We studied flow organization and heat transfer properties in mixed turbulent convection within Poiseuille–Rayleigh–Bénard channels subjected to temporally modulated sinusoidal wall temperatures. Three-dimensional direct numerical simulations were performed for Rayleigh numbers in the range $10^6 \leqslant Ra \leqslant 10^8$, a Prandtl number $Pr = 0.71$ and a bulk Reynolds number $Re_b \approx 5623$. We found that high-frequency wall temperature oscillations had minimal impact on flow structures, while low-frequency oscillations induced adaptive changes, forming stable stratified layers during cooling. Proper orthogonal decomposition (POD) analysis revealed a dominant streamwise unidirectional shear flow mode. Large-scale rolls oriented in the streamwise direction appeared as higher POD modes and were significantly influenced by lower-frequency wall temperature variations. Long-time-averaged statistics showed that the Nusselt number increased with decreasing frequency by up to 96 %, while the friction coefficient varied by less than 15 %. High-frequency modulation predominantly influenced near-wall regions, enhancing convective effects, whereas low frequencies reduced these effects via stable stratified layer formation. Phase-averaged statistics showed that high-frequency modulation resulted in phase-stable streamwise velocity and temperature profiles, while low-frequency modulation caused significant variations due to weakened turbulence. Turbulent kinetic energy (TKE) profiles remained high near the wall during both heating and cooling at high frequency, but decreased during cooling at low frequencies. A TKE budget analysis revealed that during heating, TKE production was dominated by shear near the wall and by buoyancy in the bulk region; while during cooling, the production, distribution and dissipation of TKE were all nearly zero.

The resonance mechanism in the initial of wind-wave generation proposed by Phillips (1957. J. Fluid Mech. 2, 417–445) is a foundation of wind-wave generation theory, but a precise theoretical quantification of wave energy growth in this initial stage has not been obtained yet after more than six decades of research. In this study, we aim to address this knowledge gap by developing an analytical approach based on a novel complex analysis method to theoretically investigate the temporal evolution of the wave energy in the Phillips initial stage. We quantitatively derive and analyse the growth behaviour of the surface wave energy and obtain an analytical solution for its upper bound. Our result highlights the crucial effects of surface tension. Because the phase velocity of gravity–capillary waves has a minimal value at a critical wavenumber, gravity–capillary waves and gravity waves (which neglect surface tension) exhibit distinct resonance curve properties and wave energy growth behaviours. For gravity waves, the resonance curve extends indefinitely; for gravity–capillary waves, it either forms a finite-length curve or does not exist, depending on the wind speed. The leading-order term of the upper-bound solution of the energy of gravity waves increases linearly over time, while for gravity–capillary waves, the term increases linearly over time under strong wind conditions but remains finite under weak wind conditions. This theoretical study provides an analytical framework for the generation of wind-waves in the Phillips initial stage, which may inspire further theoretical, numerical and experimental research.

This study introduces a novel approach to investigate the Reynolds analogy in complex flow scenarios. It is shown that the total mechanical energy $\mathit {B}$, viz. the sum of kinetic energy and pressure work, and the field $\Gamma =\theta ^2/2$ (where $\theta$ is the transported passive scalar) are governed by two equations that are similar in form, when time-averaged for statistically stationary flows. For fully developed channel flows the integral energy balance links the mean bulk velocity and scalar with the volume averages of the respective dissipation rates, allowing the assessment of the Reynolds analogy in terms of the dissipation fields. This approach is tested on direct numerical simulation data of rough-wall turbulent channel flow at two different roughness Reynolds numbers, namely $k^+=15$ and $k^+=90$. For a unit Prandtl number, the same qualitative behaviour is observed for the mean wall-normal distributions of the budget-equation terms of $B$ and $\Gamma$, the latter being larger than the corresponding terms in the mechanical-energy budget. The Reynolds decomposition of the flow into temporal mean and stochastic parts reveals that roughness primarily affects the mean-flow dissipation. For the $k^+=90$ case, the analysis shows that attached-flow and high-shear regions dominate the integral mean scalar and momentum transfer and exhibit the greatest differences between the mean mechanical and scalar dissipation rates. In contrast, well-mixed regions, sheltered by large roughness elements, contribute similarly and minimally to the integral scalar and momentum transfer.

