The direct numerical simulation (DNS) study by Jin et al. (J. Fluid Mech, vol. 766, 2015, pp. 76–103) shows that the turbulent structures are generally restricted in size to the pore scale, leading to the pore-scale prevalence hypothesis (PSPH). Although the PSPH has been validated under most conditions, it might become invalid as the porosity approaches unity. In order to investigate the valid domain of the PSPH, we have studied the turbulent flows in porous matrices which have one or two length scales using DNS and macroscopic simulation methods. The large porous elements are made of staggered arrays of square cylinders, which might stimulate strong macroscopic (large-scale) turbulence. The small porous elements are made of aligned arrays of spheres or cubes, which suppress the macroscopic turbulence. The analyses are performed for various values of the Reynolds number, Darcy number, pore-scale ratio and porosity. Turbulent two-point correlations, integral length scales and premultiplied energy spectra are calculated from the DNS and macroscopic simulation results to determine the length scale of the turbulent structures. Our numerical results show that the flow becomes turbulent when the Reynolds number is sufficiently large. However, the length scale of turbulence is not considerably affected by the Reynolds number, Darcy number and pore-scale geometry. The PSPH is valid when the porosity has small or medium values. At a sufficiently large Reynolds number, large-scale turbulence survives if the porosity is larger than a critical value. Our DNS and macroscopic simulation results show that this critical value is in the range 0.93–0.98 for porous matrices with large Darcy numbers (0.3–1.26 using the definition in this study). The dependence of the critical porosity on the pore-scale geometry still needs to be further investigated.

Viscous flows in hyperelastic chambers are relevant to many biological phenomena such as inhalation into the lung's acinar region, and medical applications such as the inflation of a small chamber in minimally invasive procedures. In this work, we analytically study the viscous flow and elastic deformation created due to inflation of such spherical chambers from one or two inlets. Our investigation considers the shell's constitutive hyperelastic law coupled with the flow dynamics inside the chamber. For the case of a narrow tube filling a larger chamber, the pressure within the chamber involves a large spatially uniform part, and a small-order correction. We derive a closed-form expression for the inflation dynamics, accounting for the effect of elastic bistability. Interestingly, the obtained pressure distribution shows that the maximal pressure on the chamber's surface is greater than the pressure at the entrance to the chamber. The calculated series solution of the velocity and pressure fields during inflation is verified by using a fully coupled finite element scheme, resulting in excellent agreement. Our results allow the estimation of the chamber's viscous resistance at different pressures, thus enabling us to model the process of inflation and deflation.

The application of control tools to complex flows frequently requires approximations, such as reduced-order models and/or simplified forcing assumptions, where these may be considered low rank or defined in terms of simplified statistics (e.g. white noise). In this work we propose a resolvent-based control methodology with causality imposed via a Wiener–Hopf formalism. Linear optimal causal estimation and control laws are obtained directly from full-rank, globally stable systems with arbitrary disturbance statistics, circumventing many drawbacks of alternative methods. We use efficient, matrix-free methods to construct the matrix Wiener–Hopf problem, and we implement a tailored method to solve the problem numerically. The approach naturally handles forcing terms with space–time colour; it allows inexpensive parametric investigation of sensor/actuator placement in scenarios where disturbances/targets are low rank; it is directly applicable to complex flows disturbed by high-rank forcing; it has lower cost in comparison to standard methods; it can be used in scenarios where an adjoint solver is not available; or it can be based exclusively on experimental data. The method is particularly well suited for the control of amplifier flows, for which optimal control approaches are typically robust. Validation of the approach is performed using the linearized Ginzburg–Landau equation. Flow over a backward-facing step perturbed by high-rank forcing is then considered. Sensor and actuator placement are investigated for this case, and we show that while the flow response downstream of the step is dominated by the Kelvin–Helmholtz mechanism, it has a complex, high-rank receptivity to incoming upstream perturbations, requiring multiple sensors for control.

When a liquid drop strikes a deep pool of a target liquid, an impact crater opens while the liquid of the drop decelerates and spreads on the surface of the crater. When the density of the drop is larger than the target liquid, we observe mushroom-shaped instabilities growing at the interface between the two liquids. We interpret this instability as a spherical Rayleigh–Taylor instability due to the deceleration of the interface, which exceeds the ambient gravity. We investigate experimentally the effect of the density contrast and the impact Froude number, which measures the importance of the impactor kinetic energy to gravitational energy, on the instability and the resulting mixing layer. Using backlighting and planar laser-induced fluorescence methods, we obtain the position of the air–liquid interface, an estimate of the instability wavelength, and the thickness of the mixing layer. We derive a model for the evolution of the crater radius from an energy conservation. We then show that the observed dynamics of the mixing layer results from a competition between the geometrical expansion of the crater, which tends to thin the layer, and entrainment related to the instability, which increases the layer thickness. The mixing caused by this instability has geophysical implications for the impacts that formed terrestrial planets. Extrapolating our scalings to planets, we estimate the mass of silicates that equilibrates with the metallic core of the impacting bodies.

