This paper investigates the transient characteristics of uniform momentum zones (UMZs) in a rapidly accelerating turbulent pipe flow using direct numerical simulation datasets starting from an initial friction Reynolds number ($Re_{\tau 0}) = 500$ up to a final friction Reynolds number ($Re_{\tau 1}) = 670$. Instantaneous UMZs are identified following the identification methodology proposed by Adrian et al. (2000 J. Fluid Mech. vol. 422, pp. 1–54). The present results reveal that, as the flow rapidly accelerates, the average number of UMZs drops. However, as the flow recovers, it is regained. This result is complemented by the temporal evolution of the average number of internal shear layers. The temporal evolution of UMZs reveals that UMZs sustain their hierarchical flow arrangement with slower zones near the wall and faster zones away from the wall throughout the rapid turbulent flow acceleration. The results show that UMZs speed up during the inertial and pre-transition phases, and progressively slow down during the transition and core-relaxation stages. It is also revealed that UMZs near the wall respond first to flow instability and show earlier signs of recovery based on UMZ kinematic results. Finally, the dominant quadrant behaviour of Reynolds shear stress within UMZs has been investigated. It is found that, prior to the flow excursion, the UMZs nearest to the wall are always $Q2$ dominated, while the rest of the UMZs are always $Q4$ dominated. This behaviour is detected to not change during and after the flow excursion, suggesting that this is a characteristic behaviour of UMZs in accelerating turbulent wall-bounded flows.

For smectic C* (SmC*) liquid crystals, configured in a bookshelf-type geometry between two horizontal parallel plates, with the bottom plate fixed and the top plate free to move, it is known from experiment that pumping can occur when an electric field is applied, i.e. an upward movement of the top plate through mechanical vibrations when the electric field is suddenly reversed. In this paper we revisit an earlier mathematical model for fast electric field reversal by removing an assumption made there on the velocity field; instead, we arrive at a time-dependent, two-dimensional squeeze-film model, which can ultimately be formulated in terms of a highly nonlinear integro-differential equation. Subsequent analysis leads to an unexpected solvability condition involving the five SmC* viscosity coefficients regarding the existence and uniqueness of solutions. Furthermore, we find that, when solutions do exist, they imply that the plate can move down as well as up, with the final resting position turning out to be dependent on the initial conditions; this is in stark contrast to the results of the earlier model.

Permanent gravity waves propagating in deep water, spanning amplitudes from infinitesimal to their theoretical limiting values, remain a classical yet challenging problem due to its inherent nonlinear complexities. Traditional analytical and numerical methods encounter substantial difficulties near the limiting wave condition due to singularities at sharp wave crests. In this study, we propose a novel hybrid framework combining the homotopy analysis method (HAM) with machine learning (ML) to efficiently compute convergent series solutions of Stokes waves in deep water for arbitrary wave amplitudes from small to theoretical limiting values, which show excellent agreement with established benchmarks. We introduce a neural network trained using only 20 representative cases whose series solution are given by means of HAM, which can rapidly predict series solutions across arbitrary steepness levels, substantially improving computational efficiency. Additionally, we develop a neural network to gain the inverse mapping from the conformal coordinates $(\theta , r)$ to the physical coordinates $(x,y)$, facilitating explicit and intuitive representations of series solutions in physical plane. This HAM–ML hybrid framework represents a powerful and efficient approach to compute convergent series in a whole range of physical parameters for water waves with arbitrary wave height including even limiting waves. In this way we establish a new paradigm to quickly obtain convergent series solutions of complex nonlinear systems for a whole range of physical parameters, thereby significantly broadening the scope of series solutions that can be easily gained by means of HAM even for highly nonlinear problems in science and engineering.

Magneto-gravity-precessional instability, which results from the excitation of resonant magneto-inertia-gravity (MIG) waves by a background shear generic to precessional flows, is addressed here. Two simple background precession flows, that of Kerswell (1993 Geophys. Astrophys. Fluid Dyn. vol 72, no. 1–4, pp. 107–144), and that of Mahalov (1993 Phys. Fluids A: Fluid Dyn. vol. 5, no. 4, pp. 891–900), are considered. We analytically perform an asymptotic analysis to order ${ O}(\varepsilon ),$ where $\varepsilon$ denotes the Poincaré number, i.e. the precession parameter, and determine the maximum growth rate of the destabilizing subharmonic resonances of MIG waves: that between two fast modes, that between two slow modes and that between a fast mode and a slow mode (mixed modes). The domains of the $(K_0 B_0/\varOmega _0, N/\varOmega _0)\hbox{-}$plane for which this instability operates are identified, where $1/K_0$ denotes a characteristic length scale, $B_0$ is the unperturbed Alfvén velocity, $\varOmega _0$ is the rotation rate and $N$ denotes the Brunt–Väisälä frequency. We demonstrate that the $N\rightarrow 0$ limit is, in fact, singular (discontinuous). At large $K_0B_0/\varOmega _0,$ stable stratification acts to suppress the destabilizing resonance between two fast modes as well as that between two slow modes, whereas it revives the destabilizing resonance between a fast mode and a slow mode provided $N\lt \varOmega _0,$ because, without stratification, the maximal growth rate of this instability approaches zero as $K_0B_0/\varOmega _0\rightarrow +\infty .$ This would be relevant for the generation of the mean electromotive force, and hence, the $\alpha \hbox{-}$effect in helical magnetized precessional flows under weak stable stratification. Diffusive effects on the instability is considered in the simple case where the magnetic and thermal Prandtl numbers are both equal to one.

Recent research at the Chimú site of Quebrada del Oso in the Chicama Valley, Peru indicates that the site functioned as a pre-Hispanic agricultural centre. This finding is relevant to debates about the nature and viability of the Chicama-Moche canal built by the Chimú state around the eleventh century AD.