Transient, steady and oscillatory flows in a $180^{\circ }$ curved pipe are investigated both numerically and experimentally to understand secondary flow vortex formation and interactions. The results of numerical simulations and particle image velocimetry experiments are highly correlated, with a low error. To enable simulations in a smaller domain with shorter inlet section, an analytical solution for the unsteady Navier–Stokes equation is obtained with non-zero initial conditions to provide physical velocity profiles for the simulations. The vorticity transport equation is studied and its terms are balanced to find the mechanism of vorticity transfer to structures in the curved pipe. Several vortices are identified via various vortex identification (ID) methods and their results are compared. Isosurfaces of the $\unicode[STIX]{x1D706}_{2}$ vortex ID are used to explain the temporal and spatial evolution of vortices in the curved pipe. Eigenvalues and eigenvectors of the velocity gradient tensor are calculated for the swirling strength vortex ID method, which also determines vortex axis orientation. The classical Lyne vortex in oscillatory flow with an inviscid core is also revisited and its results are compared with the transient and steady flows. These in-depth analyses provide a better understanding and characterization of vortical structures in the curved pipe flow. Our findings show that, although there are some visual similarities between cross-sectional views of steady/transient flows and oscillatory flows, the structure herein designated as Lyne-type vortex detected in the cross-sections (under steady, transient and pulsatile flows) is not the same as the classical Lyne vortex pair (in oscillatory flows).

Accurate real-time simulations and forecasting of phase-revolved ocean surface waves require nonlinear effects, both geometrical and kinematic, to be accurately represented. For this purpose, wave models based on a Lagrangian steepness expansion have proved particularly efficient, as compared to those based on Eulerian expansions, as they feature higher-order nonlinearities at a reduced numerical cost. However, while they can accurately model the instantaneous nonlinear wave shape, Lagrangian models developed to date cannot accurately predict the time evolution of even simple periodic waves. Here, we propose a novel and simple method to perform a Lagrangian expansion of surface waves to second order in wave steepness, based on the dynamical system relating particle locations and the Eulerian velocity field. We show that a simple redefinition of reference particles allows us to correct the time evolution of surface waves, through a modified nonlinear dispersion relationship. The resulting expressions of free surface particle locations can then be made numerically efficient by only retaining the most significant contributions to second-order terms, i.e. Stokes drift and mean vertical level. This results in a hybrid model, referred to as the ‘improved choppy wave model’ (ICWM) (with respect to Nouguier et al.’s J. Geophys. Res., vol. 114, 2009, p. C09012), whose performance is numerically assessed for long-crested waves, both periodic and irregular. To do so, ICWM results are compared to those of models based on a high-order spectral method and classical second-order Lagrangian expansions. For irregular waves, two generic types of narrow- and broad-banded wave spectra are considered, for which ICWM is shown to significantly improve wave forecast accuracy as compared to other Lagrangian models; hence, ICWM is well suited to providing accurate and efficient short-term ocean wave forecast (e.g. over a few peak periods). This aspect will be the object of future work.

Stable electrospraying in the cone-jet mode is restricted to flow rates above a minimum, and understanding the physics of this constraint is important to improve this atomization technique. We study this problem by measuring the minimum flow rate of electrosprays of tributyl phosphate and propylene carbonate at varying electrical conductivity $K$ (all other physical properties such as the density $\unicode[STIX]{x1D70C}$, surface tension $\unicode[STIX]{x1D6FE}$ and viscosity $\unicode[STIX]{x1D707}$ are kept constant and equal to those of the pure liquids), and through the analysis of numerical solutions. The experiments show that the dimensionless minimum flow rate is a function of both the dielectric constant $\unicode[STIX]{x1D700}$ of the liquid and its Reynolds number, $Re=(\unicode[STIX]{x1D70C}\unicode[STIX]{x1D700}_{o}\unicode[STIX]{x1D6FE}^{2}/\unicode[STIX]{x1D707}^{3}K)^{1/3}$. This result is unexpected in the light of existing theories which, for the conditions investigated, predict a minimum flow rate that depends only on $\unicode[STIX]{x1D700}$ and/or is marginally affected by $Re$. The experimental dependency on the Reynolds number requires the viscous stress to be a factor in the determination of the minimum flow rate. However, the numerical solutions suggest that a balance of opposing forces including the fixing viscous stress, which at decreasing flow rates may lower the acceleration of the flow to the point of making it unstable, is unlikely to be the cause. An alternative mechanism is the significant viscous dissipation taking place in the transition from cone to jet, and which at low flow rates cannot be supplied by the work done by the tangential electric stress in the same area. Instead, mechanical energy injected into the system farther downstream must be transferred upstream where dissipation predominantly takes place. This mechanism is supported by the balance between the energy dissipated and the work done by the electric stress in the transition from cone to jet, which yields a relationship between the minimum flow rate, the Reynolds number and the dielectric constant that compares well with experiments.