We perform a theoretical investigation of the instability of a helical vortex filament beneath a free surface in a semi-infinite ideal fluid. The focus is on the leading-order free-surface boundary effect upon the equilibrium form and instability of the vortex. This effect is characterised by the Froude number $F_r = U(gh^*)^{-{1}/{2}}$ where $g$ is gravity, and $U = \varGamma /(2{\rm \pi} b^*)$ with $\varGamma$ being the strength, $2{\rm \pi} b^*$ the pitch and $h^*$ the centre submergence of the helical vortex. In the case of $F_r \rightarrow 0$ corresponding to the presence of a rigid boundary, a new approximate equilibrium form is found if the vortex possesses a non-zero rotational velocity. Compared with the infinite fluid case (Widnall, J. Fluid Mech., vol. 54, no. 4, 1972, pp. 641–663), the vortex is destabilised (or stabilised) to relatively short- (or long-)wavelength sub-harmonic perturbations, but remains stable to super-harmonic perturbations. The wall-boundary effect becomes stronger for smaller helix angle and could dominate over the self-induced flow effect depending on the submergence. In the case of $F_r > 0$, we obtain the surface wave solution induced by the vortex in the context of linearised potential-flow theory. The wave elevation is unbounded when the $m$th wave mode becomes resonant as $F_r$ approaches the critical Froude numbers ${\mathcal {F}} (m) = (C_0^*/U)^{-1} (mh^*/b^*)^{-{1}/{2}}$, $m=1, 2, \ldots,$ where $C_0^*$ is the induced wave speed. We find that the new approximate equilibrium of the vortex exists if and only if $F_r < {\mathcal {F}}(1)$. Compared with the infinite fluid and $F_r \rightarrow 0$ cases, the wave effect causes the vortex to be destabilised to super-harmonic and long-wavelength sub-harmonic perturbations with generally faster growth rate for greater $F_r$ and smaller helix angle.

Direct numerical simulations are performed for incompressible, turbulent channel flow over a smooth wall and different sinusoidal wall roughness configurations at a constant $Re_\tau = 720$. Sinusoidal walls are used to study the effects of well-defined geometric features of roughness-amplitude, $a$, and wavelength, $\lambda$, on the flow. The flow in the near-wall region is strongly influenced by both $a$ and $\lambda$. Establishing appropriate scaling laws will aid in understanding the effects of roughness and identifying the relevant physical mechanisms. Using inner variables and the roughness function to scale the flow quantities provides support for Townsend's hypothesis, but inner scaling is unable to capture the flow physics in the near-wall region. We provide modified scaling relations considering the dynamics of the shear layer and its interaction with the roughness. Although not a particularly surprising observation, this study provides clear evidence of the dependence of flow features on both $a$ and $\lambda$. With these relations, we are able to collapse and/or align peaks for some flow quantities and, thus, capture the effects of surface roughness on turbulent flows even in the near-wall region. The shear-layer scaling supports the hypothesis that the physical mechanisms responsible for turbulent kinetic energy production in turbulent flows over rough walls are greatly influenced by the shear layer and its interaction with the roughness elements. Finally, a semiempirical model is developed to predict the contribution of pressure and skin friction drag on the roughness element based purely on its geometric parameters and the corresponding shear-layer velocity scale.

