We use the linearized Navier-Stokes equations to study the large-scale flow structures in unstably stratified turbulent channel flows. The impulse response of the linear operator at bulk Richardson numbers from ${\mathrm{Ri}}_b=0.001$ to ${\mathrm{Ri}}_b=1.0$ are considered, corresponding to the increasing influence of buoyancy relative to shear. We compare the streamwise-constant flow structures predicted by the linear model to the quasistreamwise rolls that emerge with increasing ${\mathrm{Ri}}_b$ in direct numerical simulations (DNSs) [e.g., Pirozzoli et al., J. Fluid Mech. 821, 482 (2017)]. The linearized Navier-Stokes equations augmented with eddy-viscosity and eddy-diffusivity capture the emergence of the quasistreamwise rolls well. With increasing ${\mathrm{Ri}}_b$, the temperature fluctuations of the streamwise-constant flow structures transition from having a peak in intensity at the channel centerline to having two peaks, one at each wall, consistent with DNS.

The Childress-Soward model, consisting of a an electrically conducting Rayleigh-Bénard layer rotating about a vertical axis, is the conceptually simplest model configuration that captures all essentials of convectively driven dynamos. Here we study the effects of different boundary conditions on this type of dynamo. This closes a gap in the existing literature, which has primarily focused on simple, but geophysically not very realistic, cases. Furthermore, the extensive literature on boundary layers in nonrotating and rotating Rayleigh-Bénard convection makes the Childress-Soward model an ideal test bed for illuminating the fundamental effects that the boundary conditions have on convection-driven dynamos. In this study we systematically vary the thermal, mechanical, and electrical boundary conditions in direct numerical simulations, with a focus on flow regimes characterized by geostrophic turbulence. One key result applies to both dynamos and nonmagnetic, rotating convection. We show that for no-slip boundaries, the Nusselt number increases significantly when a fixed heat flux is imposed instead of a given temperature difference. This effect can be explained by an interplay of Ekman pumping and the internal structure of the thermal boundary layer, which is very sensitive to thermal boundary conditions. Dynamical changes are shown to exist only within the boundary layers, such that the bulk dynamics remains largely unaffected. In the dynamo case, we argue that care needs to be taken in order to ensure comparable energetics when changing from fixed-temperature to fixed-flux conditions. If done properly, no significant differences in the leading order features of the resulting dynamos are observed. In particular, the thermal boundary conditions have no noticeable influence on the horizontal flow scales, as might have been expected from studies in spherical geometry. In contrast, the mechanical boundary conditions largely control whether or not large-scale flows and fields can be generated. For no-slip boundaries, Ekman friction strongly suppresses upscale transport and eliminates the large-scale vortex dynamos that exist in the stress-free case. Finally, the magnetic boundary conditions are shown to strongly affect the topology of the generated magnetic fields. For an insulating exterior, the magnetic field is most intense in the central part of the fluid layer, whereas we observe a strong magnetic field buildup close to perfectly conducting boundaries. For large magnetic Reynolds numbers, we further observe thin layers of intense horizontal field attached to perfect conductors. The horizontal flow scales, however, remain largely unaffected in the investigated parameter regime.

Gaseous cellular detonation is unsteady, and its propagation dynamics in a uniform mixture have been widely studied, but there are few works on cellular detonations in continuously disturbed media. Based on two fundamental propagation modes: stable (with regular cells) or unstable (with irregular cells), this study uses the Euler equations coupled with a two-step chemical reaction model to investigate two-dimensional cellular detonations with longitudinal disturbances. Disturbed detonations are generated by introducing a longitudinal sinusoidal density disturbance whose bifurcation parameter is the disturbance wavelength λ. The detonation cell distributions and propagation features are analyzed by recording the maximum local pressure and presenting the frequency spectrum of the averaged cell pressure. It is observed that the ratio of longitudinal disturbance wavelength λ to reaction zone width $W_{\mathrm{R}}$ plays an important role in cell morphology. For regular detonations, the cell scale changes periodically with the disturbance cycle, and the fundamental frequency of the averaged pressure signals is consistent with the disturbance frequency when this ratio is much greater than 1. If the ratio has a single-digit value, the original coupling relationship of shock waves and reaction fronts is destroyed and rebuilt, leading to an intermittent and local detonation decoupling and reinitiation. The size of newly formed large cells reaches about 3–6 times the size of the undisturbed cell. However, there are different cell-size spectra for stable and unstable detonations attributed to different transverse wave regularities. By introducing acoustic impedance analyses, the interaction of the detonation wave and varying density interface is presented, and the role of a sinusoidal density disturbance in wave dynamics is discussed.

