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.