We use linear proportional control for the suppression of the Marangoni instability in a thin film heated from below. Our keen interest is focused on the recently revealed oscillatory mode caused by a coupling of two long-wave monotonic instabilities, the Pearson and deformational ones. Shklyaev et al. (Phys. Rev. E, vol. 85, 2012, 016328) showed that the oscillatory mode is critical in the case of a substrate of very low conductivity. To stabilize the no-motion state of the film, we apply two linear feedback control strategies based on the heat flux variation at the substrate. Strategy (I) uses the interfacial deflection from the mean position as the criterion of instability onset. Within strategy (II) the variable that describes the instability is the deviation of the measured temperatures from the desired, conductive values. We perform two types of calculations. The first one is the linear stability analysis of the nonlinear amplitude equations that are derived within the lubrication approximation. The second one is the linear stability analysis that is carried out within the Bénard–Marangoni problem for arbitrary wavelengths. Comparison of different control strategies reveals feedback control by the deviation of the free surface temperature as the most effective way to suppress the Marangoni instability.

Dense granular flows can spontaneously self-channelise by forming a pair of parallel-sided static levees on either side of a central flowing channel. This process prevents lateral spreading and maintains the flow thickness, and hence mobility, enabling the grains to run out considerably further than a spreading flow on shallow slopes. Since levees commonly form in hazardous geophysical mass flows, such as snow avalanches, debris flows, lahars and pyroclastic flows, this has important implications for risk management in mountainous and volcanic regions. In this paper an avalanche model that incorporates frictional hysteresis, as well as depth-averaged viscous terms derived from the $\unicode[STIX]{x1D707}(I)$-rheology, is used to quantitatively model self-channelisation and levee formation. The viscous terms are crucial for determining a smoothly varying steady-state velocity profile across the flowing channel, which has the important property that it does not exert any shear stresses at the levee–channel interfaces. For a fixed mass flux, the resulting boundary value problem for the velocity profile also uniquely determines the width and height of the channel, and the predictions are in very good agreement with existing experimental data for both spherical and angular particles. It is also shown that in the absence of viscous (second-order gradient) terms, the problem degenerates, to produce plug flow in the channel with two frictionless contact discontinuities at the levee–channel margins. Such solutions are not observed in experiments. Moreover, the steady-state inviscid problem lacks a thickness or width selection mechanism and consequently there is no unique solution. The viscous theory is therefore a significant step forward. Fully time-dependent numerical simulations to the viscous model are able to quantitatively capture the process in which the flow self-channelises and show how the levees are initially emplaced behind the flow head. Both experiments and numerical simulations show that the height and width of the channel are not necessarily fixed by these initial values, but respond to changes in the supplied mass flux, allowing narrowing and widening of the channel long after the initial front has passed by. In addition, below a critical mass flux the steady-state solutions become unstable and time-dependent numerical simulations are able to capture the transition to periodic erosion–deposition waves observed in experiments.

Normal and oblique drop impact on a solid surface is numerically analysed for yield stress fluids. A rich diversity of results are generated as a consequence of the exploration of the inertial, elastic, plastic and thixotropic features of the process, as well as the inclination of the solid surface. We show that drops of more thixotropic fluids have a higher tendency to bounce in the normal impact, and to roll or to bounce in the case of an oblique drop impact. Concerning elasticity, we found a critical value for the elastic Ohnesorge number above which no bouncing takes place. Experimental findings such as the fact that the stored energy due to the elasticity of the fluid drop plays a role similar to the stored energy of an interfacial nature in inelastic fluid drops are corroborated in the present study.

