from them are studied using the multiscale triple decomposed coherent kinetic energy budgets developed by Baj & Buxton (Phys. Rev. Fluids, vol. 2, 2017, 114607). Different frequencies forming the tip vortex system (such as the blade passing frequency, turbine's rotational frequency and their harmonics) are found to be energised by different sources such as production from the mean flow or nonlinear triadic interaction or both, similar to the primary, secondary or the mixed modes discussed in Biswas et al. (J. Fluid Mech., vol. 941, 2022, A36). The tip vortex system forms a complex network of nonlinear triadic energy transfers, the nature and the magnitudes of which depend on the tip speed ratio ($\lambda$). Contrastingly, the modes associated with the sheddings from the nacelle or tower and wake meandering are found to be primarily energised by the mean flow. We show that the tip vortex system exchanges energy with the mean flow primarily through the turbine's rotational frequency. In fact, the system transfers energy back to the mean flow through the turbine's rotational frequency at some distance downstream marking the onset location of wake recovery ($x_{wr}$). Here $x_{wr}$ is shown to reduce with $\lambda$ due to stronger interaction and earlier merging of the tip vortices at a higher $\lambda$.

The present experimental study shows that a nozzle with optimal flexibility can enhance the impulse and entrainment of a pulsed jet. Near the nozzle exit, vortex rings emanating from the flexible nozzle move faster because of the timely release of the elastic energy (stored during the expansion) to the jet, which is maximized at the structural stiffness that needs to be optimally tuned to the jet acceleration. The total circulation, hydrodynamic impulse and entrained fluid volume are enhanced substantially. Interestingly, we find that the same condition for optimal flexibility to maximize the hydrodynamic impulse and circulation of the primary vortex ring of the continuous jet (Choi & Park, J. Fluid Mech., vol. 949, 2022, A39) holds universally for the pulsed jet, indicating that abrupt jet termination is irrelevant to the impulse augmentation mechanism. Compared to the rigid counterpart, increments of the impulse (${\sim }400\,\%$) and entrainment (${\sim }220\,\%$) of a pulsed jet in the present study are considerably larger than those ($200\,\%$ and $50\,\%$, respectively) in a continuous jet from previous studies, which is attributed to the significant suppression of negative pressure at the nozzle exit by the collapsing motion of the flexible nozzle in the phase with the jet-driven upstream propagation of the surface wave on the nozzle. This universal mechanism provides a guideline for a novel jet propulsor using a flexible nozzle, for example, for small-scale underwater robots.

The effectiveness of utilizing heating patterns as a drag-reduction tool in sloping channels is analysed. The usefulness of heating is judged by determining the pressure gradient required to maintain the same flow rate as in the isothermal case. The key to reducing pressure loss is the formation of separation bubbles, although these bubbles are washed away at relatively large Reynolds numbers. The bubbles reduce the direct contact between the stream and the side walls, thereby reducing the friction experienced by the flow. Moreover, the fluid inside the bubbles tends to rotate, a motion provoked by longitudinal temperature gradients. This rotation also seems to reduce the resistance. On the other hand, the existence of the bubbles tends to obstruct the stream, increasing the flow resistance. In general, channels oriented close to horizontal experience a relatively small pressure loss, but this loss grows markedly as the channel inclines towards the vertical. When modest heating is applied, the pressure loss is approximately proportional to the square of the associated Rayleigh number. It is also shown that if the heating wavelength is too short or too long, the heating loses its effectiveness. In certain circumstances, it turns out that the theoretical pressure-gradient reduction achieved by judicious heating is so large that it exceeds the pressure gradient required to drive the flow in the isothermal problem. The conclusion is that in these instances, a pressure gradient of the opposite sign must be applied to prevent flow acceleration.

Predicting the magnitude of the slip velocity of non-tracer particles with respect to the surrounding fluid is crucial to address both fundamental and practical questions involving dispersed turbulent flows. Here we derive an analytical model to predict the slip velocity of spherical particles in homogeneous isotropic turbulence. We modulate the particle equation of motion according to the inertial filtering framework, and obtain closed-form expressions for the mean slip velocity magnitude as a function of the governing parameters. These are compared against laboratory measurements and direct numerical simulations, demonstrating close agreement for both light and heavy particles, both smaller and larger than the Kolmogorov scales. The predictive value of the model and its implications are discussed, as well as the range of validity of the underlying assumptions.

Direct numerical simulation of the three-dimensional (3-D) wake transition of a heated square cylinder subjected to horizontal cross-flow is performed in the presence of buoyancy. In order to capture the effects of large-scale heating, a non-Oberbeck–Boussinesq model is utilized, which includes the governing equations for compressible gas flow. All computations are performed at low free stream Mach number $M=0.1$ using air (free stream Prandtl number, $Pr=0.71$) as the working fluid. The 3-D instability modes A and B, which correspond to free stream Reynolds numbers of 180 and 250, are observed with longer and shorter spanwise wavelengths, respectively, and the onset of three-dimensionality is triggered at a Reynolds number of 173. In the presence of buoyancy, baroclinic vorticity production in the near-wake plays an important role for streamwise vorticity generation. The chaotic wake of the Mode-A instability bifurcates into periodic and quasiperiodic wakes at various heating levels, expressed by the overheat ratio, $\varepsilon =(T_w-T_\infty )/T_\infty$, where $T_w$ and $T_\infty$ are the temperature of the cylinder surface and the ambient air, respectively. At low heating ($\varepsilon =0.2$), the 3-D Mode-A instability is suppressed leading to a two-dimensional wake flow. Further increase in heating, again brings back the three-dimensionality in the wake through Mode-E instability. The variation of thermophysical properties and the effective Reynolds number with increase in heating level around the cylinder is examined. It is shown that the effect of thermophysical properties competes with the baroclinic streamwise vorticity generation at higher levels of heating ($\varepsilon \geqslant 0.4$) to control the 3-D modes and wake dynamics.