The advection–diffusion of a small surface element of scalar in three dimensions (or of a small line element in two dimensions) is solved analytically thanks to the Ranz transform (Ranz, AIChE J., vol. 25, issue 1, 1979, pp. 41–47). As the quantum or elementary brick of any complex mixture, we call this element a diffuselet. Its evolution is computed numerically from the integration of the velocity gradient along the trajectory, as classically done for the Lyapunov exponents. The concentration profile across the diffuselet is obtained from the product of its initial orientation with a dimensionless tensor. Averaging over all initial orientations yields simple formulae for the mean scalar variance and the scalar probability distribution function (p.d.f.). This technique is then applied to two-dimensional and three-dimensional sine flows, in excellent agreement with direct numerical simulations. For these simple flows, the temporal integration is obtained analytically leading to simple integrals for the scalar variance and p.d.f. Statistics of stretching rates are calculated as well. The Lyapunov exponent is close to the value for short-time correlated flows (Kraichnan, J. Fluid Mech., vol. 64, issue 4, 1974, pp. 737–762) in the case of a small displacement during each step; it is close to the value for a simple shear in the case of a large displacement. The p.d.f. of stretching factors are log normal with a ratio between the mean and the variance equal to half the dimension of space for small displacements (in agreement with Kraichnan, J. Fluid Mech., vol. 64, issue 4, 1974, pp. 737–762), but increases strongly for large displacements.

An isolated charge-neutral droplet in a uniform electric field experiences no net force. However, a droplet pair can move in response to field-induced dipolar and hydrodynamic interactions. If the droplets are identical, the centre of mass of the pair remains fixed. Here, we show that if the droplets have different properties, the pair experiences a net motion due to non-reciprocal electrohydrodynamic interactions. We analyse the three-dimensional droplet trajectories using asymptotic theory, assuming spherical droplets and large separations, and numerical simulations based on a boundary integral method. The dynamics can be quite intricate depending on the initial orientation of the droplets line-of-centres relative to the applied field direction. Drops tend to migrate towards a configuration with line-of-centres either parallel or perpendicular to the applied field direction, while either coming into contact or indefinitely separating. We elucidate the conditions under which these different interaction scenarios take place. Intriguingly, we find that in some cases droplets can form a pair (tandem) that translates either parallel or perpendicular to the applied field direction.

A numerical study on the effect of surface slip on the flow in a constricted channel is presented, with the aim of exploring the use of surface slip to control flow separation. Our focus is on two-dimensional flow in a channel over a bump, with a fixed aspect ratio, upon which a Robin-type slip boundary condition is imposed. When the channel walls are fully no-slip, such a flow is known to develop a region of separation behind the bump, at sufficiently large Reynolds numbers. The effect of slip on the separation bubble dynamics occurring behind the bump is investigated, for Reynolds numbers $2000$ and $4000$. It is shown that surface slip (i) attenuates the intensity of separation as it diminishes the minimum of the streamwise velocity within the recirculation region; (ii) delays the onset of flow separation, shifting it downstream, along the bump, and (iii) reduces the dimensions of the separation bubble behind the bump, allowing the flow to reattach sooner. Ultimately, slip inhibits separation, with both the points of separation and reattachment coalescing, for a slip length $\lambda$ of approximately $0.2$.

