Evolution of solitary waves and an undular bore intruding through an abrupt transition from a wide basin into a narrow channel with opposing current is investigated. The laboratory experiments are performed in a wave tank that is crafted to achieve a steady and symmetrical shallow-water jet in the basin. The channel has a breadth comparable to the wave lengths, and the flow has Froude number approximately 0.1. The opposing current amplifies and slows the incoming waves on the jet in the basin, but the propagation speed is faster than the local Doppler effect of the current due to the influence of the wave propagating in the flank of the jet. At the channel mouth, the wave amplitude is enhanced due to the waveform altered by the current in the basin, although the amplification in the upstream channel is similar with and without the current. The longer incident waves have greater amplification into the channel. The leading wave of the undular bore is impacted by the opposing flow and transition similarly to the solitary waves. In contrast, the subsequent waves of the undular bore have a complex phase interference on the jet that causes disconnection in the lateral wave formation across the breadth of the jet. At the transition, the subsequent waves exhibit greater amplification than the leading one due to accumulated wave energy at the channel mouth. The intrusion of the undular bore against the current further enhances a rise in mean water level in the channel.

Although both butterflies and dragonflies are four-winged insects, their wing geometries and kinematics differ significantly. Butterflies have a much narrower gap between their forewing and hindwing than dragonflies. While previous research has extensively investigated the forewing–hindwing interactions in dragonfly flight, this work focuses on their interactions in butterfly flight. The interactions are studied based on numerical simulations of the Navier–Stokes equations around a butterfly-inspired flapping wing with an adjustable slot, representing the narrow gap between the forewing and hindwing. The slot is controlled by a dihedral angle between the forewing and hindwing. The lift coefficients of wings with different slot sizes and locations are investigated in detail. The results show that the forewing–hindwing interactions can significantly enhance the lift if the slot is properly configured. When the slot is configured by elevating the forewing at a 10-degree dihedral angle relative to the hindwing during flapping flight, the wing generates over 20 % more lift than the model without a slot. The streamwise ram effect and tip-vortex capture are shown to be responsible for the lift enhancement by using a lift decomposition formula. The streamwise ram effect reduces the streamwise velocity beneath the forewing, decreasing the negative vortex lift associated with spanwise vorticity. The tip-vortex capture enhances the positive vortex lift associated with streamwise vorticity when the hindwing captures the tip vortex shedding from the forewing.

Liouville-type theorems for the steady incompressible Navier–Stokes system are investigated for solutions in a three-dimensional (3-D) slab with either no-slip boundary conditions or periodic boundary conditions. When the no-slip boundary conditions are prescribed, we prove that any bounded solution is trivial if it is axisymmetric or $ru^r$ is bounded, and that general 3-D solutions must be Poiseuille flows when the velocity is not big in $L^\infty$ space. When the periodic boundary conditions are imposed on the slab boundaries, we prove that the bounded solutions must be constant vectors if either the swirl or radial velocity is independent of the angular variable, or $ru^r$ decays to zero as $r$ tends to infinity. The proofs are based on the fundamental structure of the equations and energy estimates. The key technique is to establish a Saint-Venant type estimate that characterizes the growth of the Dirichlet integral of non-trivial solutions.

Small-scale shear layers arising from the turbulent motion of viscoelastic fluids are investigated through direct numerical simulations of statistically steady, homogeneous isotropic turbulence in a fluid described by the FENE-P model. These shear layers are identified via a triple decomposition of the velocity gradient tensor. The viscoelastic effects are examined through the Weissenberg number ($\textit{Wi}$), representing the ratio of the longest polymer relaxation time scale to the Kolmogorov time scale. The mean flow around these shear layers is analysed within a local reference frame that characterises shear orientation. In both Newtonian and viscoelastic turbulence, shear layers appear in a straining flow, featuring stretching in the shear vorticity direction and compression in the layer normal direction. Polymer stresses are markedly influenced by the shear and strain, which enhance kinetic energy dissipation due to the polymers. The shear layers in viscoelastic turbulence exhibit a high aspect ratio, undergoing significant characteristic changes once $\textit{Wi}$ exceeds approximately 2. As $\textit{Wi}$ increases, the extensive strain weakens, diminishing vortex stretching. This change coincides with an imbalance between extension and compression in the straining flow. In the shear layer, the interaction between vorticity and polymer stress causes the destruction and production of enstrophy at low and high $\textit{Wi}$ values, respectively. Enstrophy production at high $\textit{Wi}$ is induced by normal polymer stress oriented along the shear flow, associated with the diminished extensive strain. The $\textit{Wi}$-dependent behaviour of these shear layers aligns with the overall flow characteristics, underscoring their pivotal roles in vorticity dynamics and kinetic energy dissipation in viscoelastic turbulence.