Line fountains form when heavy miscible fluid is ejected steadily upwards as a jet from a high-aspect-ratio rectangular slot, of length $L$ and half-width $b_{0}$, into lighter quiescent surroundings. Viewed along the slot from one end, previous observations reveal that the ejected fluid mixes with the environment and reaches a peak height before partially collapsing back downward under gravity to form a fountain whose top thereafter fluctuates vertically about a mean height. While the motion as perceived from this single view has provided insights that have successfully guided theoretical predictions for the initial rise height, until now a wider understanding of line fountains, and corresponding predictive capability, has been limited to this single prediction due to a lack of any other observational data. Indeed, the general behaviour of line fountains, including the structure internally and along the spanwise length $L$ of the slot, has not been reported previously. To address this, flow visualisations and comprehensive measurements of saline fountains in an aqueous environment are presented here that reveal their complex overall structure and behaviours. After establishing the uniformity of the source conditions from slots of aspect ratio $600:1$ and $300:1$, we first show that double-averaged (spanwise and time) rise heights $\overline{\overline{z}}_{v}/b_{0}$ scale on $Fr_{0}^{4/3}$, $Fr_{0}$ being the source Froude number, with vertical fluctuations being circa 20 % of these heights. Then, simultaneously interrogating the flow as viewed from above and from the side onto the spanwise dimension, we identify three distinct patterns of behaviour. Instrumental to distinguishing these behaviours were the contrasting signatures we observed in the time series of rise height departures from the mean which led us to the following classification: (i) non-uniform flapping for $0.05\lesssim \overline{\overline{z}}_{v}/L\lesssim 0.30$, in which the lateral motion of the fountain takes the form of an oscillatory wave with a wavelength of $2L/3$ (approx.); (ii) uniform flapping for $0.30\lesssim \overline{\overline{z}}_{v}/L\lesssim 0.45$, in which the entire fountain sways to the left and then to the right side of the slot; and (iii) disorganised flapping for $\overline{\overline{z}}_{v}/L\gtrsim 0.45$. Regarding the internal structure, we show that unlike a classic round fountain, eddying structures comparable in scale with the rise height form towards the top of the fountain, and the counterflow forms predominantly to one side of the jet. We then identify the single dominant mechanism driving the flapping motions, successfully linking the wave-like behaviour observed along the span to the internal structure and vertical oscillations. Quantifying the oscillatory motions, both the vertical and flapping frequencies scale as $Fr_{0}^{-2}$, and we demonstrate and explain a robust coupling between these frequencies that follows a ratio of 2:1.

The contributions of vortex stretching, dilatation, baroclinic torque and viscous diffusion to Reynolds-averaged enstrophy transport in turbulent swirl flames were experimentally measured using tomographic particle image velocimetry and $\text{CH}_{2}\text{O}$ planar laser induced fluorescence at jet Reynolds numbers of 26 000–51 000. The mean baroclinic torque was determined by subtracting the other terms in the enstrophy transport equation from the mean Lagrangian derivative. Enstrophy production from baroclinic torque was found to be significant relative to the other transport terms across all conditions studies. This result contrasts with direct numerical simulations of flames in homogeneous isotropic turbulence, which show a decreasing relative significance of baroclinic torque with increasing turbulence intensity (e.g. Bobbitt, Lapointe & Blanquart, Phys. Fluids, vol. 28 (1), 2016, 015101). Hence, the significance of baroclinic enstrophy production in flames is not determined entirely by the local turbulence and flame properties, but also depends on the configuration-specific pressure field.

In this paper, we experimentally study the influence of large-scale Taylor rolls on the small-scale statistics and the flow organization in fully turbulent Taylor–Couette flow for Reynolds numbers up to $Re_{S}=3\times 10^{5}$. The velocity field in the gap confined by coaxial and independently rotating cylinders at a radius ratio of $\unicode[STIX]{x1D702}=0.714$ is measured using planar particle image velocimetry in horizontal planes at different cylinder heights. Flow regions with and without prominent Taylor vortices are compared. We show that the local angular momentum transport (expressed in terms of a Nusselt number) mainly takes place in the regions of the vortex in- and outflow, where the radial and azimuthal velocity components are highly correlated. The efficient momentum transfer is reflected in intermittent bursts, which becomes visible in the exponential tails of the probability density functions of the local Nusselt number. In addition, by calculating azimuthal energy co-spectra, small-scale plumes are revealed to be the underlying structure of these bursts. These flow features are very similar to the one observed in Rayleigh–Bénard convection, which emphasizes the analogies of these systems. By performing a complex proper orthogonal decomposition, we remarkably detect azimuthally travelling waves superimposed on the turbulent Taylor vortices, not only in the classical but also in the ultimate regime. This very large-scale flow pattern, which is most pronounced at the axial location of the vortex centre, is similar to the well-known wavy Taylor vortex flow, which has comparable wave speeds, but much larger azimuthal wavenumbers.