Dynamos driven by rotating convection in the plane layer geometry are investigated numerically for a range of Ekman number ($E$), magnetic Prandtl number ($Pm$) and Rayleigh number ($Ra$). The primary purpose of the investigation is to compare results of the simulations with previously developed asymptotic theory that is applicable in the limit of rapid rotation. We find that all of the simulations are in the quasi-geostrophic regime in which the Coriolis and pressure gradient forces are approximately balanced at leading order, whereas all other forces, including the Lorentz force, act as perturbations. Agreement between simulation output and asymptotic scalings for the energetics, flow speeds, magnetic field amplitude and length scales is found. The transition from large-scale dynamos to small-scale dynamos is well described by the magnetic Reynolds number based on the small convective length scale, $\widetilde {Rm}$, with large-scale dynamos preferred when $\widetilde {Rm} \lesssim O(1)$. The magnitude of the large-scale magnetic field is observed to saturate and become approximately constant with increasing Rayleigh number. Energy spectra show that all length scales present in the flow field and the small-scale magnetic field are consistent with a scaling of $E^{1/3}$, even in the turbulent regime. For a fixed value of $E$, we find that the viscous dissipation length scale is approximately constant over a broad range of $Ra$; the ohmic dissipation length scale is approximately constant within the large-scale dynamo regime, but transitions to a $\widetilde {Rm}^{-1/2}$ scaling in the small-scale dynamo regime.

Both one-dimensional in the horizontal direction (1DH, dispersive and non-dispersive) and two-dimensional in the horizontal direction (2DH) axisymmetric (approximate, non-dispersive) analytical solutions are derived for water waves generated by moving atmospheric pressures. For 1DH, three wave components can be identified: the locked wave propagating with the speed of the atmospheric pressure, $C_p$, and two free wave components propagating in opposite directions with the respective wave celerity, according to the linear frequency dispersion relationship. Under the supercritical condition ($C_p > C$, which is the fastest celerity of the water wave), the leading water wave is the locked wave and has the same sign (i.e. phase) as the atmospheric pressure, while the trailing free wave has the opposite sign. Under the subcritical condition ($C >C_p$) the fastest moving free wave component leads, and its free surface elevation has the same sign as the atmospheric pressure. For a long atmospheric pressure disturbance, the induced free surface profile mimics that of the atmospheric pressure. The 2DH problem involves an axisymmetric atmospheric pressure decaying in the radial direction as $O(r^{-1/2})$. Due to symmetry, only two wave components, locked and free, appear. The tsunami DART data captured during Tonga's volcanic eruption event are analysed. Corrections are necessary to isolate the free surface elevation data. Comparisons between the corrected DART data and the analytical solutions, including the arrival times of the leading locked waves and the trailing free waves, and the amplitude ratios, are in agreement in order of magnitude.

We report a systematic experimental study of the mean temperature profile $\theta (\delta z)$ and temperature variance profile $\eta (\delta z)$ across a stable and immiscible liquid–liquid (water–FC770) interface formed in two-layer turbulent Rayleigh–Bénard convection. The measured $\theta (\delta z)$ and $\eta (\delta z)$ as a function of distance $\delta z$ away from the interface for different Rayleigh numbers are found to have the scaling forms $\theta (\delta z/\lambda )$ and $\eta (\delta z/\lambda )$, respectively, with varying thermal boundary layer (BL) thickness $\lambda$. By a careful comparison with the simultaneously measured BL profiles near a solid conducting surface, we find that the measured $\theta (\delta z)$ and $\eta (\delta z)$ near the liquid interface can be well described by the BL equations for a solid wall, so long as a thermal slip length $\ell _T$ is introduced to account for the convective heat flux passing through the liquid interface. Direct numerical simulation results further confirm that the turbulent thermal diffusivity $\kappa _t$ near a stable liquid interface has a complete cubic form, $\kappa _t(\xi )/\kappa \sim (\xi +\xi _0)^3$, where $\kappa$ is the molecular thermal diffusivity of the convecting fluid, $\xi =\delta z/\lambda$ is the normalized distance away from the liquid interface and $\xi _0$ is the normalized slip length associated with $\ell _T$.