A large eddy simulation is performed to study secondary tones generated by a NACA0012 airfoil at angle of attack of $\alpha = 3^{\circ}$ with freestream Mach number of $M_{\infty} = 0.3$ and Reynolds number of $Re = 5 \times 10^4$. Laminar separation bubbles are observed over the suction side and near the trailing edge, on the pressure side. Vortex shedding occurs aft of the suction side separation bubble, and vortex interaction results in merging or bursting such that coherent structures or turbulent packets are advected towards the trailing edge. This mechanism modulates the amplitude of the incident pressure signal, leading to different levels of noise emission. Despite the intermittent occurrence of laminar–turbulent transition, the noise spectrum depicts a main tone with multiple equidistant secondary tones. To understand the role of flow instabilities on the tones, the linearised Navier–Stokes equations are examined in their operator form through biglobal stability and resolvent analyses, and by time evolution of disturbances using a matrix-free method. These linear global analyses reveal amplification of disturbances over the suction side separation bubble. Spanwise-averaged pressure fluctuations elucidate aspects of the acoustic feedback loop mechanism in the nonlinear solutions. This feedback process is self-sustained by acoustic waves radiated from the trailing edge, which reach the most sensitive flow location near the leading edge, as identified by the resolvent analysis. Flow disturbances arising from secondary diffraction and phase interference among the most unstable frequencies computed in the eigenspectrum are shown to have an important role in the feedback loop.

Euler's equations govern the behaviour of gravity waves on the surface of an incompressible, inviscid and irrotational fluid of arbitrary depth. We investigate the spectral stability of sufficiently small-amplitude, one-dimensional Stokes waves, i.e. periodic gravity waves of permanent form and constant velocity, in both finite and infinite depth. We develop a perturbation method to describe the first few high-frequency instabilities away from the origin, present in the spectrum of the linearization about the small-amplitude Stokes waves. Asymptotic and numerical computations of these instabilities are compared for the first time, with excellent agreement.

The objective of the present study is to investigate turbulence–coagulation interaction via direct numerical simulation (DNS) coupled with the population balance equation (PBE). Coagulation is an important process in several environmental and engineering applications involving turbulent flow, including soot formation, gas-phase synthesis of nanoparticles and atmospheric processes, but its interaction with turbulence is not yet fully understood. Particle dynamics can be described by the PBE, whose Reynolds decomposition leads to unclosed terms involving correlations of number density fluctuations. In this work, we employ a discretisation (sectional) method for the solution of the PBE, which is free of a priori assumptions regarding the particle size distribution (PSD), and couple it with a DNS for the flow field in order to study the behaviour and significance of the unknown correlations. At present, it is not feasible to resolve the Batchelor scales that result from diffusion at high Schmidt number, hence a unity Schmidt number is employed. The investigation is conducted on a three-dimensional planar jet laden with monodisperse nanoparticles, and coagulation in the free-molecule regime is considered. The correlations due to turbulent fluctuations of the particle number density are calculated at several points in the domain and found to be positive in most cases, except close to the jet break-up. The transport equation for the moments of the PSD is also studied, and it is found that the correlations make a considerable contribution to the time-averaged coagulation source term, up to $20\,\%$ on the jet centreline and $40\,\%$ close to the edges.

We have numerically investigated the turbulent flow and sediment grain motion in an open-channel flow configuration over a subaqueous sediment bed featuring two-dimensional transverse ripples at moderate Reynolds number and super-critical Shields number values. The simulation data, which were generated by means of particle-resolved direct numerical simulation, are the same as in our previous work (Kidanemariam & Uhlmann, J. Fluid Mech., vol. 818, 2017, pp. 716–743). By carefully choosing the computational box sizes, we were able to accommodate single ripple units which form over an initially flat sediment bed at a wavelength equal to the domain length. The ripples then evolve into their asymmetric shape relatively quickly and eventually migrate downstream steadily while maintaining their shape and size. In the present study, using a ripple-conditioned phase-averaging procedure, we are able to obtain novel insights into the evolution of the turbulent flow and particle motion over the bedforms, in particular the spatial structure of the basal shear stress and its relation to the particle flow rate. Our analysis confirms that the boundary shear-stress maximum is located upstream of the ripple crest, while the particle flow rate is essentially in phase with the ripple topology, with an average phase difference between the two in the range of 18–19 particle diameters for the considered parameter values. We were further able to confirm the link between the sediment flux relaxation behaviour and the observed shear-stress/geometry lag, by direct evaluation of the saturation length scale.

