Sub-convective wall pressure fluctuations play a critical role in vibroacoustic and noise analyses of vehicle structures as they serve as the primary forcing function. However, measuring these fluctuations is challenging due to their weak pressure magnitudes, typically $10^{-3}{-}10^{-5}$ of convective fluctuations. This study introduces a non-intrusive measurement technique using an array of multi-pore Helmholtz resonator sensors to capture sub-convective fluctuations with high resolution. The array features large-area, spanwise-oriented sensors arranged linearly for optimal sampling. Results provide a continuous streamwise wavenumber–frequency spectrum, resolving sub-convective fluctuations with sufficient range and accuracy. Convergence analysis indicates that long sampling durations, $\mathcal{O}(10^6 \delta ^*/U_\infty )$, $\delta^*$ is the displacement thickness of the boundary layer. $U_\infty$ is the freestream velocity are necessary to capture true sub-convective levels. Comparisons with four existing wall pressure models, which account for sensor area averaging, reveal discrepancies in predicted levels, convection speed relations and convective ridge characteristics. Notably, the measured data align most closely with the Chase (1980, J. Sound Vib., vol.70, pp. 29–67) model at convective peak levels and in the sub-convective domain. However, the observed roll-off at wavenumbers exceeding the convective wavenumber decays more slowly than predicted, giving the convective ridge an asymmetric profile about the convective line. These findings underscore the need for improved wall pressure models that incorporate frequency-dependent convective speed relations, ridge asymmetry, and more accurate sub-convective levels. Further validation using a microphone array from Farabee & Geib (1991) confirms the accuracy of our measurements, which indicate sub-convective pressure levels lower than reported previously.

For Stokes waves in finite depth within the neighbourhood of the Benjamin–Feir stability transition, there are two families of periodic waves, one modulationally unstable and the other stable. In this paper we show that these two families can be joined by a heteroclinic connection, which manifests in the fluid as a travelling front. By shifting the analysis to the setting of Whitham modulation theory, this front is in wavenumber and frequency space. An implication of this jump is that a permanent frequency downshift of the Stokes wave can occur in the absence of viscous effects. This argument, which is built on a sequence of asymptotic expansions of the phase dynamics, is confirmed via energetic arguments, with additional corroboration obtained by numerical simulations of a reduced model based on the Benney–Roskes equation.

This paper explores the construction of quadratic Lyapunov functions for establishing the conditional stability of shear flows described by truncated ordinary differential equations, addressing the limitations of traditional methods like the Reynolds–Orr equation and linear stability analysis. The Reynolds–Orr equation, while effective for predicting unconditional stability thresholds in shear flows due to the non-contribution of nonlinear terms, often underestimates critical Reynolds numbers. Linear stability analysis, conversely, can yield impractically high limits due to subcritical transitions. Quadratic Lyapunov functions offer a promising alternative, capable of proving conditional stability, albeit with challenges in their construction. Typically, sum-of-squares programs are employed for this purpose, but these can result in sizable optimisation problems as system complexity increases. This study introduces a novel approach using linear transformations described by matrices to define quadratic Lyapunov functions, validated through nonlinear optimisation techniques. This method proves particularly advantageous for large systems by leveraging analytical gradients in the optimisation process. Two construction methods are proposed: one based on general optimisation of transformation matrix coefficients, and another focusing solely on the system’s linear aspects for more efficient Lyapunov function construction. These approaches are tested on low-order models of subcritical transition and a two-dimensional Poiseuille flow model with degrees of freedom nearing 1000, demonstrating their effectiveness and efficiency compared with sum-of-squares programs.

The passive flight of a thin wing or plate is an archetypal problem in flow–structure interactions at intermediate Reynolds numbers. This seemingly simple aerodynamic system displays an impressive variety of steady and unsteady motions that are familiar from fluttering leaves, tumbling seeds and gliding paper planes. Here, we explore the space of flight behaviours using a nonlinear dynamical model rooted in a quasisteady description of the fluid forces. Efficient characterisation is achieved by identification of the key dimensionless parameters, assessment of the steady equilibrium states and linear analysis of their stability. The structure and organisation of the stable and unstable flight equilibria proves to be complex, and seemingly related factors such as mass and buoyancy-corrected weight play distinct roles in determining the eventual flight patterns. The nonlinear model successfully reproduces previously documented unsteady states such as fluttering and tumbling while also predicting new types of motions, and the linear analysis accurately accounts for the stability of steady states such as gliding and diving. While the conditions for dynamic stability seem to lack tidy formulae that apply universally, we identify relations that hold in certain regimes and which offer mechanistic interpretations. The generality of the model and the richness of its solution space suggest implications for small-scale aerodynamics and related applications in biological and robotic flight.