Numerical studies of dimple and jet formation from a collapsing cavity often model the initial cavity shape as a truncated sphere, mimicking a bursting bubble. In this study, we present a minimal model containing only nonlinear inertial and capillary forces, which produces dimples and jets from a collapsing capillary wave trough. The trough in our simulation develops from a smooth initial perturbation, chosen to be an eigenmode to the linearised ${O}(\epsilon )$ problem ($\epsilon$ is the non-dimensional amplitude). We explain the physical mechanism of dimple formation and demonstrate that, for moderate $\epsilon$, the sharp dimple seen in simulations is well captured by the weakly nonlinear ${O}(\epsilon ^3)$ theory developed here. For $\epsilon \gg 1$ the regime is strongly nonlinear, spreading surface energy into many modes, and the precursor dimple now develops into a sharply rising jet. Here, simulations reveal a novel localised window (in space and time) where the jet evolves self-similarly following inviscid (Keller & Miksis, SIAM J. Appl. Maths, vol. 43, issue 2, 1983, pp. 268–277) scales. We develop an analogy of this regime to a self-similar solution of the first kind, for linearised capillary waves. Our first-principles study demonstrates that, at sufficiently small scales, dimples and jets can form from radial inward focusing of capillary waves, and the formation of this may be described by a relatively simple model employing (nonlinear) inertial and capillary effects. Viscosity and gravity can, however, significantly influence the focusing process, either intensifying the singularity or weakening it (Walls et al., Phys. Rev. E, vol. 92, issue 2, 2015, 021002; Gordillo & Rodríguez-Rodríguez, J. Fluid Mech., vol. 867, 2019, pp. 556–571). This leads, in particular, to critical values of Ohnesorge and Bond numbers, which cannot be obtained from our minimal model.

We present experiments on large air cavities spanning a wide range of sizes relative to the Hinze scale $d_{H}$, the scale at which turbulent stresses are balanced by surface tension, disintegrating in turbulence. For cavities with initial sizes $d_0$ much larger than $d_{H}$ (probing up to $d_0/d_{H} = 8.3$), the size distribution of bubbles smaller than $d_{H}$ follows $N(d) \propto d^{-3/2}$, with $d$ the bubble diameter. The capillary instability of ligaments involved in the deformation of the large bubbles is shown visually to be responsible for the creation of the small bubbles. Turning to dynamical, three-dimensional measurements of individual break-up events, we describe the break-up child size distribution and the number of child bubbles formed as a function of $d_0/d_{H}$. Then, to model the evolution of a population of bubbles produced by turbulent bubble break-up, we propose a population balance framework in which break-up involves two physical processes: an inertial deformation to the parent bubble that sets the size of large child bubbles, and a capillary instability that sets the size of small child bubbles. A Monte Carlo approach is used to construct the child size distribution, with simulated stochastic break-ups constrained by our experimental measurements and the understanding of the role of capillarity in small bubble production. This approach reproduces the experimental time evolution of the bubble size distribution during the disintegration of large air cavities in turbulence.

Shallow mixing layers (SMLs) behind a splitter plate were studied in a tilted rectangular open-channel flume for a range of flow depths and the initial shear parameter ${\lambda = (U_{2}-U_{1})/(U_{2}+U_{1})}$, where $U_1$ and $U_2$ are streamwise velocities of the slow and fast streams, respectively. The main focus of the study is on (i) key parameters controlling the time-averaged SMLs; and (ii) the emergence and spatial development of Kelvin–Helmholtz coherent structures (KHCSs) and large- and very-large-scale motions (LSMs and VLSMs) and associated turbulence statistics. The time-averaged flow features of the SMLs are mostly controlled by bed-friction length scale $h/c_f$ and shear parameter $\lambda$ as well as by time-averaged spanwise velocities $V$ and momentum fluxes $UV$, where $h$ and $c_f$ are flow depth and bed-friction coefficient, respectively. For all studied cases, the effect of shear layer turbulence on the SML growth is comparatively weak, as the fluxes $UV$ dominate over the spanwise turbulent fluxes. Initially, the emergence of KHCSs and their length scales largely depend on $\lambda$. The KHCSs cannot form if ${\lambda \lessapprox 0.3}$ and the turbulence behind the splitter plate resembles that of free mixing layers. Further downstream, shear layer turbulence becomes dependent on the bed-friction number $S = c_f \delta _v /(4 h \lambda )$, where $\delta _v$ is vorticity thickness. When $S \gtrapprox 0.01$, the KHCSs are longitudinally stretched and the scaled transverse turbulent fluxes decrease with increasing $S$. The presence and streamwise development of LSMs/VLSMs away from the splitter plate depends on the $\lambda$-value, particularly when $\lambda > 0.3$, resembling LSMs/VLSMs in conventional open-channel flows when $\lambda$ is small.

