Applying a sufficiently rapid start–stop to the outer cylinder of the Taylor–Couette system, structures approximately aligned with the rotation axis were recorded in the classic work of Coles (1965 J. Fluid Mech. vol. 21, no. 3, pp. 385–425). These short-lived rolls are oriented perpendicular to the classic Taylor-vortex rolls. In this work we report numerical observation of this instability, guided by a more recent experimental observation. The instability is shown to be related to an inflection in the azimuthal velocity profile, a finding consistent with the experimental observations of its emergence during the deceleration phase. Despite the transient nature of start–stop experiments, we show that the instability can be linked to that of the oscillating boundary layer problem of Stokes. There are several reasons why the instability may have remained elusive, both for experimental observation and for the idealised system. We look in more detail at dependence on the radius ratio for the Taylor–Couette system, $\eta=R_i/R_o$, where $R_i$ and $R_o$ are the inner and outer radii. We find that, in the case where the size of the rolls scales with the gap width, for radius ratios any lower than that used by Coles, $\eta=0.874$, the instability is quickly overrun by axisymmetric rolls of Görtler type.

We discuss flow-induced vibrations of an equilateral triangular prism confined to travel on a circular path when placed in the concave or convex orientations with respect to the flow. In each orientation, we consider three different initial angles for the prism. In Case 1, one side of the prism sees the flow first; in Case 2, one sharp edge sees the flow first; and in Case 3, one side of the prism is parallel to the incoming flow. We show that the response of the structure as well as the observed wake depend heavily on both the orientation and the initial angle of the prism. Case 1 exhibits vortex-induced vibration (VIV) in the concave orientation and galloping in the convex orientation. Case 2 does not oscillate in the concave orientation; however, oscillates about a mean deflection after a critical reduced velocity in the convex orientation. Case 3 exhibits small-amplitude oscillations in the concave orientation about a mean deflection, while in the convex orientation, exhibits VIV at low reduced velocities, followed by an asymmetric response with VIV features in a half-cycle and galloping features in the other half, and divergence at higher reduced velocities. These different types of responses are accompanied by a myriad of vortex patterns in the wake, from two single vortices shed in the wake in each cycle of oscillations to two vortex pairs, two sets of co-rotating vortices, and a combination of single vortices and vortex pairs depending on the prism’s orientation and its initial angle.

This study presents an analytical advancement in predicting the growth rate of perturbation amplitude in two-dimensional non-standard Richtmyer–Meshkov instability (RMI), driven by the interaction of a first-phase rippled shock wave at moderate Mach number with a heavy–light interface. We extend the irrotational model to encompass non-standard RMI scenarios, establishing a generalised framework validated through numerical simulations. Distinct from previous models, our model is free of empirical coefficients, and demonstrates superior accuracy across diverse perturbation configurations and Mach numbers. The analyses reveal the fundamental disparity of non-standard RMI from classical RMI: the vorticity deposition mechanism in non-standard RMI arises not only from normal pressure gradients at the shock front but crucially from tangential pressure gradients behind the shock wave. The asymptotic circulations are also well predicted by our model. Moreover, the relationship of the amplitudes between sinusoidal shock and perturbed interface is derived based on the model to realise the freeze-out of interface amplitude. The initial fundamental mode’s amplitude growth is frozen well, and the mixing width is greatly suppressed.

To investigate the characteristics of a turbulent boundary layer (TBL) over the curved edge of the bow of submarine technology program office (SUBOFF) model, wall-resolved large-eddy simulation is conducted at a Reynolds number of $\mathop {\textit{Re}}\nolimits _L = 1.1 \times {10^6}$ based on the model length and free-stream velocity. Instead of using a trip wire at the bow surface, turbulent inflow is added to the simulation to induce boundary layer transition. The effects of geometric curvature and inflow turbulence intensity (ITI) are examined. With a low ITI level, natural transition takes place at the rear end of the straight section. With higher ITI levels, turbulence emerges immediately and evolves gradually, following a strong favourable-pressure-gradient (FPG) region near the forehead, which is significantly influenced by the large streamwise curvature. Within the FPG region, the root mean square of the wall pressure fluctuation (WPF) decreases rapidly, with the frequency spectra of WPF exhibiting good scalability with outer variables. Moreover, higher turbulence intensity levels lead to larger skin friction, which is related to the development of the TBL. To elucidate the generation mechanism of skin friction, the dynamic decomposition is derived in the curvilinear coordinate system. The mean convection and streamwise pressure gradient make the largest contributions to the local skin friction. Furthermore, an analysis of the energy transfer process based on the Reynolds stress transport equations in the curvilinear coordinate system is presented, highlighting the significant impact of geometric effects, particularly on the production term.