We analysed the performance of convolutional autoencoders in generating reduced-order representations of the temperature field of two-dimensional Rayleigh–Bénard flows at $\textit{Pr} =1$ and Rayleigh numbers extending from $10^6$ to $10^8$, capturing the range where the flow transitions to turbulence. We present a way of estimating the minimum number of dimensions needed by the autoencoders to capture all the relevant physical scales of the data that is more apt for highly multiscale flows than previous criteria applied to lower-dimensional systems. We compare our architecture with two regularized variants as well as with linear methods, and find that manually fixing the dimension of the latent space produces the best results. We show how the estimated minimum dimension presents a sharp increase around $Ra\sim 10^7$, when the flow starts to transition to turbulence. Furthermore, we show how this dimension does not follow the same scaling as the physically relevant scales, such as the dissipation length scale and the thermal boundary layer.

We investigate the linear instability of flows that are stable according to Rayleigh’s criterion for rotating fluids. Using Taylor–Couette flow as a primary test case, we develop large-Reynolds-number-matched asymptotic expansion theories. Our theoretical results not only aid in detecting instabilities previously reported by Deguchi (Phys. Rev. E, vol 95, 2017, p. 021102(R)) across a wide parameter range, but also clarify the physical mechanisms behind this counterintuitive phenomenon. Instability arises from the interaction between large-scale inviscid vortices and the viscous flow structure near the wall, which is analogous to Tollmien–Schlichting waves. Furthermore, our asymptotic theories and numerical computations reveal that similar instability mechanisms occur in boundary layer flows over convex walls.

Experiments on microfluidic core–annular flows demonstrated a transition from a continuous core jet to core-fluid drops and slugs separated by the annular fluid films/slugs due to absolute instability. The flows in the higher-generation airways could be modelled as core–annular flow with the laminar core airflow and annular airway surface liquid (ASL). Thus, if an absolute instability exists in the higher-generation airways, then it could lead to ASL film/slug-induced airway closure, necessitating the present study. Taking cues from previous studies, we derive an evolution equation using the lubrication approximation. The analysis, using the dispersion relation obtained from the evolution equation, predicts the existence of the critical capillary number $Ca_c$ such that, for $Ca < Ca_c$, the flow will be absolutely unstable for vanishing Reynolds number $Re$. The parameter $Ca_c$ exhibits the scaling as $Ca_c \sim (1-H)^2/\mu _r$, where $1-H$ is the dimensionless thickness of the ASL, and $\mu _r$ is the ratio of the air viscosity to the ASL viscosity. In agreement with the experimental observations, for a healthy lung, the analysis predicts absolute instability triggered airway closure only at the end of expiration during a breathing cycle. For a diseased lung, the ASL thickness and viscosity drastically increase the possibility of absolutely unstable flow and, thus, airway closure. Increasing inertial effect (i.e. $Re$) exacerbates airway closure by curtailing the convectively unstable region. Similarly, the ASL shear thinning widens the absolute instability parametric region. Thus, the present analysis demonstrates a pathway for airway closure in the higher-generation airways due to absolute instability.

This study investigates the spatial distribution of inertial particles in turbulent Taylor–Couette flow. Direct numerical simulations are performed using a one-way coupled Eulerian–Lagrangian approach, with a fixed inner-wall Reynolds number of 2500 for the carrier flow, while the particle Stokes number ($St$) varies from 0.034 to 1 for the dispersed phase. We first examine the issue of preferential concentration of particles near the outer-wall region. Employing two-dimensional Voronoï analysis, we observe a pronounced particle clustering with increasing $St$, particularly evident in regions of low fluid velocity. Additionally, we investigate the concentration balance equation, inspired by the work of Johnson et al. (J. Fluid Mech., vol. 883, 2020, A27), to examine the particle radial distribution. We discern the predominant sources of influence, namely biased sampling, turbophoresis and centrifugal effects. Across all cases, centrifugal force emerges as the primary driver, causing particle migration toward the outer wall. Biased sampling predominantly affects smaller inertial particles, driving them toward the inner wall due to sampling within Taylor rolls with inward radial velocity. Conversely, turbophoresis primarily impacts larger inertial particles, inducing migration towards both walls where turbulent intensity is weaker compared with the bulk. With the revealed physics, our work provides a basis for predicting and controlling particle movement and distribution in industrial applications.