In this paper, we report numerical results of turbulent transport of heat Nu and angular momentum ${\nu }_t/\nu$ in Taylor-Couette (TC) flows subjected to a radial temperature gradient. Direct numerical simulations are performed in a TC cell with a radius ratio $\eta =0.5$ and an aspect ratio $\mathrm{\Gamma }=8$ for two Rayleigh numbers ($\text{Ra}={10}^5$, ${10}^6$) and two Prandtl numbers ($\text{Pr}=0.7$, 4.38), while the Reynolds number Re varies in the range of $0\le \text{Re}\le 15000$. With increasing Re, the flows undergo evolution of different flow states: a first transition being from the convection-dominated regime to the transitional regime, with the large-scale meridional circulation evolving into spiral vortices; a second flow evolution occurring in the rotation-dominated regime when Taylor vortices turn from a weakly nonlinear state into a turbulent state. In particular, when the flows are governed by turbulent Taylor vortices, we find that both transport processes exhibit power-law scaling: $\text{Nu}\sim {\text{Re}}^{0.619\pm 0.015}$ for $\text{Pr}=4.38$, $\text{Nu}\sim {\text{Re}}^{0.590\pm 0.025}$ for $\text{Pr}=0.7$ and ${\nu }_t/\nu \sim {\text{Re}}^{0.588\pm 0.036}$ for both Pr. These scaling exponents suggest an analogous mechanism for the radial transport of heat and angular momentum, which is further evidenced by the fact that the ratio of effective viscosity to diffusivity is independent of Re. To illustrate the underlying mechanism of turbulent transport, we extract the coherent structures by analyzing the spatial distributions of heat and momentum flux densities. Our results reveal mutual turbulent structures through which both heat and angular momentum are transported efficiently.

We show that the relative dynamics of charged water droplets settling in still air contains fixed points determined by the combination of hydrodynamic interactions, particle and fluid inertia, and electrostatic forces. For droplets with large enough opposite charges, the stable manifold of a saddle forms a separatrix that divides colliding trajectories from those that do not collide. We analyzed experimental data of hydrodynamically interacting, micron-sized water droplets in still air with Lagrangian droplet tracking and with a numerical model including gravity, particle inertia, hydrodynamic interactions, fluid inertia, and Coulomb interactions. The predictions of the model are in excellent agreement with the experiments. A consequence of our findings is that, for large charges, collision outcomes are not sensitive to the breakdown of hydrodynamics at small distances.

The addition of nanoparticles in fluids significantly influences the fluid's viscosity and can be helpful to control viscosity-driven instability. In this work, we analyze how such nanoparticles modulate viscosity and impact miscible viscous fingering (VF) dynamics. We consider the flow configuration such that the Hele-Shaw cell is initially filled with a viscous fluid and then displaces it with other viscous fluid-carrying nanoparticles through the inlet boundary, which corresponds to the absorbing boundary condition. A closed-form solution of base-state flow using the Laplace-transform method is obtained, which overcomes the discrepancy of the base-state solution known in the form of an infinite series as available in the literature. Due to the time-dependency and nonmonotonic nature of the base state, nonmodal linear stability analysis in the self-similar domain is used to determine the onset time of instability. In this work, the effects of various governing flow parameters such as nanoparticles diffusive coefficient (${\alpha }_{np}$), effective log-mobility ratio ($R$), and deposition rate of nanoparticles ($D{a}_{\text{dep}}$) on the instability are studied. Our finding suggests that the onset occurs early with increasing $D{a}_{\text{dep}}$ for ${\alpha }_{\text{np}}>1$, whereas such onset time is a nonmonotonic function of $D{a}_{\text{dep}}$ for smaller values of ${\alpha }_{\text{np}}$. In addition, our results indicate that the onset time is a nonmonotonic function of ${\alpha }_{\text{np}}$ for the smaller value of $D{a}_{\text{dep}}$, whereas such onset time is an increasing function of ${\alpha }_{np}$ for the larger value of $D{a}_{\text{dep}}$. Further, nonlinear simulations are performed using comsol multiphysics, and the nonmonotonic nature on the onset of instability for different ${\alpha }_{np}$ is observed which is in good agreement with the linear stability analysis results. The present investigation removes various inconsistencies in the literature about the impact of the nanoparticles on VF with the quasi-steady-state approximation.

