The deformation, movement and breakup of a wall-attached droplet subject to Couette flow are systematically investigated using an enhanced lattice Boltzmann colour-gradient model, which accounts for not only the viscoelasticity (described by the Oldroyd-B constitutive equation) of either droplet (V/N) or matrix fluid (N/V) but also the surface wettability. We first focus on the steady-state deformation of a sliding droplet for varying values of capillary number ($Ca$), Weissenberg number ($Wi$) and solvent viscosity ratio ($\beta$). Results show that the relative wetting area $A_r$ in the N/V system is increased by either increasing $Ca$, or by increasing $Wi$ or decreasing $\beta$, where the former is attributed to the increased viscous force and the latter to the enhanced elastic effects. In the V/N system, however, $A_r$ is restrained by the droplet elasticity, especially at higher $Wi$ or lower $\beta$, and the inhibiting effect strengthens with an increase of $Ca$. Decreasing $\beta$ always reduces droplet deformation when either fluid is viscoelastic. The steady-state droplet motion is quantified by the contact-line capillary number $Ca_{cl}$, and a force balance is established to successfully predict the variations of $Ca_{cl}/Ca$ with $\beta$ for each two-phase viscosity ratio in both N/V and V/N systems. The droplet breakup is then studied for varying $Wi$. The critical capillary number of droplet breakup monotonically increases with $Wi$ in the N/V system, while it first increases, then decreases and finally reaches a plateau in the V/N system.

The wake of an isolated model-scale wind turbine is analysed in a set of inflow conditions having free stream turbulence intensity between 3 % and 12 %, and integral time scales in the range of 0.1–10 times the convective time scale based on the turbine diameter. It is observed that the wake generated by the turbine evolves more rapidly, with the onset of the wake evolution being closer to the turbine, for high turbulence intensity and low integral time scale flows, in accordance with literature, while flows at higher integral time scales result in a slow wake evolution, akin to that generated by low-turbulence inflow conditions despite the highly turbulent ambient condition. The delayed onset of the wake evolution is connected to the stability of the shear layer enveloping the near-wake, which is favoured for low-turbulence or high-integral time scale flows, and to the stability of the helical vortex set surrounding the wake, as this favours interaction events and prevents momentum exchange at the wake boundary which hinder wake evolution. The rate at which the velocity in the wake recovers to undisturbed conditions is instead analytically shown to be a function of the Reynolds shear stress at the wake centreline, an observation that is confirmed by measurements. The rate of production of Reynolds shear stress in the wake is then connected to the power harvested by the turbine to explain the differences between flows at equivalent turbulence intensity and different integral time scales. The wake recovery rate, and by extension the behaviour of the turbine wake in high-integral time scale flows, is seen to be a linear function of the free stream turbulence intensity for flows with Kolmogorov-like turbulence spectrum, in accordance with literature. This relation is seen not to hold for flows with different free stream turbulence spectral distribution; however, this trend is recovered if the contributions of low frequency velocity components to the turbulence intensity are ignored or filtered out from the computation.

We use an established discrete element method (DEM) Reynolds-averaged Navier–Stokes (RANS)-based numerical model to simulate non-suspended sediment transport across conditions encompassing almost seven orders of magnitude in the particle–fluid density ratio $s$, ranging from subaqueous transport ($s=2.65$) to aeolian transport in the highly rarefied atmosphere of Pluto ($s=10^7$), whereas previous DEM-based sediment transport studies did not exceed terrestrial aeolian conditions ($s\approx 2000$). Guided by these simulations and by experiments, we semi-empirically derive simple scaling laws for the cessation threshold and rate of equilibrium aeolian transport, both exhibiting a rather unusual $s^{1/3}$-dependence. They constitute a simple means to make predictions of aeolian processes across a large range of planetary conditions. The derivation consists of a first-principle-based proof of the statement that, under relatively mild assumptions, the cessation threshold physics is controlled by only one dimensionless control parameter, rather than two expected from dimensional analysis. Crucially, unlike existing models, this proof does not resort to coarse-graining the particle phase of the aeolian transport layer above the bed surface. From the pool of existing models, only that by Pähtz et al. (J. Geophys. Res.: Earth, vol. 126, 2021, e2020JF005859) is somewhat consistent with the combined numerical and experimental data. It captures the scaling of the cessation threshold and the $s^{1/3}$-dependence of the transport rate, but fails to capture the latter's superimposed grain size dependence. This hints at a lack of understanding of the transport rate physics and calls for future studies on this issue.