The turbulent boundary layer is a region where both preferential dissipation of energy and the production of significant vorticity arises as a consequence of the strong velocity gradients. Previous work has shown that, following a Reynolds decomposition, the purely fluctuating component of the enstrophy production is the dominant term. Near the wall this varies in a complex manner with height. In this study, we additionally decompose the strain rate and vorticity terms into normal and non-normal components using a Schur decomposition and are able to explain all these features in terms of contributions at different heights from constituents involving different combinations of normal and non-normal quantities. What is surprising about our results is that, while the mean shear and the action of larger-scale structures should mean that non-normal effects are of over-riding importance at the wall, the most important individual term involves the fluctuating normal strain rate in the transverse direction. In part, this is because of a strong correlation between this term and the non-normal vorticity with a transverse axis, but it is also the case that individual components of the purely non-normal enstrophy production are negative in the mean. Hence, a local strain rate that is orthogonal to the direction of the dominant mean and fluctuating shear plays a crucial role in amplifying vorticity that is yet to have developed a local component. These conclusions support the emphasis in the control literature on the transverse velocity components at the wall.

Inspired by laboratory experiments showing internal waves generated by a plume impinging upon a stratified fluid layer (Ansong & Sutherland. 2010 J. Fluid Mech. 648, 405–434), we perform large eddy simulations in three dimensions to examine the structure and source of internal waves emanating from the top of a plume that rises vertically into stratification whose strength ranges over two orders of magnitude between different simulations. Provided the plume is sufficiently energetic to penetrate into the stratified layer, internal waves are generated with frequencies in a relatively narrow band moderately smaller than the buoyancy frequency. Through adaptations of ray theory including viscosity and use of dynamic mode decomposition, we show that the waves originate from within the turbulent flow rather than at the turbulent/non-turbulent interface between the fountain top and the surrounding stratified fluid.

Understanding wave kinematics is crucial for analysing the thermodynamic effects of sloshing, which can lead to pressure drops in non-isothermal cryogenic fuel tanks. In the research reported here, Faraday waves in a horizontal circular tank (partially filled with water) under vertical excitation are investigated. The tank geometry is referred to as a horizontal circular tank throughout, with its circular face oriented perpendicular to the horizontal plane. Firstly, this paper addresses the eigenvalue problem through linear potential flow theory, in order to provide theoretical evidence of Faraday waves in horizontal circular tanks, the impact the density ratio has on the eigenvalues is then considered. Secondly, an experimental investigation testing multiple liquid fill levels is conducted. A soft-spring nonlinear response is demonstrated throughout the parameter space. The results showed larger sloshing amplitudes for low fill levels and smaller sloshing amplitudes for high fill levels. Asymmetry between anti-nodes at the container sidewalls and through the tank centreline are evident for low fill levels. Moreover, the sloshing wave amplitude at which breaking waves occur is smaller for high fill level conditions. Finally, period tripling was observed for all fill levels tested, confirming nonlinear mode interactions before the onset to wave breaking.

We report the first shock-tube experiments on Richtmyer–Meshkov instability at a single-mode light–heavy interface accelerated by a strong shock wave with Mach number higher than 3.0. Under the proximity effect of the transmitted shock and its induced secondary compression effect, the interface profile is markedly different from that in weakly compressible flows. For the first time, the validity of the compressible linear theory and the failure of the impulsive model in predicting the linear amplitude evolution in highly compressible flows are verified through experiments. Existing nonlinear and modal models fail to accurately describe the perturbation evolution, as they do not account for the shock proximity and secondary compression effects on interface evolution. The shock proximity effect manifests mainly in the early stages when the transmitted shock remains close to the interface, while the effect of secondary compression manifests primarily at the period when interactions of transverse shocks occur at the bubble tips. Based on these findings, we propose an empirical model capable of predicting the bubble evolution in highly compressible flows.

Acoustic resonances in cascade structures may cause structural damage and instability problems in aero-engines and other industrial plants; thus, developing corresponding prediction methods is important. However, works published in the open literature mostly focus on the special case of the stationary Parker modes and provide little knowledge into the rotating resonances in annular cascades, especially in the presence of non-zero background mean flows. This paper develops a three-dimensional semi-analytic model to study the acoustic resonances in an annular cascade in the presence of axial mean flow. The model applies an unsteady cascade response based on the three-dimensional lifting surface method to construct a matrix equation. Characteristic frequencies are solved in the complex domain by numerically searching for singular points. Both the oscillation frequency and the growth rate of the three-dimensional resonance modes are theoretically calculated for the first time under non-zero mean flow conditions. The results reveal an organised distribution with varying inter-blade phase angle and show obvious change with the background flow speed. It is found that the unsteady vortex shedding from the trailing edges of the cascade is a key factor influencing the dissipation rate of the resonance modes. In addition, the important effects of acoustic scattering by the cascade during resonances are examined, which qualitatively corroborate some previous experimental observations.