The economics, environmental impact, and mechanical properties of paper-based storage containers have been widely studied. However, knowledge of the physical processes relevant to the end-user experience is unavailable. This paper outlines the main effects associated with the closing and opening of telescoping boxes, which are used, for instance, to store and transport board games, footwear, mobile phones, and tablet computers. The sliding motion of the lid is controlled by the flow in a thin film of air in the gap separating the lid and the base of the box. Based on a broad comparison between theory and experiments on real and synthetic boxes, we find that the process is primarily controlled by the shape of the gap between the base and the lid. We derive a master equation for the lid motion and identify the origin of three distinct experimental regimes. Finally, an optimal design for a rapidly closing box is identified.

This paper presents a numerical method to study the pulsing behavior of soft corals. Evidence indicates that the pulsing behavior of soft corals in the family Xeniidae facilitates photosynthesis of their symbiotic algae. One way to investigate this complex behavior is through mathematical modeling and numerical simulations. The immersed boundary method is used to model the interaction of the tentacles with the surrounding fluid. The flow is then coupled with a photosynthesis model. The photosynthesis is modeled by advecting and diffusing oxygen, the byproduct of photosynthesis, where the coral tentacles act as a moving source of the oxygen. This study develops a methodology for solving a partial differential equation with boundary conditions on a moving immersed elastic boundary. In this study, the Reynolds and Péclet numbers are varied in the simulations to gain an understanding of how these parameters affect the mixing and photosynthesis. The mixing is quantified using both the fluid flow and oxygen concentration dynamics. The results show that for the biologically relevant Péclet number, the fluid dynamics significantly affect the photosynthesis and that the biologically relevant Reynolds number is advantageous for mixing and photosynthesis.

Flow topology and enstrophy production in chemically reacting compressible isotropic turbulence are studied by using numerical simulations with solenoidal forcing at initial turbulent Mach numbers ranging from 0.2 to 0.6 and at initial Taylor Reynolds numbers ranging from 32 to 160. A detailed chemical kinetic mechanism including nine species and 19 elementary reactions is employed to represent the ${\mathrm{H}}_2/{\mathrm{O}}_2$ reaction in turbulence. It is found that heat release leads to an increase of internal energy and turbulent length scales. After strong heat release during the chemical reaction process, the instantly increased temperature results in the increase of viscosity and pressure work, leading to the decrease of turbulent Mach number and Taylor Reynolds number, as well as the decrease of intrinsic flow compressibility and density gradient magnitude. Various statistical properties of eight flow topologies based on the three invariants of velocity gradient tensor are investigated with a specific focus on the effect of reaction heat release and compressibility. The topologies unstable focus/compressing (UFC), unstable node/saddle/saddle (UN/S/S), and stable focus/stretching (SFS) are predominant flow patterns at three turbulent Mach numbers. The topologies UN/S/S and SFS have major contributions to the overall enstrophy production in expansion regions, while the topology UFC leads to evident destruction of enstrophy in compression regions. The strong compression motions cause the destruction of enstrophy by the interaction between the vorticity and strain rate tensor, while strong expansion motions significantly enhance the generation of enstrophy. The most probable eigenvalue ratios for the strain rate tensor at three turbulent Mach numbers are found to be $-4$:1:3 in the overall flow field. Overall, the heat release by chemical reaction significantly reduces the compressibility effect on the local flow topologies and enstrophy production in chemically reacting compressible turbulence.