We perform direct numerical simulations (DNS) of the fully developed turbulent channel flow with a passive scalar subjected to constant time-averaged scalar fluxes at the wall. The first case (case I) considers a constant time-averaged scalar flux $\left \langle q_w \right \rangle$ along with the specific condition of a non-fluctuating scalar $\theta _w$ imposed at the wall implying zero wall scalar fluctuation $\theta '_w=0$ and zero variance (isoscalar boundary condition) whereas the second case (case II) accounts for a constant instantaneous scalar flux $q_w$ in time and space leading to zero gradient of scalar fluctuation along the normal to the wall $(\partial \theta '/ \partial x_n)_w = 0$ (isoflux boundary condition) implying a non-zero variance. The friction Reynolds number takes on the value $R_\tau =395$ and the molecular Prandtl numbers considered are $P_r=0.01$, 0.1, 1 and 10. The purpose is to investigate the effect of the wall scalar fluctuations on the scalar field. Emphasis is put on the mean passive scalar $\left \langle \theta \right \rangle$, the half-scalar variance $k_\theta$, the turbulent scalar fluxes $\tau _{i \theta }$, the correlation coefficients $R_{i \theta }$, the passive scalar to dynamic time-scale ratio $\mathcal {R}$, the turbulent Prandtl number $Pr_t$ and higher-order scalar statistics. Systematic comparisons between these two scalar fields are undertaken. As a result of interest, it is found that the mean scalar remains almost the same whatever the type of the boundary layer condition but not the scalar variance. The budgets of transport equations for the half-scalar variance and turbulent fluxes reveal that some scalar quantities such as the dissipation-rate and the molecular diffusion terms are highly modified in the near-wall region but not really the production, diffusion and the scalar-pressure gradient correlation terms in a first approximation. Visualization of the instantaneous scalar fields indicates that the topology of the structures is strongly modified as the Prandtl number increases from $P_r=0.01$ up to $10$. Finally, it is shown how to use this DNS database to devise and calibrate scalar flux equation models in the framework of both first and second moment closures. This study suggests that accounting for wall scalar fluctuations should be considered in the simulation of turbulent flows involving fluid and solid combinations at the interface and provides a useful high resolution DNS database.

The transport induced by ocean mesoscale eddies remains unresolved in most state-of-the-art climate models and needs to be parametrized instead. The natural scale separation between the forcing and the emergent turbulent flow calls for a diffusive parametrization, where the eddy-induced fluxes are related to the large-scale gradients by a diffusion tensor. The standard parametrization scheme in climate modelling consists in adopting the Gent–McWilliams/Redi (GM/R) form for the diffusion tensor, initially put forward based on physical intuition and educated guesses before being put on firm analytical footing using a thickness-weighted average (TWA). In the present contribution, we provide a direct derivation of this diffusion tensor from the quasi-geostrophic (QG) dynamics of a horizontally homogeneous three-dimensional patch of ocean hosting a large-scale vertically sheared zonal flow on the $\beta$ plane. The derivation hinges on the identification of a useful cross-invariant defined as the product of the buoyancy and QG potential vorticity fluctuations. While less general than the TWA approach, the present QG framework leads to rigorous constraints on the diffusion tensor. First, there is no diapycnal diffusivity arising in the QG GM/R tensor for low viscosity and small-scale diffusivities. The diffusion tensor then involves only two vertically dependent coefficients, namely the GM transport coefficient $K_{GM}(z)$ and the Redi diffusivity $K_R(z)$. Second, as identified already by previous authors, the vertical structures of the two coefficients are related by the so-called Taylor–Bretherton relation. Finally, while the two coefficients differ generically in the interior of the water column, we show that they are equal to one another near the surface and near the bottom of the domain for low-enough dissipative coefficients. We illustrate these findings by simulating numerically the QG dynamics of a horizontally homogeneous patch of ocean hosting a vertically sheared zonal current resembling the Antarctic Circumpolar Current.