Ocean turbulence at meso- and submesocales affects the propagation of surface waves through refraction and scattering, inducing spatial modulations in significant wave height (SWH). We develop a theoretical framework that relates these modulations to the current that induces them. We exploit the asymptotic smallness of the ratio of typical current speed to wave group speed to derive a linear map – the U2H map – between surface current velocity and SWH anomaly. The U2H map is a convolution, non-local in space, expressible as a product in Fourier space by a factor independent of the magnitude of the wavenumber vector. Analytic expressions of the U2H map show how the SWH responds differently to the vortical and divergent parts of the current, and how the anisotropy of the wave spectrum is key to large current-induced SWH anomalies. We implement the U2H map numerically and test its predictions against WAVEWATCH III numerical simulations for both idealised and realistic current configurations.

In the present research, the effect of streamwise finlets on the coherent structures of a turbulent boundary layer and their relation with pressure fluctuations and trailing-edge noise is investigated experimentally over a NACA0018 airfoil. A synthetic measurement is performed using time-resolved particle image velocimetry, wall-pressure transducers and a far-field microphone. The finlets induce strong momentum transport within the boundary layer, leading to the formation of a detached shear layer and backward flow separation. A strong velocity deficit is produced close to the wall. The instantaneous flow organisation reveals the formation of hairpin-like vortices on top of the finlets and spanwise rollers in the near-wall separation bubble. The newly generated vortices disrupt the turbulent coherent structures of the untreated case remarkably. An overall lift-up process of the unsteady turbulent structures is produced, bringing the most energetic turbulent structures away from the wall and reducing the near-wall shear stress. The spatial and temporal relation between instantaneous unsteady flow features and wall-pressure fluctuations is analysed quantitatively. A notable reduction of the correlation and coherence intensity in the mid- and high-frequency bands is achieved due to the modification of the turbulent structures. The former frequency ranges agree with that of the pressure fluctuations and far-field noise suppression, revealing the noise-reduction mechanisms.

Sea ice is a mushy layer, a porous material whose properties depend on the relative proportions of solid and liquid. The growth of sea ice is governed by heat transfer through the ice together with appropriate boundary conditions at the interfaces with the atmosphere and ocean. The salinity of sea ice has a major effect on its thermal properties so might naïvely be expected to have a major effect on its growth rate. However, previous studies observed a low sensitivity throughout the winter growth season. The goal of this study is to identify the controlling physical mechanisms that explain this observation. We develop a simplified quasi-static framework by applying a similarity transformation to the underlying heat equation and neglecting the explicit time dependence. We find three key processes controlling the sensitivity of growth rate to salinity. First, the trade-off between thermal conductivity and (latent) heat capacity leads to low sensitivity to salinity even at moderately high salinity and brine volume fraction. Second, the feedback on the temperature profile reduces the sensitivity relative to models that assume a linear profile, such as zero-layer Semtner models. Third, thicker ice has the opposite sensitivity of growth rate to salinity compared with thinner ice, sensitivities that counteract each other as the ice grows. Beyond its use in diagnosing these sensitivities, we show that the quasi-static approach offers a valuable sea-ice model of intermediate complexity between zero-layer Semtner models and full partial-differential-equation-based models such as Maykut–Untersteiner/Bitz–Lipscomb and mushy-layer models.

The lattice Boltzmann method has become a popular tool for simulating complex flows, including incompressible turbulent flows; however, as an artificial compressibility method, it can generate spurious pressure oscillations whose impact on the statistics of incompressible turbulence has not been systematically examined. In this work, we propose a theoretical approach to analyse the origin of compressibility-induced oscillations (CIOs) and explore ways to suppress or remove them. We begin by decomposing the velocity field and pressure field each into the solenoidal component and the compressive component, and then study the evolution of these two components analytically and numerically. The analysis yields an evolution equation of the mean-square pressure fluctuation which reveals several coupling effects of the two components. The evolution equation suggests that increasing the bulk-to-shear viscosity ratio can suppress CIOs, which is confirmed by numerical simulations. Furthermore, based on the derived evolution equation and data from the simulation, a model is developed to predict the long-term behaviours of the mean-square pressure fluctuations. In the case of decaying turbulence in a periodic domain, we show that the Helmholtz–Hodge decomposition can be used to obtain the solenoidal components reflecting the true evolution of incompressible turbulent flow, from the mesoscopic artificial compressibility approach. The study provides general theoretical guidelines to understand, suppress and even remove CIOs in other related pseudo-compressibility methods.