The linear stability of high-Reynolds-number corrugated jets is investigated by solving the compressible Rayleigh equation linearized about the time-averaged flow field. A Floquet ansatz is used to account for periodicity of this base flow in the azimuthal direction. The origin of multiple unstable solutions, which are known to appear in these non-circular configurations, is traced through gradual perturbations of a parametrized base-flow profile. It is shown that all unstable modes are corrugated jet continuations of the classical Kelvin–Helmholtz modes of circular jets, highlighting that the same instability mechanism, modified by corrugations, leads to the growth of disturbances in such flows. It is found that under certain conditions the eigenvalues may form saddles in the complex plane and display axis switching in their eigenfunctions. A parametric study is also conducted to understand how penetration and number of corrugations impact stability. The effect of these geometric properties on growth rates and phase speeds of the multiple unstable modes is explored, and the results provide guidelines for the development of nozzle configurations that more effectively modify the Kelvin–Helmholtz instability.

We examine the statistical properties of extreme and rogue wave activity in crossing directional seas, to constrain the probabilistic distributions of wave heights and wave crests in complex sea states; such crossing seas alter the statistical structure of surface waves and are known to have been involved in several marine accidents. Further, we examine the relationship between the kurtosis as an indicator of nonlinearity in the spectrum and the directionality and crossing angles of the sea-state components. Experimental tests of two-component directionally spread irregular waves with varying frequency, directional spreading and component crossing angles were carried out at the Ocean Basin Laboratory in Trondheim, Norway. The results from the experiments show that wave heights are well described by a first-order (linear) statistical distribution, while for the wave crest heights several cases exceed a second-order distribution. The number of rogue waves is relatively low overall, which agrees with previous findings in directionally spread seas. The kurtosis and wave and crest height exceedance probabilities were more affected by varying the directional spreading of the components than by varying the crossing angles between components; reducing the component directional spreading increases the kurtosis and increases the exceedance probabilities. The kurtosis can be estimated quite well for two-component seas from the directional spreading using an empirical relationship based on the two-dimensional Benjamin–Feir index when the effects of bound modes are included. This result may allow forecasting of the probability of extreme waves from the directional spreading in complex sea states.

We study the joint mixing of colloids and salt released together in a stagnation point or in a globally chaotic flow. In the presence of salt inhomogeneities, the mixing time is strongly modified depending on the sign of the diffusiophoretic coefficient $D_{dp}$. Mixing is delayed when $D_{dp}>0$ (salt-attracting configuration), or faster when $D_{dp}<0$ (salt-repelling configuration). In both configurations, as for molecular diffusion alone, large scales are barely affected in the dilating direction while the Batchelor scale for the colloids, $\ell _{c,diff}$, is strongly modified by diffusiophoresis. We propose here to measure a global effect of diffusiophoresis in the mixing process through an effective Péclet number built on this modified Batchelor scale. Whilst this small scale is obtained analytically for the stagnation point, in the case of chaotic advection, we derive it using the equation of gradients of concentration, following Raynal & Gence (Intl J. Heat Mass Transfer, vol. 40 (14), 1997, pp. 3267–3273). Comparing to numerical simulations, we show that the mixing time can be predicted by using the same function as in absence of salt, but as a function of the effective Péclet numbers computed for each configuration. The approach is shown to be valid when the ratio $D_{dp}^{2}/D_{s}D_{c}\gg 1$, where $D_{c}$ and $D_{s}$ are the diffusivities of the colloids and salt.