Convective dissolution is an important mechanism for long-term CO$_2$ sequestration in deep saline aquifers. The presence of an unstable geothermal gradient can affect the process of dissolution. In this paper, we present direct numerical simulations in a three-dimensional porous medium at three different concentration Rayleigh numbers $Ra_S$ with a set of thermal Rayleigh numbers $Ra_T$. Simulations reveal that the flow structures alter when ${\textit {Ra}}_T$ increases for a fixed ${\textit {Ra}}_S$. Strong thermal gradient can yield large-scale convection rolls which change the horizontal distribution and motions of concentration fingers. The time evolution of fluxes also has different responses to different ${\textit {Ra}}_T$. A theoretical model is developed and successfully describes the evolution of concentration flux and volume averaged concentration during the final shutdown stage. We further calculate the dissolved CO$_2$ into the interior over time, which shows non-monotonic variations as ${\textit {Ra}}_T$ increases. At the end of our simulations, the maximum increment of dissolved CO$_2$ occurs when density ratio is around unity for all three concentration Rayleigh numbers we have explored. We apply our results to a typical geological reservoir and discuss their implications.

In many natural settings, spatial variations in a fluid's viscosity arise due to changes in its local physico-chemical environment. We consider the low-Reynolds-number dynamics of slender bodies in fluids with a linearly varying viscosity. Assuming the spatial change in viscosity to be small compared to the spatial deviation of the body but large relative to the body's aspect ratio, we derive the modifications to resistive-force theory in a fluid due to a constant viscosity gradient. At leading order in the body slenderness, the results are identical to the classical theory in a constant-viscosity fluid but with the viscosity taking everywhere its local, non-constant value. At next order in slenderness, non-local terms arise due to the non-zero viscosity gradient. We use our results to predict the motion of straight and toroidal filaments settling under the action of gravity. We show that viscosity gradients induce rigid-body rotation of the filaments at a rate proportional to the components of the gradients along the filaments. This result contrasts with constant-viscosity fluids where the filaments do not rotate. We demonstrate further that if the viscosity gradient acts in the direction opposite to the gravitational field, then the filaments rotate towards a stable orientation, whose value depends on the ratio between the viscosity gradients parallel and perpendicular to the gravitational field; otherwise, the filaments align in the direction of the gravitational field. Our work shows that viscosity gradients can exert new forces on slender bodies, which could, for example, be used to control their orientation and drift.

Shock-tube experiments are performed on the convergent Richtmyer–Meshkov (RM) instability of a multimode interface. The temporal growth of each Fourier mode perturbation is measured. The hydrodynamic instabilities, including the RM instability and the additional Rayleigh–Taylor (RT) effect, imposed by the convergent shock wave on the dual-mode interface, are investigated. The mode-coupling effect on the convergent RM instability coupled with the RT effect is quantified. It is evident that the amplitude growths of all first-order modes and second-order harmonics and their couplings depend on the variance of the interface radius, and are influenced by the mode-coupling from the very beginning. It is confirmed that the mode-coupling mechanism is closely related to the initial spectrum, including azimuthal wavenumbers, relative phases and initial amplitudes of the constituent modes. Different from the conclusion in previous studies on the convergent single-mode RM instability that the additional RT effect always suppresses the perturbation growth, the mode-coupling might result in the additional RT effect promoting the instability of the constituent Fourier mode. By considering the geometry convergence, the mode-coupling effect and other physical mechanisms, second-order nonlinear solutions are established to predict the RM instability and the additional RT effect in the cylindrical geometry, reasonably quantifying the amplitude growths of each mode, harmonic and coupling. The nonlinear solutions are further validated by simulations considering various initial spectra. Last, the temporal evolutions of the mixed mass and normalized mixed mass of a shocked multimode interface are calculated numerically to quantify the mixing of two fluids in the cylindrical geometry.

