Using weak wave turbulence theory analysis, we distinguish three main regimes for two-dimensional (2-D) stratified fluids in the dimensionless parameter space defined by the Froude number and the Reynolds number: discrete wave turbulence, weak wave turbulence and strong nonlinear interaction. These regimes are investigated using direct numerical simulation (DNS) of the 2-D Boussinesq equations with shear modes removed. In the weak wave turbulence regime, excluding slow frequencies, we observe a spectrum that aligns with recent predictions from kinetic theory. This finding represents the first DNS-based confirmation of wave turbulence theory for internal gravity waves. At strong stratification, in both the weak and strong interaction regimes, we observe the formation of layers accompanied by spectral peaks at low discrete frequencies. We attribute this layering to an inverse kinetic-energy transfer in combination with discrete wave–wave interactions at large scales. This analysis allows us to predict the layer thickness and typical flow velocity in terms of the control parameters.

In this experimental work, a two-dimensional (wedge) and three-dimensional solids (conus, 4 and 6-sided pyramids) with different deadrise angles (1–$5^\circ$) impact a deep liquid pool (distilled water or 2.5 % butanol–water solution) at a speed varying from 0.50 to 19.75 cm s−1. Below a limit speed dependent on the deadrise angle, ‘exotic’ terminal forms of air entrapment are observed: a large central bubble, two parallel lines of bubbles for the two-dimensional solid, a trail of bubbles, necklace of bubbles, doughnut-shaped bubble and large central bubble for the three-dimensional solids. Above this limit speed, the collapse of the air film forms a line of bubbles near the central edge for the two-dimensional solid, and one/multiple bubbles near the vertex for the three-dimensional solids. The entrapment dynamic is observed using a high-speed camera with a total internal reflection set-up. The outer border of the wetted area expands linearly in time, with a speed that agrees with Wagner’s theory for wedge and conus, which provides the lower and upper limites for genuinely three-dimensional cases (pyramids). The decrease in the size of the air film over time is exponential. The measured initial characteristic size of the air film is proportional to the air dynamic viscosity and inversely proportional to the liquid density, impact velocity and squared deadrise angle, as expected from an air–water lubrication–inertia balance. The prefactor in the scaling law depends on the shape of the solid with a slight but detectable effect of liquid surface tension on its value.

This study demonstrates a non-monotonic relation between pool temperature and thawing time for the ice-core thawing problem in a water pool. Numerical simulations reveal that this non-monotonicity arises from competing flow mechanisms from the non-Oberbeck–Boussinesq effect driven by the density-temperature anomaly at ${\sim}4\,^\circ \text{C}$ of water. The sides come from the anomaly-triggered chaotic flow and the normal natural convection stabilised by the buoyancy force. During the thawing process, the flow in the pool experiences a transient stable, an oscillatory, a transitional and the finally chaotic state over time. The pool size modulates the competition between chaotic flow and natural convection through the Rayleigh numbers with a critical value $\varLambda _{c}$. Within the considerations of this study, a smaller pool size leads to a more non-monotonic appearance. The competition governs both the extreme points in thawing time and the extent of the non-monotonic effect, thereby enabling accurate control over thawing kinetics. These insights clarify how the non-Oberbeck–Boussinesq effects from density and viscosity govern the ice-core thawing dynamics and pave the way for advanced controlled-thawing technologies in applications such as cryopreservation and organ resuscitation.

This work introduces closed-form solutions to describe the compressible, cyclonic motion evolving in a hemispherical chamber configuration. The analysis begins with an expansion of the compressible Bragg–Hawthorne equation in spherical coordinates. Our basic assumptions include an adiabatic and impermeable wall, a uniformly distributed stagnation enthalpy, a chamber mass balance in the equatorial plane and a vanishing centreline cross-flow velocity. Using a Rayleigh–Janzen expansion in the squared injection Mach number, the leading-order solution is seen to recover the problem’s incompressible profile as a limiting case. Meanwhile, the first-order compressible correction is shown to produce closed-form expressions for the velocity and vorticity fields, most thermodynamic properties, the local Mach number and the helicity density. At the outset, dilatational effects on all variables are evaluated and determined to be most pronounced near the equatorial plane, and least appreciable at the chamber apex, where a stagnation region seems to form. In this process, the net integrated helicity is transformed into a single volume integral that can be directly specified at both leading and first orders as a function of the Ekman-type inflow parameter. We also manage to capture rather explicitly the dilatational distortions of two characteristic surfaces: the mantle interface that separates the updraft and downdraft regions, and the vortex core surface that tracks the peak swirl intensity. Lastly, a group parameter that combines the injection Mach number and the inflow parameter is found to effectively scale all dilatational contributions caused by variations in the mass influx, chamber geometry and characteristic speed of sound.