We analyse the instability of a vortex column in a dilute polymer solution at large ${{Re}}$ and ${{De}}$ with ${{El}} = {{De}}/{{Re}}$, the elasticity number, being finite. Here, ${{Re}} = \varOmega _0 a^2/\nu$ and ${{De}} = \varOmega _0 \tau$ are, respectively, the Reynolds and Deborah numbers based on the core angular velocity ($\varOmega _0$), the radius of the column ($a$), the total (solvent plus polymer) kinematic viscosity ($\nu = (\mu _s +\mu _p)/\rho$ with $\mu _s$ and $\mu _p$ being the solvent and polymer contributions to the viscosity) and the polymeric relaxation time ($\tau$). The stability of small-amplitude perturbations in this distinguished limit is governed by the elastic Rayleigh equation whose spectrum is parameterized by ${E} = {{El}}(1-\beta )$, $\beta$ being the ratio of the solvent to the solution viscosity. The neglect of the relaxation terms, in the said limit, implies that the polymer solution supports undamped elastic shear waves propagating relative to the base-state flow. Unlike the neutrally stable inviscid case, an instability of the vortex column arises for finite ${E}$ due to a pair of elastic shear waves being driven into a resonant interaction under the differential convection by the irrotational shearing flow outside the core. An asymptotic analysis for the Rankine profile shows the absence of an elastic threshold for this instability. The growth rate is $O(\varOmega _0)$ for order unity $E$, although it becomes transcendentally small for ${E} \ll 1$, being $O(\varOmega _0 {E}^2{\rm e}^{-1/{E}^{{1}/{2}}})$. An accompanying numerical investigation shows that the instability persists for smooth monotonically decreasing vorticity profiles, provided the radial extent of the transition region (from the rotational core to the irrotational exterior) is less than a certain ${E}$-dependent threshold.

The dynamics of a cylinder arranged between two sidewalls in a uniform flow is experimentally investigated. To investigate the effect of sidewalls on flow-induced vibration, both circular and square cylinders are considered. The gap between cylinder and sidewalls is sufficiently small to induce the oscillating cylinder to periodically impact the walls under certain conditions. The dynamic responses of a circular cylinder change dramatically depending on whether the cylinder impacts the walls. An impacting circular cylinder can oscillate with a large amplitude beyond a critical reduced velocity, the magnitude of which is restricted by the gap distance, whereas a non-impacting circular cylinder only oscillates in a lock-in region of the reduced velocity. The periodic impact with the sidewalls, rather than lock-in with vortex shedding, allows the large-amplitude oscillations of the impacting cylinder to persist. The impacting circular cylinder exhibits strong hysteresis, which is not observed for the non-impacting cylinder. Furthermore, the oscillation frequency of the impacting cylinder is proportional to the reduced velocity. The periodic impact acts to improve the power extracted by a damping mechanism in a broader range of reduced velocity. Meanwhile, for a square cylinder between sidewalls, oscillation by galloping is suppressed, and no impacts occur over the entire range of the reduced velocity. The suppression is caused by shear-layer reattachment on the side surface of the square cylinder, which is generally observed at a large angle of incidence for an isolated square cylinder.

Natural convection adjacent to a curved vertical wall is widely present. Unfortunately, the effect of curvature on the transient thermal boundary layer (TBL) adjacent to the concave vertical wall has been neglected. In this study, dynamical evolution and thermal process of transient natural convection in a vertical circular pipe are discussed using scaling analysis, a boundary flow regime for the thin TBL without merging and a duct flow regime for the TBL with merging at the axis of the pipe are distinguished. The scaling laws quantifying the dependence of thickness, velocity and flow rate of the TBL of the fluid with the fixed Prandtl number in the vertical pipe on the Rayleigh number (RaT and Raq) and the ratio of height to radius of the pipe (A) are first reported for the isothermal and isoflux conditions. The curvature effect becomes stronger with the increase of the thickness of the TBL. Under the duct flow regime, the non-dimensional flow rate is scaled with $Ra_T^{1/2}{A^{ - 1}}$ for the isothermal condition and with $Ra_q^{1/2}{A^{ - 3/2}}$ for the isoflux condition. The scaling laws of the thickness, velocity and the flow rate of the TBL in the vertical pipe are validated based on the numerical results from direct numerical simulation (DNS) with good precision. The scaling coefficient is also presented under different regimes and conditions, which can serve as a design guide to determine natural convection in the vertical circular pipe.

The inertial sublayer of adverse pressure-gradient (APG) turbulent boundary layers is investigated using new experimental measurements ($7000 \lesssim \delta ^+ \lesssim 7800$), existing lower Reynolds number experimental ($\delta ^+ \approx 1000$) and computational ($\delta ^+<800$) data sets, where $\delta ^+$ is the friction Reynolds number. In the present experimental set-up the boundary layer is under modest APG conditions, where the Clauser PG parameter $\beta$ is ${\leq }1.8$. Well-resolved hot-wire measurements are obtained at the Flow Physics Facility at the University of New Hampshire in the region of an APG ramp. Comparisons are made with zero pressure-gradient turbulent boundary layer (ZPG TBL) experimental data at similar Reynolds number and numerical simulation data at lower Reynolds number. The main aims of the present study centre on the inertial sublayer of the APG TBL and the degree to which its characteristics are similar to those of the ZPG TBL. This investigation utilizes equation-based analyses and empirical approaches. Among other results, the data suggest that even though the APG TBL streamwise variance does not exhibit a logarithmic profile (unlike the ZPG TBL) both ZPG and APG TBLs exhibit distance-from-the-wall scaling on the inertial sublayer. Theoretical arguments suggest that wall-distance scaling resulting from a self-similar dynamics is consistent with both a single velocity scale leading to a log-law in mean velocity profile as well as multiple velocity scales leading to a power-law mean velocity profile.