A two-dimensional (2-D) double-distribution lattice Boltzmann method (LBM) is implemented to study isothermal drying of a colloidal suspension considering local nanoparticle effects. The two LBMs solve isothermal two-phase flow and nanoparticle transport, respectively. The three local nanoparticle effects on the fluid dynamics considered in this paper are viscosity increase, surface tension drop and local drying rate reduction. The proposed model is first validated by the study of the drying of a 2-D suspended colloidal droplet for two different Péclet numbers, where the evolution of the diameter squared agrees well with experimental results. The model is further validated looking at drying of a colloid in a 2-D capillary tube with two open ends. Compared with experimental results, the best agreement in terms of deposition profile and drying time is obtained when considering all three nanoparticle effects. Afterwards, we apply the model to investigate the complicated drying of a colloidal suspension in a 2-D porous asphalt, considering all three local nanoparticle effects. The drying dynamics, resultant nanoparticle transport, accumulation and deposition are first analysed for a base case. Then a parametric study is conducted varying the initial nanoparticle concentration, porous medium contact angle, nanoparticle contact angle and nanoparticle diffusion coefficient. The influence of these parameters on drying dynamics, drying rate, deposition process and final deposition configurations is analysed in detail, together with the mutual influence of local nanoparticle behaviour. Finally, a unified relation between the average drying rate and the studied parameters is proposed and verified, covering the full parameter ranges of simulations.

This paper presents a numerical analysis of the instability developing in horizontally sheared Poiseuille flow, when stratification extends along the vertical direction. Our study builds on the previous work that originally detected the linear instability of such a configuration, by means of experiments, theoretical analysis and numerical simulations (Le Gal et al., J. Fluid Mech., vol. 907, 2021, R1). We extend this investigation beyond linear theory, investigating nonlinear regimes with direct numerical simulations. We find that the flow loses its vertical homogeneity through a secondary bifurcation, due to harmonic resonances, and describe this symmetry-breaking mechanism in the vicinity of the instability threshold. When departing from this limit, we observe a series of bursting events that break down the flow into disordered motions driven by localized shear instabilities. This intermittent dynamics leads to the coexistence of horizontal localized layers of stratified turbulence surrounded by quiescent regions of meandering waves.

Coherent structures in two-dimensional Navier–Stokes turbulence are ubiquitously observed in nature, experiments and numerical simulations. The present study conducts a comparison between several structure detection schemes based on the Okubo–Weiss criterion, the vorticity magnitude and Lagrangian coherent structures (LCSs), focusing on the inverse cascade in two-dimensional hydrodynamic turbulence. A recently introduced vortex scaling phenomenology (Burgess & Scott, J. Fluid Mech., vol. 811, 2017, pp. 742–756) allows the quantification of the respective thresholds required by these methods based on physical properties of the flow. The resulting improved comparability allows us to identify characteristic relative differences in the detection sensitivity between the employed structure detection techniques. With respect to the inverse cascade of energy, coherent structures contribute, as expected, substantially less to the cross-scale flux than the residual incoherent parts of the flow although the energetically dominant coherent structures lead to an important large-scale deformation of the energy spectrum. This cascade inactivity can be understood by an increased misalignment of strain-rate and subgrid stress tensors within coherent structures. At the same time, the structures exhibit strong and localised nonlinear cross-scale interactions that appear to stabilise them. We quantify and interpret the resulting shape preservation of coherent structures in terms of a multi-scale gradient approach (Eyink, J. Fluid Mech., vol. 549, 2006, pp. 191–214) as the depletion of strain rotation and vorticity gradient stretching whereas the dynamics of the residual fluctuations are consistent with the vortex thinning picture.