A dielectric-barrier-discharge plasma actuator with annular shape electrode geometry has been studied for evaluating the effectiveness in flow control applications. The flow field is investigated using time-resolved particle-image-velocimetry measurements and light-sheet flow visualization. The characterization of the actuator is carried out for both continuous- and burst-mode actuation. The Reynolds number, Re, of flow generated by the actuator is a function of actuation amplitude, ${\varphi }_{pp}$, and burst frequency, $f_b$, of the actuation signal, which governs the acceleration, development, and vortical structures of the wall-normal jet generated by the actuator. The maximum velocity generated by the actuator in continuous-mode actuation is higher than that of the burst-mode actuation. The velocity of the wall-normal jet increases in the wall-normal direction to a maximum value, $v_{\max }$, followed by a gradual decay for both modes of actuation. The decay rate of $v_{\max }$ is a function of actuation mode due to the difference in nature of the vortex structure evolution and interaction. The overall flow field generated by the actuator can be divided into four zones: (i) entrainment zone, (ii) recirculation zone, (iii) developing zone, and (iv) self-similar zone. Three different types of vortices dominate the induced flow, i.e., (i) starting vortex or periodic vortex generated due to impulsive action, (ii) shear layer vortex formed due to roll-up of the shear layer, and (iii) recirculation vortex ring created due to deflection of the approaching wall boundary layer. The self-similar velocity profile of the wall-normal jet generated by the actuator is akin to that of a free jet. The wall-normal jet generated by continuous-mode actuation shows low-frequency $(f<100\mathrm{Hz})$ vortical structures. In the burst mode, fluctuations are locked in with burst frequency for $f_b<200\mathrm{Hz}$. For a higher value of burst frequency ($f_b>200\mathrm{Hz}$), the effect is confined to the neighborhood of the exposed electrode, and flow field behavior approaches that of continuous-mode actuation.

Parallel two-phase flows are omnipresent in technological applications that require contact between two immiscible fluids for a finite amount of time. Precise control over the flow and separation of the fluids once they have been in contact are therefore the key challenges in these applications. Here, using experiments and numerical simulations, we show that the interface between two immiscible fluids flowing at the same flow rate in a symmetric channel can become unstable locally near the exit junction, where the two fluids are separated. This instability leads to the shedding of the droplets of one phase into the other, preventing a complete separation. We characterize this instability and show that the period of drop shedding is inversely proportional to the flow rate. We derive a stability criterion based on the balance between the Laplace pressure across the liquid-liquid interface and viscous pressure drop along each flow stream. The stability criterion and our experimental results are used to highlight the extreme sensitivity of this flow system to the parameters involved such as viscosity difference and exit geometry, which introduces gravitational effects and characteristics of the exit tubing.

The search of finite-time singularity solutions of Euler equations is considered for the case of an incompressible and inviscid fluid. Under the assumption that a finite-time blow-up solution may be spatially anisotropic as time goes by such that the flow contracts more rapidly into one direction than into the other, it can be shown that the dynamics of an axially symmetric flow with swirl may be approximated to a simpler hyperbolic system. By using the method of characteristics, it can be shown that generically the velocity flow exhibits multivalued solutions appearing on a rim at a finite distance from the axis of rotation, which displays a singular behavior in the radial derivatives of velocities. Moreover, the general solution shows a genuine blow-up, which is also discussed. This singularity is generic for a vast number of smooth finite-energy initial conditions and is characterized by a local singular behavior of velocity gradients and accelerations.

Analytical wind turbine wake models are an integral component of wind farm design and optimization. However, when the turbine induction factor increases, these models are prone to failure, as they do not account for the increasingly important effects of low wake pressure. To resolve this issue, this paper proposes an analytical wake model which incorporates the effect of wake pressure in its predictions. The model is based on inviscid flow theory for the initial wake region [K. Steiros and M. Hultmark. J. Fluid Mech. 853, R3 (2018)] and an extension of Morton's [B. R. Morton. J. Fluid Mech. 10, 101 (1961)] theory for the far wake, both of which include the effects of wake pressure. Comparison with high-fidelity wind turbine simulations shows that the model is comparable to conventional ones at low induction factors, but continues to be accurate at higher induction factors where existing models break down.