In this work, we show that the double-periodic boundary conditions typically applied in numerical simulations of elastic turbulence can lead to significantly incorrect results if not treated properly. This is demonstrated by simulating elastic turbulence using the popular four-roll mill benchmark at different levels of periodicity, namely, 16, 36 and 64 rolls using the popular Oldroyd-B model with added artificial diffusivity. We find that the initial onset of elastic turbulence causes a breakdown in symmetry independent of periodicity, which is characterised by a leading vortex and is known to be attributed to artificial diffusivity. Beyond this initial transition, the standard four-roll mill case transitions into a periodic state, a well-known characteristic from the literature. On the other hand, the cases with higher levels of periodicity quickly overcome the effects of a leading vortex and experience purely chaotic flow fluctuations, characterised by a broadband spectrum and steep power law behaviour. Certain qualities of the flow at higher levels of periodicity are reminiscent of the true solutions of elastic turbulence obtained numerically without any artificial diffusivity (Gupta & Vincenzi, J. Fluid Mech., vol. 870, 2019). These results suggest that the well-known periodic states observed for the four-roll mill are due to insufficient periodicity as the problem transitions into the elastic turbulence regime, leading to a dominant vortex cycling around all four quadrants of the unit cell throughout time unable to recover the initial symmetry. This work demonstrates the importance and caution required when applying periodic boundary conditions in numerical experiments of the elastic turbulence regime and further emphasises the impact and care required for artificial diffusivity.

Predictive models for near-wall velocity and temperature fluctuations in compressible wall-bounded turbulence are developed in the present study based on the model proposed by Marusic et al. (Science, vol. 329 (5988), 2010, pp. 193–196), which incorporates the superposition and amplitude modulation effects of the large-scale motions in the outer region on near-wall turbulence. The density variation is involved in the predictive model for velocity fluctuations to achieve Mach number independence. The predictive model for temperature fluctuations is derived to keep its consistency with the strong Reynolds analogy, in which the modulation effect is supposed to be cast as the quadratic function of the large-scale velocity fluctuations. An algebraic method is proposed to directly determine the modulation coefficients and extract the universal signals. A direct numerical simulation (DNS) of turbulent channel flow at the friction Reynolds number of $1170$ and bulk Mach number of $2.88$ is carried out for parameter calibration and validations. The variances and joint probability density functions of the predicted velocity and temperature fluctuations agree well with the DNS results.

The flow of granular materials through a vertical channel is examined using the discrete element method (DEM) and the recent continuum models of Henann & Kamrin (Proc. Natl Acad. Sci. USA, vol. 110, 2013, pp. 6730–6735), Barker et al. (Proc. R. Soc. Lond. A, vol. 473, 2017, p. 20160846), Schaeffer et al. (J. Fluid Mech., vol. 874, 2019, pp. 926–951) and Dsouza & Nott (J. Fluid Mech., vol. 888, 2020, p. R3). The channel is bounded by walls separated by a distance $2 \, W$ in the $x$-direction. For the DEM, periodic boundary conditions are used in the $z$- and $y$- (vertical) directions with no exit at the bottom of the channel. The governing equations reduce to ordinary differential equations in the $x$-direction. There is a plug layer near the centre and a shear layer near the wall, as observed in experiments. There is a decrease in the solids fraction $\phi$ in the shear layer, except for the models of Barker et al. and Henann & Kamrin. A modification of the latter gives more realistic $\phi$ profiles. The thickness of the shear layer depends on $2\,W$ and the bulk solids fraction $\bar {\phi }$. For all the models, solutions could not be obtained for some parameter values. An example is the negative fluidity in the model of Henann & Kamrin. The model of Dsouza & Nott predicts much higher normal stresses, possibly because of large contributions from the non-local terms. None of the models specify a complete set of boundary conditions (b.c.). The DEM results suggest that the slip velocity and the wall friction b.c. lead to a slip length and an angle of wall friction that are independent of $2\,W$. The models are based on extensions of the equations for slow, rate-independent flow. A model that includes collisional effects, such as kinetic theory, should be combined with the present models. A preliminary analysis of the kinetic theory model of Berzi et al. (J. Fluid Mech., vol. 885, 2020, p. A27), shows that it may have undesirable feature.