The physics of leading-edge vortex (LEV) stability on flapping wings and autorotating seeds is still underexplored due to its complex dependency on Reynolds number ($\textit {Re}$), aspect ratio (AR) and Rossby number (Ro). Our previous study observed an interesting dual-stage vortex tilting between radial and tangential components in a stable LEV. Here, the establishment of this novel mechanism, i.e. dual-stage radial–tangential vortex tilting (DS-VT$_{r-t}$), is investigated and explained in detail using numerical methods. The contributions of other tangential vorticity transport terms are also considered. It is shown that the stable LEV region coincides mostly with a constant ratio of tangential and radial vorticity components. The DS-VT$_{r-t}$ mechanism functions as a negative feedback loop for radial vorticity, thereby contributing to the LEV stability at $\textit {Re} > 500$. Specifically, this mechanism involves a dual-stage vortex tilting starting from negative radial component to positive tangential component, and then back to positive radial component, thereby leading to a $180^{\circ }$ reversal of radial vorticity. The radial Coriolis acceleration can also assist the DS-VT$_{r-t}$ by enhancing the tangential vorticity component and the reduction of radial vorticity inside the LEV via the second stage of DS-VT$_{r-t}$. The effects of $\textit {Re}$, AR and Ro on the constant radial–tangential vorticity ratio and DS-VT$_{r-t}$ are then analysed. The coupled effects of AR and Ro are separated into rotational effects and those of tip and root vortices. Our results establish an evident relationship among the LEV stability, the constant radial–tangential vorticity ratio, and the DS-VT$_{r-t}$, thereby deepening the understanding in the vorticity transport of LEV formation and stability.

Many key environmental, industrial and energy processes rely on controlling fluid transport within subsurface porous media. These media are typically structurally heterogeneous, often with vertically layered strata of distinct permeabilities – leading to uneven partitioning of flow across strata, which can be undesirable. Here, using direct in situ visualization, we demonstrate that polymer additives can homogenize this flow by inducing a purely elastic flow instability that generates random spatio-temporal fluctuations and excess flow resistance in individual strata. In particular, we find that this instability arises at smaller imposed flow rates in higher-permeability strata, diverting flow towards lower-permeability strata and helping to homogenize the flow. Guided by the experiments, we develop a parallel-resistor model that quantitatively predicts the flow rate at which this homogenization is optimized for a given stratified medium. Thus, our work provides a new approach to homogenizing fluid and passive scalar transport in heterogeneous porous media.

The perturbation response of small-scale shear layers in turbulence is investigated with direct numerical simulations (DNS). The analysis of shear layers in isotropic turbulence suggests that the typical layer thickness is about four times the Kolmogorov scale $\eta$. Response for sinusoidal perturbations is investigated for an isolated shear layer, which models a mean flow around the shear layers in turbulence. The vortex formation in the shear layer is optimally promoted by the perturbation whose wavelength divided by the layer thickness is about 7. These results indicate that the small-scale shear instability in turbulence is efficiently promoted by velocity fluctuations with a wavelength of about $30\eta$. Furthermore, DNS are carried out for decaying turbulence initialised by the artificially modified velocity field of isotropic turbulence. The vortex formation from shear layers is accelerated under the influence of external perturbations with the efficient wavelength to promote the instability. When velocity fluctuations with this wavelength are eliminated by a band-cut filter, the shear layers tend to persist for a long time without producing vortices. These behaviours affect the number of vortices in turbulence, which increases and decreases when velocity perturbations with the unstable wavelength of the instability are artificially amplified and damped, respectively. The increase in the number of vortices results in the enhancement of kinetic energy dissipation, enstrophy production and strain self-amplification. These results indicate that the perturbation response of shear layers is important in the small-scale dynamics of turbulence as well as the modulation of small-scale turbulent motions by external disturbance.