We investigate wind wave growth by direct numerical simulations solving for the two-phase Navier–Stokes equations. We consider the ratio of the wave speed $c$ to the wind friction velocity $u_*$ from $c/u_*= 2$ to 8, i.e. in the slow to intermediate wave regime; and initial wave steepness $ak$ from 0.1 to 0.3; the two being varied independently. The turbulent wind and the travelling, nearly monochromatic waves are fully coupled without any subgrid-scale models. The wall friction Reynolds number is 720. The novel fully coupled approach captures the simultaneous evolution of the wave amplitude and shape, together with the underwater boundary layer (drift current), up to wave breaking. The wave energy growth computed from the time-dependent surface elevation is in quantitative agreement with that computed from the surface pressure distribution, which confirms the leading role of the pressure forcing for finite amplitude gravity waves. The phase shift and the amplitude of the principal mode of surface pressure distribution are systematically reported, to provide direct evidence for possible wind wave growth theories. Intermittent and localised airflow separation is observed for steep waves with small wave age, but its effect on setting the phase-averaged pressure distribution is not drastically different from that of non-separated sheltering. We find that the wave form drag force is not a strong function of wave age but closely related to wave steepness. In addition, the history of wind wave coupling can affect the wave form drag, due to the wave crest shape and other complex coupling effects. The normalised wave growth rate we obtain agrees with previous studies. We make an effort to clarify various commonly adopted underlying assumptions, and to reconcile the scattering of the data between different previous theoretical, numerical and experimental results, as we revisit this longstanding problem with new numerical evidence.

The average wave drag in unsteady motion is studied experimentally with force measurements. Towing hulls of size $L$ at sinusoidal speed, the mean drag is measured for different amplitudes and frequencies of the fluctuating velocity, as well as different Froude numbers $\mathcal {F}_0$ associated with the mean velocity $V_0$ ($\mathcal {F}_0 = V_0/\sqrt {gL}$). The wave drag is reported to be either increased or decreased by velocity fluctuations depending on $\mathcal {F}_0$. For small fluctuation amplitudes, this drag change is proportional to the square of the amplitude. The effect is maximized for a resonance frequency identified as the Wehausen frequency, which scales as $\sqrt {g/L}$ times the inverse of the Froude number. All these results are rationalized by developing an extension to Havelock's theory.

Resonant response of water waves in a narrow gap, the so-called gap resonance, is a hydrodynamic phenomenon with practical applications. When coupled to body motions, the physics becomes rather complicated, involving body motions, fluid resonance and damping that determines the response amplitude. Gap resonances between two identical elongated bodies, with one held fixed and the other floating, are investigated experimentally for unidirectional waves with broadside incidence. Transient wave groups with different maximum surface elevations are generated, to examine the nonlinear physics. Sub- and super-harmonics, which can be substantially larger than the linear component, are observed in the responses. When going from the diffraction problem (both bodies fixed) to the coupled problem (allowing one body to move), the gap responses are significantly amplified, i.e. by a factor of 2. The first resonant mode that dominates the diffraction problem disappears in the coupled problem. A new resonant mode, which is shown to arise from body motions, is excited inside the gap through nonlinear processes. This mode features a double-humped ‘camel-back’ shape, leading to remarkably large responses. The floating body is observed to oscillate in sway with significant amplitudes at two distinct natural frequencies that are far apart. This is of great interest for the design of mooring lines connecting the two bodies, as it appears to cause resonances at the wave frequencies in addition to the low frequencies. A semi-analytical model is developed to investigate the multiple natural frequencies in sway, yielding further insight into gap resonances.