Linearly stable shear flows first transition to turbulence in the form of localised patches. At low Reynolds numbers, these turbulent patches tend to suddenly decay, following a memoryless process typical of rare events. How far in advance their decay can be forecasted is still unknown. We perform massive ensembles of simulations of pipe flow and a reduced-order model of shear flows (Moehlis et al. 2004 New J. Phys. vol. 6, issues 1, p. 56) and determine the first moment in time at which decay becomes fully predictable, subject to a given magnitude of the uncertainty on the flow state. By extensively sampling the chaotic sets, we find that, as one goes back in time from the point of inevitable decay, predictability degrades at greatly varying speeds. However, a well-defined (average) rate of predictability loss can be computed. This rate is independent of the uncertainty and also of the type of rare event, i.e. it applies to decay and to other extreme events. We leverage our databases to define thresholds that approximately separate phase-space regions of distinct decay predictability. Our study has implications for the development of predictive models, in particular it sets their theoretical limits. It also opens avenues to study the causes of extreme events in turbulent flows: a state which is predictable to produce an extreme event is causal to it from a probabilistic perspective.

This study investigates the influence of free-stream turbulence (FST) and the thrust coefficient ($C_T$) on wind turbine wakes. Wakes generated at $C_T \in \{0.5, 0.7,0.9\}$ are exposed to turbulent inflows with varying FST intensities ($1\,\% \lesssim {\textit{TI}}_{\infty } \lesssim 11\,\%$) and integral length scales ($0.1 \lesssim {\mathcal L}_x/\!D \lesssim 2$, $D$ is the rotor diameter). For high-${\textit{TI}}_{\infty }$ inflows, a flow region in the wake is observed where a mean momentum deficit persists despite the turbulence intensity having already homogenised with that of the free stream, challenging traditional wake definitions. A ‘turning point’ in the mean wake width evolution is identified, beyond which wakes spread at slower rates. Near-field ($x\!/\!D \lesssim 7$) wake growth rate increases with higher ${\textit{TI}}_{\infty }$ and $C_T$, while far-field ($x\!/\!D \gtrsim 15$) wake growth rate decreases with higher ${\textit{TI}}_{\infty }$ – a finding with profound implications for wind turbine wake modelling that also aligns with the entrainment behaviours observed in bluff- and porous-body wakes exposed to FST. Increasing ${\mathcal L}_x$ delays wake recovery onset and reduces the mean wake width, with minimal effect on the spreading rate. Both $C_T$ and FST influence the high- and low-frequency wake dynamics, with varying contributions in the near and far fields. For low-${\textit{TI}}_{\infty }$ and small-${\mathcal L}_x$ inflows, wake meandering is minimal, sensitive to $C_T$ and appears to be triggered by a shear-layer instability. Wake meandering is enhanced for high-${\textit{TI}}_{\infty }$ and large-${\mathcal L}_x$ inflows, with the integral length scale playing a leading role. This emphasises the complex role of FST integral length scale: while increasing ${\mathcal L}_x$ amplifies meandering, it does not necessarily translate to larger mean wake width due to the concurrent suppression of entrainment rate.

We present an analysis of the coherent structures in Langmuir turbulence, a state of the ocean surface boundary layer driven by the interactions between water waves and wind-induced shear, via a resolvent framework. Langmuir turbulence is characterised by multiscale vortical structures, notably counter-rotating roll pairs known as Langmuir circulations. While classic linear stability analyses of the Craik–Leibovich equations have revealed key instability mechanisms underlying Langmuir circulations, the vortical rolls characteristic of Langmuir turbulence, the present work incorporates the turbulent mean state and varying eddy viscosity using data from large-eddy simulations (LES) to investigate the turbulence dynamics of fully developed Langmuir turbulence. Scale-dependent resolvent analyses reveal a new formation mechanism of two-dimensional circulating rolls and three-dimensional turbulent coherent vortices through linear amplification of sustained harmonic forcing. Moreover, the integrated energy spectra predicted by the principal resolvent modes in response to broadband harmonic forcing capture the dominant spanwise length scales that are consistent with the LES data. These results demonstrate the feasibility of resolvent analyses in capturing key features of multiscale turbulence–wave interactions in the statistical stationary state of Langmuir turbulence.