This paper aims to numerically verify the large Reynolds number asymptotic theory of magneto-hydrodynamic (MHD) flows proposed in the companion paper Deguchi (J. Fluid Mech., vol. 868, 2019, pp. 176–211). To avoid any complexity associated with the chaotic nature of turbulence and flow geometry, nonlinear steady solutions of the viscous resistive MHD equations in plane Couette flow have been utilised. Two classes of nonlinear MHD states, which convert kinematic energy to magnetic energy effectively, have been determined. The first class of nonlinear states can be obtained when a small spanwise uniform magnetic field is applied to the known hydrodynamic solution branch of plane Couette flow. The nonlinear states are characterised by the hydrodynamic/magnetic roll–streak and the resonant layer at which strong vorticity and current sheets are observed. These flow features, and the induced strong streamwise magnetic field, are fully consistent with the vortex/Alfvén wave interaction theory proposed in the companion paper. When the spanwise uniform magnetic field is switched off, the solutions become purely hydrodynamic. However, the second class of ‘self-sustained shear-driven dynamos’ at the zero external magnetic field limit can be found by homotopy via the forced states subject to a spanwise uniform current field. The discovery of the dynamo states has motivated the corresponding large Reynolds number matched asymptotic analysis in the companion paper. Here, the reduced equations derived by the asymptotic theory have been solved numerically. The asymptotic solution provides remarkably good predictions for the finite Reynolds number dynamo solutions.

Self-similar turbulent vortex rings are investigated theoretically in the framework of the semi-empirical turbulence theory for the modified Helmholtz equation. The velocity and vorticity fields are established, as well as the transport of passive admixture by turbulent vortex rings. Turbulent vortex rings of propellant gases originating from the muzzle of a gun after a gunshot are an important phenomenon to consider in crime scene reconstruction. In this work, it is shown that this has a significant repercussion on the outcome of backward blood spatter resulting from a gunshot. Turbulent vortex rings of propellant gases skew the distribution of bloodstains on the ground and can either propel blood droplets further from the target, or even turn them backwards towards the target. This is revealed through the final bloodstain locations and the respective distributions of the number of stains and their area as a function of distance from the target for two different shooter-to-target distances. An image of the propagating muzzle gases after bullet ejection is overlaid with the predicted flow field, which reveals satisfactory agreement. Gunshot residue is an important factor in determining the events of a violent crime due to a gunshot and are considered to be entrained and transported by the propellant gases. The self-similar solutions for the flow, vorticity and concentration of gunpowder particles are predicted and the results are shown to be within the measured range of a limited set of experimental data.

Experiments were performed within Sandia National Labs’ Multiphase Shock Tube to measure and quantify the shock-induced dispersal of a shock/dense particle curtain interaction. Following interaction with a planar travelling shock wave, schlieren imaging at 75 kHz was used to track the upstream and downstream edges of the curtain. Data were obtained for two particle diameter ranges ($d_{p}=106{-}125$, $300{-}355~\unicode[STIX]{x03BC}\text{m}$) across Mach numbers ranging from 1.24 to 2.02. Using these data, along with data compiled from the literature, the dispersion of a dense curtain was studied for multiple Mach numbers (1.2–2.6), particle sizes ($100{-}1000~\unicode[STIX]{x03BC}\text{m}$) and volume fractions (9–32 %). Data were non-dimensionalized according to two different scaling methods found within the literature, with time scales defined based on either particle propagation time or pressure ratio across a reflected shock. The data show that spreading of the particle curtain is a function of the volume fraction, with the effectiveness of each time scale based on the proximity of a given curtain’s volume fraction to the dilute mixture regime. It is seen that volume fraction corrections applied to a traditional particle propagation time scale result in the best collapse of the data between the two time scales tested here. In addition, a constant-thickness regime has been identified, which has not been noted within previous literature.

The problem of linear instability of a nonlinear travelling wave in a canonical Hamiltonian system with translational symmetry subject to superharmonic perturbations is discussed. It is shown that exchange of stability occurs when energy is stationary as a function of wave speed. This generalizes a result proved by Saffman (J. Fluid Mech., vol. 159, 1985, pp. 169–174) for travelling wave solutions exhibiting a wave profile with reflectional symmetry. The present argument remains true for any non-canonical Hamiltonian system that can be cast in Darboux form, i.e. a canonical Hamiltonian form on a submanifold defined by constraints, such as a two-dimensional surface wave on a constant shearing flow, revealing a general feature of Hamiltonian dynamics.