The motion of Taylor bubbles in capillaries is typical of many engineering and biological systems, ranging from subsurface flows to small-scale reactors. Although the hydrodynamics of elongated bubbles has been the object of several studies, the case where a solute is transported in the surrounding liquid and surface mass-transfer mechanisms act on the solid wall or the bubble–fluid interface is much less understood. To fill this gap, we investigate the transport problem around a confined Taylor bubble to access the competition between advection, diffusion and surface mass transfer in the different regions of the bubble. With this aim, we derive a one-dimensional advection–diffusion–mass-transfer equation where the transport mechanisms are described through an effective velocity, an effective diffusion coefficient and an effective Sherwood number. Our model generalises the Aris–Taylor dispersion to the case of a Taylor bubble and clarifies the impact of surface mass transfer in the advection and diffusion dominated regimes for both the front and rear menisci. The model recovers the typical Pèclet square relationship of the effective diffusion coefficient, which also depends on the film thickness. Also, when the Pèclet number balances with the Sherwood number, there exist conditions that lead to the formation of hot spots of concentration. We show that the typical shape oscillations of the bubble rear locally enhance superficial mass transfer. Finally, we study the transport problem in the uniform film region where the concentration field can be found analytically.

Small drag-reducing riblets and larger drag-increasing ridges are longitudinally invariant and laterally periodic surface structures that differ only in the details of their lateral periodicity and their size in viscous units. Due to their different drag behaviour, typically riblets and ridges have been analysed separately. By studying experimentally trapezoidal-grooved surfaces of different sizes, we address systematically the transition from riblet-like to ridge-like behaviour in a unified framework. The structure height and lateral wavelength are varied both physically, by considering eight different surfaces, and in their viscous-scaled form, by spanning a wide range of bulk Reynolds number $Re_b$. The effective skin-friction coefficient $C_f$ is determined via pressure-drop measurement in a turbulent channel flow facility designed for accurate drag measurements. An unexpectedly rich drag behaviour is unveiled, in which different drag regimes are distinguished depending on the value of $l_g^+$, the viscous-scaled square root of the groove area. The well-known drag-reducing regime of riblets that spans up to $l_g^+=17$ is followed by a regime in which the roughness function ${\rm \Delta} U^+$ increases logarithmically with $l_g^+$, indicating an apparent fully rough behaviour up to $l_g^+\approx 40$. Further increase of $l_g^+$ leads to a clear departure from the fully rough regime, and an unexpected non-monotonic behaviour of the roughness function ${\rm \Delta} U^+$ for $50< l_g^+<200$ is reported for the first time. For sufficiently large $Re_b$ and $l_g$, it is shown that a single parameter, similar to the classical hydraulic diameter, is sufficient to describe the drag behaviour of ridges. We find that an appropriate definition of the effective channel height is crucial for interpreting the drag behaviour. When the longitudinal protrusion height of the structured surface is accounted for in the channel height definition, a laminar flow exhibits the same $C_f(Re_b)$ relation known for flat surfaces. This approach thus allows us to discern the modification of $C_f$ induced by turbulence. We provide predictive correlations for the fully rough regime and the high Reynolds number range of trapezoidal-grooved surfaces that become possible thanks to the chosen channel height definition.

