Intermittent swimming behaviour is commonly observed in larval zebrafish, often attributed to energy-saving mechanisms. In this study, we utilize a hybrid approach combining deep reinforcement learning and the immersed boundary–lattice Boltzmann method to train a larval zebrafish-like swimmer to reach a target with minimized energy expenditure. We find that when the tail-beat period is fixed, continuous swimming emerges as the optimal strategy. However, when the tail-beat period is allowed to vary, intermittent swimming proves superior in energy performance, achieved through reductions in tail-beat amplitude and frequency. Our detailed analysis reveals that intermittent swimmers employ rapid backward tail flicks to attain high speeds, coupled with slower forward tail flicks and coasting phases to conserve energy. Furthermore, we derive scaling laws governing the swimming performance of trained fish. These results offer valuable insights into the intermittent swimming patterns of fish, with implications for understanding bio-inspired locomotion and informing the design of energy-efficient aquatic systems.

The impact of intrinsic compressibility effects – changes in fluid volume due to pressure variations – on high-speed wall-bounded turbulence has often been overlooked or incorrectly attributed to mean property variations. To quantify these intrinsic compressibility effects unambiguously, we perform direct numerical simulations of compressible turbulent channel flows with nearly uniform mean properties. Our simulations reveal that intrinsic compressibility effects yield a significant upward shift in the logarithmic mean velocity profile that can be attributed to the reduction in the turbulent shear stress. This reduction stems from the weakening of the near-wall quasi-streamwise vortices. In turn, we attribute this weakening to the spontaneous opposition of sweeps and ejections from the near-wall expansions and contractions of the fluid, and provide a theoretical explanation for this mechanism. Our results also demonstrate that intrinsic compressibility effects play a crucial role in the increase in inner-scaled streamwise turbulence intensity in compressible flows, as compared with incompressible flows, which was previously regarded to be an effect of mean property variations alone.

Coherent structures over two distinct, organized wall perturbations – a transverse sinusoidal bump with and without small-scale longitudinal grooves – are studied using direct numerical simulations. Large-scale spanwise rollers (SRs) form via shear layer rollup past the bump peak, enveloping a large separation bubble (SB) for both a smooth wall (SW) and a grooved wall (GW). In a GW, small-scale alternatingly spinning jets emanating from the crests’ corners merge with the shear layer, altering the SRs compared with SRs in a SW. The underlying coherence of the highly turbulent SRs is educed via phase-locked ensemble averaging. Coherent vorticity contours of SRs are ellipses tilted downward, hence causing co-gradient Reynolds stress. The limited streamwise length of SB precludes SR tumbling, unlike in a free shear layer. The coherent field reveals minibubbles attached to the bump’s downstream wall with circulation opposite to that of the SB – they are larger, stronger and more numerous in GW than in SW – reducing skin friction. Compared with SW, the swirling jets in GW increase coherent production while decreasing incoherent production. Additionally, the jets push the SRs to travel faster and farther before reattachment. The SB experiences two different modes of oscillation due to high-frequency advection of the shear layer SR and low-frequency breathing of the SB, where the former dominates in GW and the latter in SW. Negative production is caused by counter-rotating vortex dipoles inducing flow ejections (for both SW and GW) and single vortices penetrating the grooves – both occurring in the region of flow acceleration.

This study investigates how the spatial configuration of submerged three-dimensional patches of vegetation impacts turbulence. Laboratory experiments were conducted in a channel with submerged patches of model vegetation configured with different patch area densities ($\phi _{p}$), representing the bed area fraction occupied by patches, ranging from 0.13 to 0.78, and different spatial patterns transitioning from two dimensional (channel-spanning patches) to three dimensional (laterally unconfined patches). These configurations produced a range of flow regimes within the canopy, from wake interference flow to skimming flow. At low area density ($\phi _{p}\lt0.5$), turbulence within the canopy increased with increasing $\phi _{p}$ regardless of spatial configuration, while at high area density ($\phi _{p}\gt0.5$), the relationship between turbulence and $\phi _{p}$ depended on the spatial configuration of the patches. For the same patch area density, the configuration with smaller lateral gaps generated stronger turbulence within the canopy. The relative contributions of wake and shear production also varied with the spatial configuration of the patches. At low area densities, wake production dominated over shear production, while at high area densities, shear production was more dominant due to an enhanced shear layer at the top of the canopy and reduced mean velocity within the canopy. A new predictive model for the channel-averaged turbulent kinetic energy (TKE) was developed as a function of channel-averaged velocity, canopy geometry, and patch area density, which showed good agreement with the measured TKE.