We present a theoretical study, supported by simulations and experiments, on the spreading of a silicone oil drop under MHz-frequency surface acoustic wave (SAW) excitation in the underlying solid substrate. Our time-dependent theoretical model uses the long-wave approach and considers interactions between fluid dynamics and acoustic driving. While similar methods have analysed the micron-scale oil and water film dynamics under SAW excitation, acoustic forcing was linked to boundary layer flow, specifically Schlichting and Rayleigh streaming, and acoustic radiation pressure. For the macroscopic drops in this study, acoustic forcing arises from Reynolds stress variations in the liquid due to changes in the intensity of the acoustic field leaking from the SAW beneath the drop and the viscous dissipation of the leaked wave. Contributions from Schlichting and Rayleigh streaming are negligible in this case. Both experiments and simulations show that, after an initial phase where the oil drop deforms to accommodate acoustic stress, it accelerates, achieving nearly constant speed over time, leaving a thin wetting layer. Our model indicates that the steady speed of the drop results from the quasi-steady shape of its body. The drop speed depends on drop size and SAW intensity. Its steady shape and speed are further clarified by a simplified travelling-wave-type model that highlights various physical effects. Although the agreement between experiment and theory on drop speed is qualitative, the results’ trend regarding SAW amplitude variations suggests that the model realistically incorporates the primary physical effects driving drop dynamics.

Turbulent wall-bounded flows, although present in many practical applications, are particularly challenging to simulate because of their large velocity gradients near the walls. To avoid the necessity of an extremely fine mesh resolution in the near-wall regions of wall-bounded turbulent flows, large eddy simulation (LES) with specific modelling near the wall can be applied. Since filtering close to the boundaries of the flow domain is not uniquely defined, existing wall-modelled LES typically rely on extensive assumptions to derive suitable boundary conditions at the walls, such as assuming that the instantaneous filtered velocity behaves similarly to the unfiltered mean velocity. Volume filtering constitutes a consistent extension of filtering close to the boundaries of the flow domain. In the present paper, we derive a formally exact expression for the wall-boundary conditions in LESs using the concept of volume filtering applied to wall-bounded turbulent flows that does not make any a priori assumptions on the flow field. The proposed expression is an infinite series expansion in powers of the filter width. It is shown in an a priori study of a turbulent channel flow and an a posteriori study of the turbulent flow over periodic hills that the proposed expression can accurately predict the volume-filtered velocity at the wall by truncating the infinite series expansion after a few terms.

We consider the two-layer quasi-geostrophic model with linear bottom friction and, in certain simulations, a planetary vorticity gradient, $\beta$. We derive energy budgets in wavenumber space for eddy available potential energy (EAPE), baroclinic eddy kinetic energy (EKE) and barotropic EKE, a particular decomposition that has previously been overlooked. The conversion between EAPE and baroclinic EKE, $\widehat {T}^{{W}}$, has a strong dependence on both bottom drag strength and planetary $\beta$. At the deformation scale $\widehat {T}^{{W}}$ is always negative, representing the conversion of EAPE to EKE via baroclinic instability. For strong, linear bottom drag, $\widehat {T}^{{W}}$ is positive at large scales due to frictional energisation of the baroclinic mode, providing a large-scale EAPE source. With weak-to-moderate bottom drag and moderate-to-strong planetary $\beta$, $\widehat {T}^{{W}}$ is the dominant source of EAPE at large scales, converting baroclinic EKE that has experienced a baroclinic inverse cascade back into EAPE, and thus closing a novel and exclusively baroclinic energy loop. With planetary $\beta$, zonal jets form and the dominant large-scale processes in the energy cycle of the system, e.g. barotropic dissipation and the peak of positive $\widehat {T}^{{W}}$, occur at the meridional wavenumber corresponding to the jet spacing, with no zonal wavenumber component, i.e., $k_{x}=0$. Importantly, the traditional source of large-scale EAPE, barotropic stirring of the baroclinic mode, is not a part of this $k_{x} = 0$ energy cycle, and thus plays a secondary role. The results suggest that consideration of horizontally two-dimensional processes is requisite to understand the energetics and physics of baroclinic geophysical jets.