The strongly nonlinear Miyata–Choi–Camassa model under the rigid lid approximation (MCC-RL model) can describe accurately the dynamics of large-amplitude internal waves in a two-layer fluid system for shallow configurations. In this paper, we apply the MCC-RL model to study the internal waves generated by a moving body on the bottom. For the case of the moving body speed $U=1.1c_{0}$, where ${c_0}$ is the linear long-wave speed, the accuracy of the MCC-RL results is assessed by comparing with Euler's solutions, and very good agreement is observed. It is found that when the moving body speed increases from $U=0.8c_{0}$ to $U=1.241c_{0}$, the amplitudes of the generated internal solitary waves in front of the moving body become larger. However, a critical moving body speed is found between $U=1.241c_{0}$ and $U=1.242c_{0}$. After exceeding this critical speed, only one internal wave right above the body is generated. When the moving body speed increases from $U=1.242c_{0}$ to $U=1.5c_{0}$, the amplitudes of the internal waves become smaller.

Following the stability analysis method in classic fluid dynamics, a linear stability equation (LSE) suitable for rarefied flows is derived based on the Bhatnagar–Gross–Krook (BGK) equation. The global method and singular value decomposition method are used for modal and non-modal analysis, respectively. This approach is validated by results obtained from Navier–Stokes (NS) equations. The modal analysis shows that LSEs based on NS equations (NS-LSEs) begin to fail when the Knudsen number ($Kn$) increases past $\sim$0.01, regardless of whether a slip model is used. When $Kn\geq 0.01$, the growth rate of the least stable mode is generally underestimated by the NS-LSEs. Under a fixed wavenumber, the pattern (travelling or standing wave) of the least stable mode changes with $Kn$; when the mode presents the same pattern, the growth rate decreases almost linearly with increasing $Kn$; otherwise, rarefaction effects may not stabilize the flow. The characteristic lengths of the different modes are different, and the single-scale classic stability analysis method cannot predict multiple modes accurately, even when combined with a slip model and even for continuum flow. However, non-modal analysis shows that this error does not affect the transient growth because modes with small growth rates offer little contribution to the transient growth. In rarefied flow, as long as the Mach number ($Ma$) is large enough, transient growth will occur in some wavenumber ranges. The rarefaction effect plays a stabilizing role in transient growth. The NS-LSEs-based method always overestimates the maximum transient growth.

In this paper, we study the local receptivity of the inviscid Mack modes in hypersonic boundary layers induced by the interaction between a surface heating or cooling source (HCS) and a freestream acoustic wave. The asymptotic analysis reveals that among the three distinguished layers, i.e. the main, wall and Stokes layers, the leading-order receptivity is attributed to the interaction of the HCS-induced mean-flow distortion and the acoustic signature in the wall layer; the second-order contribution appears in the Stokes layer; the third-order contribution appears in both the main and wall layers. Interestingly, at a moderate Reynolds number, the third-order contribution to the receptivity efficiency may be quantitatively greater than the second-order one, but this does not lead to breakdown of this asymptotic theory. Assuming the HCS intensity to be sufficiently weak, the asymptotic predictions are made for four representative cases involving different Mach numbers and wall temperatures, which are compared with the results obtained by the finite-Reynolds-number theory based on either the extended compressible Orr–Sommerfeld equations or the harmonic linearised Navier–Stokes (HLNS) calculations. Taking into account the first three orders of the receptivity efficiency, the asymptotic predictions are confirmed to be sufficiently accurate even when the Reynolds number is a few thousands, and the agreement with the finite-Reynolds-number calculations is better when the wall temperature of the base flow approaches the adiabatic wall temperature. The HLNS calculations are also conducted for moderate HCS intensities. It is found that the nonlinearity does not affect the receptivity coefficient much even when the temperature distortion of the HCS reaches $80\,\%$ of the temperature at the wall.