The interaction of gravitationally driven, free-surface flows of viscous fluid with topographic features is investigated theoretically. The motion is studied in the regime where the depth of the flow is much smaller than the streamwise extent of the topography. A lubrication model of the motion is developed, integrated numerically and analysed asymptotically. For small mounds, it is shown that the flow surmounts the obstacles, but for larger mounds the flow is deflected around it and can form dry zones in its wake into which fluid does not flow, as well as forming deeper ponded regions upstream. Which of these phenomena prevails is shown to depend upon the amplitude of the mound height and the thickness of the oncoming flow relative to the streamwise length scale over which the topography varies. By using numerical and asymptotic results, we demonstrate that relatively wide mounds lead to the development of deep ponds of material upstream, which may lead to flow overtopping if the mound is not sufficiently high. These insights can be used to inform the design of barriers that defend built infrastructures from lava flows, and it is shown how this model can also provide an upper bound on the force exerted by the flow on them.

Oceanic multiple jets are seen to possess spatio-temporal variability imposed by varying bottom topography resulting in jets that can drift and merge. The dynamics of multiple jets over a topographic zonal slope is studied in a two-layer quasi-geostrophic model. The jets tilt from the zonal direction and drift meridionally. In addition to the tilted jets, other large-scale spatial patterns are observed, which are extracted using the principal component analysis. The variances of these patterns are strongly influenced by the values of eddy viscosity and bottom friction parameters. The contribution of the tilted jets to the full flow field decreases with decreasing friction and viscosity parameters, and purely zonal large-scale modes, propagating in the meridional direction, populate the flow field. Linear stability analysis and two-dimensional kinetic-energy spectrum analysis suggest that the zonal modes gain energy from ambient eddies as well as from the tilted jets through nonlinear interactions. However, viscous dissipation and bottom friction tend to suppress the nonlinear interactions, which results in the inhibition of the upscale energy transfer from eddies to the zonal modes. These simulations suggest that, in the presence of topography, alternating jet patterns may be sustained through interactions among various large-scale modes. This is different from the classical zonal jet formation arguments, in which direct eddy forcing maintains the jets.

We simulate the flow of two immiscible and incompressible fluids separated by an interface in a homogeneous turbulent shear flow at a shear Reynolds number equal to 15 200. The viscosity and density of the two fluids are equal, and various surface tensions and initial droplet diameters are considered in the present study. We show that the two-phase flow reaches a statistically stationary turbulent state sustained by a non-zero mean turbulent production rate due to the presence of the mean shear. Compared to single-phase flow, we find that the resulting steady-state conditions exhibit reduced Taylor-microscale Reynolds numbers owing to the presence of the dispersed phase, which acts as a sink of turbulent kinetic energy for the carrier fluid. At steady state, the mean power of surface tension is zero and the turbulent production rate is in balance with the turbulent dissipation rate, with their values being larger than in the reference single-phase case. The interface modifies the energy spectrum by introducing energy at small scales, with the difference from the single-phase case reducing as the Weber number increases. This is caused by both the number of droplets in the domain and the total surface area increasing monotonically with the Weber number. This reflects also in the droplet size distribution, which changes with the Weber number, with the peak of the distribution moving to smaller sizes as the Weber number increases. We show that the Hinze estimate for the maximum droplet size, obtained considering break-up in homogeneous isotropic turbulence, provides an excellent estimate notwithstanding the action of significant coalescence and the presence of a mean shear.

We study the morphodynamics of channel width oscillations associated with the planform development of river meander bends. With this aim we develop a novel planform evolution model, based on the framework of the classical bend theory of river meanders by Ikeda et al. (J. Fluid Mech., vol. 112, 1981), that accounts for local width changes over space and time, tied to the local hydro-morphodynamics through a two-way feedback process. We focus our attention on ‘autogenic’ width variations, which are forced by flow nonlinearities driven by channel curvature dynamics. Under the assumption of regular, sinusoidal width and curvature oscillations, we obtain a set of ordinary differential equations, formally identical to those presented by Seminara et al. (J. Fluid Mech., vol. 438, 2001, pp. 213–230), with an additional equation for the longitudinal oscillation of the channel width. The proposed approach gives insight into the interaction between autogenic width variations and curvature in meander development and between forcing and damping effects in the formation of width variations. Model outcomes suggest that autogenic width oscillations mainly determine wider-at-inflection meandering river patterns, and affect their planform development particularly at super-resonant aspect ratios, where the width oscillation reaches its maximum and reduces meander sinuosity and lateral floodplain size. The coevolution of autogenic width oscillation and curvature occurs through temporal hysteresis cycles, whereby the peak in channel curvature lags behind that of width oscillation. Width oscillation amplitudes predicted by the model are consistent with those extracted from remotely sensed data.