A core unresolved challenge in rectified diffusion is the lack of predictive models, which allow accurate modelling of the growth of bubbles over millions of cycles of oscillation. The spherically symmetric problem involves two asymptotic regions in space for the convection and diffusion of the dissolved gas in the liquid, an inner region adjacent to the bubble and an outer region. It also involves three time scales: the shortest time scale associated with the bubble oscillation, the intermediate and the longest time scales for the mass transport across the bubble interface and the outer region, respectively. The problem is analysed systematically using matched asymptotic expansions in space and multi-scales in time, the large parameter being the Péclet number for mass transfer. A tractable mathematical model is formulated for rectified diffusion. It comprises the Rayleigh–Plesset equation for the spherical oscillations of the bubble on the shortest time scale, an ordinary differential equation for the mass of gas in the bubble on the intermediate time scale and a diffusion equation on the longest time scale and the long length scale. Predictions of this simplified model have excellent agreement with experimental results for a single spherical bubble in the bulk over millions of cycles of oscillation. A parametric study is undertaken with several new phenomena/features observed for acoustic frequencies in the range 12 to 62 kHz, acoustic field $0.12$ to $0.22$ bar and the initial gas concentration in the liquid being $0.95$ to $1.0$ of the saturation concentration.

We report that vertical vibration with small amplitude and high frequency can tame convective heat transport in Rayleigh–Bénard convection in a turbulent regime. When vertical vibration is applied, a dynamically averaged ‘anti-gravity’ results that stabilizes the thermal boundary layer and inhibits the eruption of thermal plumes. This eventually leads to the attenuation of the intensity of large-scale mean flow and a significant suppression of turbulent heat transport. Accounting for both the thermally led buoyancy and the vibration-induced anti-gravitational effects, we propose an effective Rayleigh number that helps to extend the Grossmann–Lohse theory to thermal vibrational turbulence. The prediction of the reduction on both the Nusselt and Reynolds numbers obtained by the extended model is found to agree well with the numerical data. In addition, vibrational influences on the mean flow structure and the temporal evolution of Nusselt and Reynolds numbers are investigated. The non-uniform characteristic of vibration-induced ‘anti-gravity’ is discussed. The present findings provide a powerful basis for studying thermal vibrational turbulence and put forward a novel strategy for actively controlling thermal turbulence.

The Richtmyer–Meshkov instability (RMI) results from the impulsive acceleration of a density interface where either it or the acceleration is perturbed. Density interfaces may arise due to a change in gas species, isotope, temperature or a combination of these. We computationally investigate the effect of interface type on the plasma RMI, which is relevant for a range of applications, including inertial confinement fusion. We simulate the evolution of single-mode perturbed thermal, species and isotope interfaces in an ideal ion–electron plasma using the multi-fluid plasma (MFP) model. We find that, in the MFP model, the evolution of different types of interface differs significantly, in contrast to single-fluid models where they behave similarly if the Atwood number is matched. The thermal and species interfaces produce the most severe response to shock acceleration, experiencing the secondary instabilities and enhanced primary mode growth. The isotope interface evolution is restrained in comparison with the former cases, resembling the response predicted by single-fluid models. The determining factor in the severity of the MFP RMI is the density ratio across the initial interface in the electron fluid, which is unity for an isotope interface. We observe that, as the density ratio across the electron interface decreases, so do the magnitudes of the self-generated fields and consequently the severity of the growth amplification. Generally, the evolution of the RMI with different types of interface becomes more similar as the level of coupling between the ion and electron fluids is increased, characterised by reducing the plasma non-dimensional skin depth.