Deep reinforcement learning (DRL) is employed to develop control strategies for drag reduction in direct numerical simulations of turbulent channel flows at high Reynolds numbers. The DRL agent uses near-wall streamwise velocity fluctuations as input to modulate wall blowing and suction velocities. These DRL-based strategies achieve significant drag reduction, with maximum rates $35.6\,\%$ at $Re_{\tau }\thickapprox 180$, $30.4\,\%$ at $Re_{\tau }\thickapprox 550$, and $27.7\,\%$ at $Re_{\tau }\thickapprox 1000$, outperforming traditional opposition control methods. An expanded range of wall actions further enhances drag reduction, although effectiveness decreases at higher Reynolds numbers. The DRL models elevate the virtual wall through blowing and suction, aiding in drag reduction. However, at higher Reynolds numbers, the amplitude modulation of large-scale structures significantly increases the residual Reynolds stress on the virtual wall, diminishing the drag reduction. Analysis of budget equations provides a systematic understanding of the underlying drag reduction dynamics. The DRL models reduce skin friction by inhibiting the redistribution of wall-normal turbulent kinetic energy. This further suppresses the wall-normal velocity fluctuations, reducing the production of Reynolds stress, thereby decreasing skin friction. This study showcases the successful application of DRL in turbulence control at high Reynolds numbers, and elucidates the nonlinear control mechanisms underlying the observed drag reduction.

We study the effect of turbulence on collisions between a finite-size bubble and small inertial particles based on interface-resolved simulations. Our results show that the interaction with the flow field around the bubble remains the dominant effect. Nonlinear dependencies in this process can enhance the turbulent collision rate by up to 100 % compared to quiescent flow. Fluctuations in the bubble slip velocity during the interaction with the particle additionally increase the collision rate. We present a frozen-turbulence model that captures the relevant effects providing a physically consistent framework to model collisions of small inertial particles with finite-sized objects in turbulence.

A numerical study supplemented with theoretical analysis is made, to analyse the electrophoresis of highly charged soft particles in electrolytes with trivalent counterions. The electrokinetic model is devised under the continuum hypothesis, which incorporates the ion–ion electrostatic correlations, hydrodynamic steric interactions of finite sized ions and ion–solvent interactions. The governing equations for ion transport and electric field are derived from the volumetric free energy of the system, which includes the first-order correction for the non-local electrostatic correlations of interacting ions, excess electrochemical potential due to finite ion size as well as the Born energy difference of ions due to dielectric permittivity variation. The electrolyte viscosity is considered to be a function of the local volume fraction of finite-sized ions, which causes the diffusivity of ions to vary locally. The occurrence of mobility reversal of a soft particle having the same polarity of its core and soft shell charge and formation of a coion-dominated zone in the soft layer is elaborated through this study. This can explain the mechanisms for the attraction between like-charged soft particles, as seen in the condensation of DNAs. The impact of ion–ion correlations and ion–solvent interactions of finite-sized ions are analysed by comparing them with the results based on the standard model. At a higher range of the core charge density, the ion–ion correlations induce a condensed layer of counterions on the outer surface of the core, which draws coions in the electric double layer, leading to an inversion in polarity of the charge density and mobility reversal. The dielectric decrement and ion steric interactions create a saturation in ion distribution and hence, modify the condensed layer of counterions. The enhanced fixed charge density of the polyelectrolyte layer diminishes the ion correlations due to the stronger screening effects and prevents the formation of a coion dominated zone in the Debye layer. The impact of the counterion size and the mixture of monovalent and trivalent counterions on mobility is analysed.

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.