This study examines the transition to turbulence downstream of fluttering and non-fluttering bioprosthetic aortic valves using global linear stability theory. During systole, increasing inflow velocities result in temporally evolving flow profiles downstream of the valve which are highly influenced by the leaflet kinematics. These profiles are time averaged at the sinotubular junction over successive windows and used as boundary conditions to obtain base flows for stability analysis. Three-dimensional global modes are computed for one design of each valve type across multiple time windows, revealing several unstable modes whose frequencies and growth rates increase over time. Notably, the non-fluttering valve exhibits higher growth rates than the fluttering valve. The resulting eigenspectra show that, for each case, the most unstable eigenvalues align along two distinct parabolic branches in the complex plane. For each valve case, the modes within each branch are found to have similar group velocities, suggesting that the unstable modes along a branch constitute a coherent structure. Motivated by this, a transient growth analysis is conducted to identify the optimal initial perturbations that maximise energy gain for a given time horizon. When superimposed onto the base flow, these perturbations generate vortical structures that closely resemble those observed in fully coupled nonlinear fluid–structure interaction simulations for a similar time scale as the one used to obtain the optimal perturbations. These results suggest that the optimal perturbations may initiate the shear-layer instabilities responsible for transition to turbulence, providing valuable insight into the underlying mechanisms in the flow fields downstream of bioprosthetic valve designs.

This study uncovers a striking similarity between massively separated laminar and turbulent flows that develop over a square wing during extreme vortex gust encounters. The evolving large-scale, vortical core structures responsible for significant transient lift variations exhibit remarkable similarity across ${\textit{Re}}=600$ and 10 000. The formation of these structures is attributed to a substantial gust-induced vorticity flux produced at the wing surface, resulting in shared large-scale topological features between the low- and high-Reynolds-number flows. Although fine-scale vortical structures quickly emerge in the ${\textit{Re}}=$ 10 000 case, the large-scale structures identified by scale decomposition of the turbulent flow resemble those observed at ${\textit{Re}}=600$. These findings suggest that large-scale vortical features present in laminar extreme aerodynamic flows provide key insights into their higher Reynolds number counterparts, potentially reducing the complexity of flow modelling and control for extreme aerodynamics.

In this paper, we propose a space-dependent eddy thermal diffusivity model for turbulent vertical natural convection in a fluid between two infinite vertical walls at different temperatures. Using this model, we derive analytical results for the mean temperature profile. Our results reveal that mean temperature profiles for different Rayleigh and Prandtl numbers are described by two universal scaling functions in the inner region next to the walls and the outer region near the centreline between the two walls, and the characteristic temperature scales in the inner and outer regions are expressed in terms of the two parameters of the model which determine the characteristic velocities for heat transfer in the two regions. We show that these results are in good agreement with direct numerical simulation data.

Active filaments, such as microtubules with attached cargo-carrying motor proteins, are important dynamic structures for fluid transport in and around living cells. The mathematical models of active filaments appearing in the literature typically involve combinations of follower forces, compressive tangential forces, along the filament, and an opposite force on the fluid that generates an effective surface flow. In this paper, we present a comparative dynamical systems study of active filament models examining the differences in dynamic states that occur when actuation is through follower forces alone, or the effect of surface flows is also included. We consider cases where actuation is applied only at the filament tip, or distributed uniformly along the filament length. By varying actuation strength, we show that the first bifurcations that provide the transition between the upright, whirling and beating states appear in all models. At higher values of actuation, when beating becomes unstable, however, qualitative differences between the models emerge. Those with distributed actuation produce a single, time-dependent state, which for the surface flow model is reminiscent of a rotating helix that periodically changes handedness and rotation direction. Tip actuation, however, yields complex transitions that ultimately produce a chaotic state. We link the differences in dynamics between tip and distributed actuation to differences in their respective internal stress distributions – differences that appear as early as the first bifurcation, where they affect the shapes of the unstable modes.