A wall model for large-eddy simulation (LES) is proposed by devising the flow as a combination of building blocks. The core assumption of the model is that a finite set of simple canonical flows contains the essential physics to predict the wall shear stress in more complex scenarios. The model is constructed to predict zero/favourable/adverse mean pressure gradient wall turbulence, separation, statistically unsteady turbulence with mean flow three-dimensionality, and laminar flow. The approach is implemented using two types of artificial neural networks: a classifier, which identifies the contribution of each building block in the flow, and a predictor, which estimates the wall shear stress via a combination of the building-block flows. The training data are obtained directly from wall-modelled LES (WMLES) optimised to reproduce the correct mean quantities. This approach guarantees the consistency of the training data with the numerical discretisation and the gridding strategy of the flow solver. The output of the model is accompanied by a confidence score in the prediction that aids the detection of regions where the model underperforms. The model is validated in canonical flows (e.g. laminar/turbulent boundary layers, turbulent channels, turbulent Poiseuille–Couette flow, turbulent pipe) and two realistic aircraft configurations: the NASA Common Research Model High-lift and NASA Juncture Flow experiment. It is shown that the building-block-flow wall model outperforms (or matches) the predictions by an equilibrium wall model. It is also concluded that further improvements in WMLES should incorporate advances in subgrid-scale modelling to minimise error propagation to the wall model.

We consider a special type of hydraulic jumps (internal bores) which, in the vertically bounded system of two immiscible fluids with slightly different densities, conserve not only the mass and impulse but also the circulation and energy. This is possible only at specific combinations of the upstream and downstream states. Two such combinations are identified with arbitrary upstream and downstream interface heights. The first has a cross-symmetry between the interface height and shear on both sides of the jump. This symmetry, which is due to the invariance of the two-layer shallow-water system with swapping the interface height and shear, ensures the automatic conservation of the impulse and energy as well as the continuity of characteristic velocities across the jump. The speed at which such jumps propagate is defined uniquely by the conservation of the mass and circulation. The other possibility is a marginally stable shear flow that can have fully conservative jumps with discontinuous characteristic velocities. Both types of conservative jumps are shown to represent a long-wave approximation to the so-called solibores that appear as smooth permanent-shape solutions in a weakly non-hydrostatic model. A new analytical solution for solibores is obtained and found to agree very well with the previous DNS results for partial-depth lock release flow. The finding that certain large-amplitude hydraulic jumps can be fully conservative, while most are not such even in the inviscid approximation, points towards the wave dispersion as a primary mechanism behind the lossy nature of internal bores.

This work describes the effects of waves on the hydroelastic response of a hydrofoil in fully wetted and ventilated flows. In the absence of vaporous cavitation (described in Part 2 of this paper series), shallow long-period non-breaking waves delayed ventilation inception because velocity fluctuations prevent the formation of a stably separated region of flow at the foil's leading edge. Aerated von Kármán vortex shedding occurred from the blunt trailing edge, producing vortex-induced vibration of the hydrofoil at a near-constant Strouhal number. Regular waves led to near sinusoidal oscillations of the load and deformations at the wave encounter frequency, while the mean response and the dynamic response at other frequency peaks corresponding to hydrodynamic and structural modes remained mostly unaffected. Significant dynamic load amplification was observed at a submerged aspect ratio of 2 for cases with low angles of attack because of coalescence between the second and third wetted structural modes; at high angles of attack, the amplitude of the load fluctuations and flow-induced vibrations reduced because energy was diverted away from the coalescence frequencies to the nearby vortex shedding frequency. In both calm water and wave conditions, transition from fully wetted to fully ventilated flow resulted in sudden and significant reduction in the load coefficients, as well as foil deflections. An impulse-like signature was observed in the time-frequency spectra during these transitions. In many of the cases, transition to fully ventilated flow also led to substantially reduced amplitudes in the load and deformation fluctuations.