The present work investigates the linear instability of three-dimensional boundary layers in thermodynamically non-ideal regimes. As a representative fluid, we consider carbon dioxide at supercritical pressure (80 bar). The flow set-up is matched to the redesigned DLR (German Aerospace Center) experiment on cross-flow instability, with identical pressure-coefficient distribution (accelerating the flow), sweep angle and Reynolds number, at a low Mach number. The flow temperature relative to the Widom line – also known as the pseudocritical line – thus characterises the non-ideality of the flow. We consider supercritical (gas-like), subcritical (liquid-like) and transcritical (pseudoboiling) regimes, where the flow temperature remains above, below or crosses the Widom line. The stability analyses of the parabolised Navier–Stokes baseflows indicate that wall heating destabilises the flow in the supercritical regime while wall cooling stabilises both effects similar to the ideal-fluid situation but being stronger. On the contrary, wall heating/cooling exhibits reversed effects in the subcritical regime, like for an ideal liquid. In the transcritical regime, with its sharp gradients of the thermodynamic and transport properties, wall heating stabilises the flow. Most substantially, however, wall cooling provokes a changeover of the leading instability mechanism: the accelerated streamwise flow attains inflectional wall-normal profiles, and the invoked inviscid Tollmien–Schlichting instability prevails with growth rates up to one order of magnitude larger than those of the cross-flow mode. We establish a two-fold mathematical relation from the momentum equation that explains the consequence of non-ideality and wall heating/cooling. The streamwise perturbation patterns of the flows in their linear instability regime are shown by mimicking wave trains emanating from virtual point-disturbance sources. From the viewpoint of keeping laminar flows, the transcritical thermodynamic state with a cooling wall must be avoided.

The present research will provide an analytical explanation to experiments destabilising turbulence in pipe flow reported in Kuehnen et al. (Nat. Phys., vol. 14, 2018, 386–390). Those experiments show four methods by which turbulence vanishes from steady-state pipe flow, without decreasing its bulk velocity, until it becomes completely laminar. The explanation is based on our theory of underlying laminar flow (TULF), which has already been successfully applied to account for other uncommon experiments reported in the literature. The TULF is founded on the Reynolds-averaged Navier–Stokes equations and thus is a theory of ensemble-averaged flows. The zero theorem for steady-state flow is introduced as a universal result that will help explain the laminarisation process described in experiments. After presenting the most comprehensive solution for the mean pipe flow governing equation that, to our knowledge, has ever been reported, we uncover a general sequence for laminarisation, called the laminarisation pattern, and we introduce a mathematical model for it. We show that a drastic decrease in a flow's mean-pressure gradient, while maintaining constant its Reynolds number, is necessary and sufficient to erase turbulence. Equations derived from our model are used to calculate the minimum pressure gradient necessary to cause complete laminarisation in each experiment. Results are then contrasted with reported experimental data, with noticeable agreement. We also propose a figure of merit to assess the efficiency of each laminarisation method. Having disclosed the intrinsic mechanism leading to complete laminarisation, we expect researchers will propose other ingenious methods to achieve it.

Using branch continuation in the FENE-P model, we show that finite-amplitude travelling waves borne out of the recently discovered linear instability of viscoelastic channel flow (Khalid et al., J. Fluid Mech., vol. 915, 2021, A43) are substantially subcritical reaching much lower Weissenberg ($Wi$) numbers than on the neutral curve at a given Reynolds ($Re$) number over $Re \in [0,3000]$. The travelling waves on the lower branch are surprisingly weak indicating that viscoelastic channel flow is susceptible to (nonlinear) instability triggered by small finite-amplitude disturbances for $Wi$ and $Re$ well below the neutral curve. The critical $Wi$ for these waves to appear in a saddle node bifurcation decreases monotonically from, for example, $\approx 37$ at $Re=3000$ down to $\approx 7.5$ at $Re=0$ at the solvent-to-total-viscosity ratio $\beta =0.9$. In this latter creeping flow limit, we also show that these waves exist at $Wi \lesssim 50$ for higher polymer concentrations, $\beta \in [0.5,0.97)$, where there is no known linear instability. Our results therefore indicate that these travelling waves, found in simulations and named ‘arrowheads’ by Dubief et al. (Phys. Rev. Fluids, vol. 7, 2022, 073301), exist much more generally in $(Wi,Re, \beta )$ parameter space than their spawning neutral curve and, hence, can either directly, or indirectly through their instabilities, influence the dynamics seen far away from where the flow is linearly unstable. Possible connections to elastic and elasto-inertial turbulence are discussed.