We study the experimental properties of exchange flows in a stratified inclined duct, which are simultaneously turbulent, strongly stratified by a mean vertical density gradient, driven by a mean vertical shear, and continuously forced by gravity. We focus on the ‘core’ shear layer away from the duct walls, where these flows are excellent experimentally realisable approximations of canonical hyperbolic-tangent stratified shear layers, whose forcing allows mean and turbulent properties to reach quasi-steady states. We analyse state-of-the-art data sets of the time-resolved density and velocity in three-dimensional subvolumes of the duct in 16 experiments covering a range of flow regimes (Holmboe waves, intermittent turbulence, full turbulence). In this Part 1 we first reveal the permissible regions in the multidimensional parameter space (Reynolds number, bulk Richardson number, velocity-to-density layer thickness ratio), and their link to experimentally controllable parameters. Reynolds-averaged balances then reveal the subtle momentum forcing and dissipation mechanisms in each layer, the broadening or sharpening of the density interface, and the importance of the streamwise non-periodicity of these flows. Mean flows suggest a tendency towards self-similarity of the velocity and density profiles with increasing turbulence, and gradient Richardson number statistics support prior ‘internal mixing’ theories of ‘equilibrium Richardson number’, ‘marginal stability’ and ‘self-organised criticality’. Turbulent volume fractions based on enstrophy and overturn thresholds quantify the nature of turbulence between different regimes in different regions of parameter space, while highlighting the challenges of obtaining representative statistics in spatiotemporally intermittent flows. These insights may stimulate and assist the development of numerical simulations with a higher degree of experimental realism.

In this Part 2 we study further experimental properties of two-layer exchange flows in a stratified inclined duct, which are turbulent, strongly stratified, shear-driven and continuously forced. We analyse the same state-of-the-art data sets using the same ‘core’ shear-layer methodology as in Part 1 (Lefauve & Linden, J. Fluid Mech., vol. 937, 2022, A34), but we focus here on turbulent energetics and mixing statistics. The detailed analysis of kinetic and scalar energy budgets reveals the specificity and scalings of ‘SID turbulence’, while energy spectra provide insight into the current strengths and limitations of our experimental data. The anisotropy of the flow at different scales characterises the turbulent kinetic energy production and dissipation mechanisms of Holmboe waves and overturning turbulence. We then assess standard mixing parameterisation models relying on uniform eddy diffusivities, mixing lengths, flux parameters, buoyancy Reynolds numbers or turbulent Froude numbers, and we compare our representative values with the stratified mixing literature. The dependence of these measures of mixing on controllable flow parameters is also elucidated, providing asymptotic estimates that may be extrapolated to more strongly turbulent flows, quantified by the product of the tilt angle of the duct and the Reynolds number. These insights may serve as benchmark for the future generation of experimental data with superior spatio-temporal resolution required to probe increasingly vigorous turbulence.

In the present work, the laminar–turbulent transition of the flow evolving around a low-pressure turbine blade has been investigated. Direct numerical simulations have been carried out for two different free stream turbulence intensity (FSTI) levels to investigate the role of free stream oscillations on the evolution of the blade boundary layer. Emphasis is placed on identifying the mechanisms driving the formation and breakup of coherent structures in the high FSTI case and how these processes are affected by the leading-edge receptivity and/or by the continuous forcing in the blade passage. Proper orthogonal decomposition (POD) has been adopted to provide a clear statistical representation of the shape of the structures. Extended POD projections provided temporal and spanwise correlations that allowed us to identify dominant temporal structures and spanwise wavelengths in the transition process. The extended POD analysis shows that the structures on the pressure side are not related to what happens at the leading edge. The results on the suction side show that the modes defining the leading edge and the passage bases correlate with coherent structures responsible for the transition. The most energetic mode of the passage basis is strongly related to the most amplified wavelength in the boundary layer and breakup events leading to transition. Modes with a smaller spanwise wavelength belong to the band predicted by optimal disturbance theory, they amplify with a smaller gain in the rear suction side, and they show the highest degree of correlation between the passage region and the rear suction side.