Electrophoretic characterization of nano- and micro-metre scaled bubbles and drops is increasingly important in environmental and health sciences. Despite more than a hundred years of study, the interpretation of bubble electrophoresis data remains an unresolved fundamental problem that bridges fluid mechanics and interfacial science. This paper examines, from a theoretical perspective, how the electrophoretic mobility of small drops and bubbles responds to the interfacial kinetic-exchange rate and interfacial-charge mobility: factors that have been largely overlooked, but which provide new insights on the interpretation of $\zeta$-potentials, which are routinely used to assess surface charge density. A variety of outcomes are demonstrated, each reflecting subtle balances of hydrodynamic and electrical forces, modulated by interfacial thermodynamics and transport. Among the findings is that irreversibly bound charge with low interfacial mobility furnishes rigid-sphere behaviour; whereas interfacial charge with high mobility produces the characteristically high electrophoretic mobilities of non-conducting, uniformly charged fluid spheres. Outcomes are more complex when drops and bubbles have interfacial charge that seeks local equilibrium with the immediately adjacent electrolyte. For example, the present model shows that interfacial-charge mobility regularizes the singular behaviour predicted by theories for fluid spheres bearing high, perfectly uniform surface charge.

The instantaneous structure of a turbulent boundary layer (TBL) subjected to freestream turbulence (FST) is investigated at several streamwise locations downstream of an active turbulence-generating grid. Using planar particle image velocimetry, three grid sequences are tested at four streamwise locations with FST intensities up to 10.9 %. A low-turbulence reference case is included for comparison. A novel method is proposed to separate the instantaneous TBL and FST flows by identifying a distinct interface for each realisation using probability density functions of the vorticity field. Two alternative approaches are used to define the interfaces, based on either constant velocity contour lines or constant vorticity magnitude contour lines. The former is found to highlight the momentum events in the velocity fields, whereas the latter outlines the vortical features of the flow. Regardless of the interface choice, when faced with FST, the interface moves closer to the wall on average, and its location fluctuates more. When FST is present, the shear and mean spanwise vorticity magnitudes increase on the TBL side of the interface. Uniform momentum zones (UMZs) beneath the velocity interfaces are identified. In the presence of FST, UMZs located closer to the wall appear to be compressed, resulting in fewer identified UMZs. Moving downstream, the FST intensity decays while the TBL develops. As a result, many characteristics of the TBL recover to an undisturbed state, with the interface moving away from the wall, vorticity and turbulent fluctuations returning to their natural state undisturbed by FST and the number of detected UMZs increasing.

We demonstrate the first successful non-invasive stabilisation of nonlinear travelling waves in a straight cylindrical pipe using time-delayed feedback control working in various symmetric subspaces. By using an approximate linear stability analysis and by analysing the frequency-domain effect of the control using transfer functions, we find that solutions with well-separated unstable eigenfrequencies can have narrow windows of stabilising time delays. To mitigate this issue we employ a ‘multiple time-delayed feedback’ approach, where several control terms are included to attenuate a broad range of unstable eigenfrequencies. We implement a gradient descent method to dynamically adjust the gain functions in order to reduce the need for tuning a high-dimensional parameter space. This results in a novel control method where the properties of the target state are not needed in advance, and speculative guesses can result in robust stabilisation. This enables travelling waves to be stabilised from generic turbulent states and unknown travelling waves to be obtained in highly symmetric subspaces.

It is widely believed that statistical closure theories for dynamical systems provide statistics equivalent to those of the governing dynamical equations from which the former are derived. Here, we demonstrate counterexamples in the context of the widely used mean-field quasi-linear approximation applied to both deterministic and stochastic two-dimensional fluid dynamical systems. We compare statistics of numerical simulations of a quasi-linear model (QL) with statistics obtained by direct statistical simulation via a cumulant expansion closed at second order (CE2). We observe that although CE2 is an exact statistical closure for QL dynamics, its predictions can disagree with the statistics of the QL solution for identical parameter values. These disagreements are attributed to instabilities, which we term rank instabilities, of the second cumulant dynamics within CE2 that are unavailable in the QL equations.

In this work, the stability and transition to turbulence over blunt flat plates with different leading-edge radii are investigated computationally. The benchmark experimental work for comparative studies is conducted by Borovoy et al. (AIAA J., vol. 60, 2022, pp. 497–507). The freestream Mach number is 5, the unit Reynolds number is $6\times 10^7$ m$^{-1}$, and the maximum nose-tip radius 3 mm exceeds the experimental reversal value. High-resolution numerical simulation and stability analysis are performed. Three-dimensional broadband perturbation is added on the far field boundary to initiate the transition. The highlight of this work is that the complete physical process is considered, including the three-dimensional receptivity, linear and nonlinear instabilities, and transition. The experimental reversal phenomenon is reproduced favourably in the numerical simulation for the first time. Linear stability analysis shows that unstable first and second modes are absent in the blunt-plate flows owing to the presence of the entropy layer, although these modes are evident in the sharp-leading-edge case. Therefore, the transition on the blunt plate is due to non-modal instabilities. Numerical results for all the blunt-plate cases reveal the formation of streamwise streaky structures downstream of the nose (stage I) and then the presence of intermittent turbulent spots in the transitional region (stage II). In stage I, a preferential spanwise wavelength approximately 0.9 mm is selected for all the nose-tip radii, and low-frequency components are dominant. In stage II, high-frequency secondary instabilities appear to grow, which participate in the eventual breakdown. By contrast, leading-edge streaks are not remarkable in the sharp-leading-edge case, where transition is induced by oblique first and Mack second modes. The transition reversal beyond the critical nose-tip radius arises from an increasing magnitude of the streaky response in the early stage, while the transition mechanism stays similar qualitatively.