In this paper, we study the effect of lateral wall vibrations on the excitation and evolution of non-modal perturbations in hypersonic boundary layers subject to low-frequency freestream vortical disturbances (FSVDs). A novel, high-efficiency numerical approach, combining the harmonic weakly nonlinear Navier–Stokes and nonlinear parabolised stability equation approaches, is developed, which is sufficient to accommodate both the rapid distortion of the perturbation in the leading-edge vicinity and the nonlinear development of finite-amplitude high-order harmonics in the downstream region. The boundary-layer response to low-frequency FSVDs shows a longitudinal streaky structure, for which the temperature perturbation shows much greater magnitude than the streamwise velocity perturbation. The lateral vibration induces a Stokes layer solution for the spanwise velocity perturbation, which interacts with the FSVD-induced perturbations and leads to a suppression of the non-modal perturbation and an enhancement of the downstream modal perturbation. The new perturbations excited by the FSVD–vibration interaction strengthen as the vibration intensifies, and they could become comparable with the FSVD-induced perturbations in downstream locations at a high vibration intensity, indicating a remarkable modification of the streaky structure and its instability property. Secondary instability (SI) analyses based on the streaky base flow indicate that the vibration could enhance or suppress the SI modes, depending on their initial phases over the vibration period. Overall, the average effect is that the low-frequency and high-frequency SI modes are stabilised and destabilised by the vibration, respectively. Since the high-frequency SI modes undergo higher amplifications, the subsequent bypass transition is likely to be promoted by relatively strong vibrations.

We perform direct numerical simulations of soluble bubbles dissolving in a Taylor–Couette (TC) flow reactor with a radius ratio of $\eta =0.5$ and Reynolds number in the range $0 \leq Re \leq 5000$, which covers the main regimes of this flow configuration, up to fully turbulent Taylor vortex flow. The numerical method is based on a geometric volume-of-fluid framework for incompressible flows coupled with a phase-change solver that ensures mass conservation of the soluble species, whilst boundary conditions on solid walls are enforced through an embedded boundary approach. The numerical framework is validated extensively against single-phase TC flows and competing mass transfer in multicomponent mixtures for an idealised infinite cylinder and for a bubble rising in a quiescent liquid. Our results show that when bubbles in a TC flow are mainly driven by buoyancy, theoretical formulae derived for spherical interfaces on a vertical trajectory still provide the right fundamental relationship between the bubble Reynolds and Sherwood numbers, which reduces to $Sh \propto \sqrt {Pe}$ for large Péclet values. For bubbles mainly transported by TC flows, the dissolution of bubbles depend on the TC Reynolds number and, for the turbulent configurations, we show that the smallest characteristic turbulent scales control mass transfer, in agreement with the small-eddy model of Lamont & Scott (AIChE J., vol. 16, 1970, pp. 513–519). Finally, the interaction between two aligned bubbles is investigated and we show that a significant increase in mass transfer can be obtained when the rotor of the apparatus is operated at larger speeds.

This work introduces a formulation of resolvent analysis that uses wavelet transforms rather than Fourier transforms in time. Under this formulation, resolvent analysis may extend to turbulent flows with non-stationary mean states. The optimal resolvent modes are augmented with a temporal dimension and are able to encode the time-transient trajectories that are most amplified by the linearised Navier–Stokes equations. We first show that the wavelet- and Fourier-based resolvent analyses give equivalent results for statistically stationary flow by applying them to turbulent channel flow. We then use wavelet-based resolvent analysis to study the transient growth mechanism in the near-wall region of a turbulent channel flow by windowing the resolvent operator in time and frequency. The computed principal resolvent response mode, i.e. the velocity field optimally amplified by the linearised dynamics of the flow, exhibits characteristics of the Orr mechanism, which supports the claim that this mechanism is key to linear transient energy growth. We also apply this method to non-stationary parallel shear flows such as an oscillating boundary layer, and three-dimensional channel flow in which a sudden spanwise pressure gradient perturbs a fully developed turbulent channel flow. In both cases, wavelet-based resolvent analysis yields modes that are sensitive to the changing mean profile of the flow. For the oscillating boundary layer, wavelet-based resolvent analysis produces oscillating principal forcing and response modes that peak at times and wall-normal locations associated with high turbulent activity. For the turbulent channel flow under a sudden spanwise pressure gradient, the resolvent modes gradually realign themselves with the mean flow as the latter deviates. Wavelet-based resolvent analysis thus captures the changes in the transient linear growth mechanisms caused by a time-varying turbulent mean profile.

Stochastically generated instantaneous velocity profiles are used to reproduce the outer region of rough-wall turbulent boundary layers in a range of Reynolds numbers extending from the wind tunnel to field conditions. Each profile consists in a sequence of steps, defined by the modal velocities and representing uniform momentum zones (UMZs), separated by velocity jumps representing the internal shear layers. Height-dependent UMZ is described by a minimal set of attributes: thickness, mid-height elevation, and streamwise (modal) and vertical velocities. These are informed by experimental observations and reproducing the statistical behaviour of rough-wall turbulence and attached eddy scaling, consistent with the corresponding experimental datasets. Sets of independently generated profiles are reorganized in the streamwise direction to form a spatially consistent modal velocity field, starting from any randomly selected profile. The operation allows one to stretch or compress the velocity field in space, increases the size of the domain and adjusts the size of the largest emerging structures to the Reynolds number of the simulated flow. By imposing the autocorrelation function of the modal velocity field to be anchored on the experimental measurements, we obtain a physically based spatial resolution, which is employed in the computation of the velocity spectrum, and second-order structure functions. The results reproduce the Kolmogorov inertial range extending from the UMZ and their attached-eddy vertical organization to the very-large-scale motions (VLSMs) introduced with the reordering process. The dynamic role of VLSM is confirmed in the $-u^{\prime }w^{\prime }$ co-spectra and in their vertical derivative, representing a scale-dependent pressure gradient contribution.

A stream of free-falling particles from a rectangular hopper, hereafter called a ‘curtain’, was characterised systematically using a well-resolved, non-intrusive optical shadowgraphic method, to reveal both an additional axial region and an additional dilute region distributed laterally on either side of the curtain, relative to those identified previously. The effects of particle size and hopper outlet thickness on the evolution of the particle curtain were separately isolated, whilst measuring particle mass flow rate. The curtains were characterised into four distinct axial regions, namely a near-field expansion region near to the hopper exit, a neck zone where the curtain contracts, a region of intermediate-field expansion and a far field with particles reaching terminal velocity. The initial expansion half-angle, $2.3^{\circ } \le \alpha \le 4.8^{\circ }$, was found to be insensitive to particle size, but to increase with hopper outlet thickness. The ‘trough’ in the neck zone was deduced to be caused by a pressure gradient driven by particle acceleration. The curtain expansion rate at the intermediate field was found to increase with a decrease in particle size and hopper outlet thickness. The outermost dilute-particle region was deduced to be caused by collisions, induced by gradients in the velocity profile near to the hopper exit. New dimensionless analysis reveals that the dynamics of curtains can be characterised broadly into two regimes, one in which the aerodynamics is dominant and the other where it is weak. Curtain transmittance was found to scale with the Froude number, highlighting the importance of particle momentum.