In this paper, the aerodynamic performance of an SD7003 airfoil with active control through momentum injection into the boundary layer is explored at a low Reynolds number of 5000. A two-dimensional incompressible flow is considered for the numerical solution of flow dynamics by employing the high-order spectral element method. The baseline airfoil cross section is modified with the presence of the rotating rod, which is placed at the suction side. The aerodynamic performance is extensively investigated in terms of mean and fluctuating components of lift and drag forces, lift-to-drag ratio, and control efficiency, as well for a range of rod location and rotational speeds for three attack angles of $4^{\circ }$, $8^{\circ }$, and ${12}^{\circ }$, respectively. Variation of flow pattern with a steady wake and unsteady shedding modes is then observed to be dependent on both the rotational speed and location. The numerical results indicated striking aerodynamic improvement at the condition of proper parameter combination, especially at incidence angles of $4^{\circ }$ and $8^{\circ }$. Pressure drop and recovery at the upstream and downstream sides of the control rod, respectively, is found to be the primary mechanism for the lift enhancement and drag reduction. Proper orthogonal decomposition (POD) analysis on the instantaneous velocity field is carried out to illustrate the mode structure modification due to the control rod. The influence of spanwise effects is also tested for some representative cases by employing three-dimensional simulation, verifying the effectiveness of the current active method.

We investigate the dynamics of sedimenting Brownian filaments using experimental, computational, and theoretical approaches. The filaments under consideration are composed of linked colloidal particles that form bead-spring-like chains. Under the action of gravitational forces, the nonlocal hydrodynamic interactions cause the filaments to bend and rotate to get their end-to-end direction perpendicular to gravity. Different reorientation mechanisms are verified for different regimes of flexibility, characterized by the elastogravitational number. The thermal forces promote shape and orientation fluctuations around the steady configurations of the reciprocal non-Brownian chains. The competition between the reorientation mechanisms and the Brownian effects results in normal distributions of the orientation of the chains. In the stiff regime, these fluctuations cause the chains to fall faster than their reciprocal non-Brownian cases. With increasing flexibility, thermal fluctuations lead to more compact configurations of the chains and higher average settling velocity. Nonetheless, chain flexibility plays an important role on lateral migration. The interplay between elastic, gravitational, and thermal forces leads to important secondary influences on the filament settling dynamics.

The flow of colloidal suspensions through porous media often leads to the deposition of particles inside the pores which increases the local hydrodynamic resistance by narrowing the pore space available and modifying the flow path of the transported particles. There is a significant flow decline in the extreme case when the entire porous medium becomes clogged. However, there are no experimental studies that determine directly the amplitude of this flow decline when compared with the dynamics of the formation of the particle deposit. This is mainly due to the great challenge of gaining experimental access to the features of the internal structure of the deposit as it grows and thus the ability to determine the flow inside it. In this paper, we show that is possible to monitor the flow decline corresponding to the successive deposition of colloidal particles inside a constriction (pore), ending by its complete blocking. The variation of the flow is determined by the measurement of the velocity of the particles through our channel. Such a technique coupled to the precise knowledge of what is deposited inside the pore, thanks to image analysis, enables us to determine the different contributions to the flow decline. We also use numerical simulations to access the flow inside the porous structure of the deposit as it grows. Together, experiments and simulations demonstrate that the obstruction process and the subsequent limited growth of the clog, corresponding to a few layers of accumulated particles, have a higher impact on the amplitude of the flow decline than the extra growth of the clog.

We show that the intermittent dynamics observed in the inertial interval of the Sabra shell model of turbulence can be rigorously related to the property of scaling self-similarity. In this connection, the space-time scaling symmetries [like in the Kolmogorov 1941 (K41) theory] are replaced by the hidden scaling symmetry, which is an exact symmetry of inviscid dynamics represented in special rescaled coordinates and times. We derive formulas expressing the anomalous scaling exponents in terms of Perron-Frobenius eigenvalues of linear operators based on the self-similar statistics. Theoretical conclusions are verified by extensive numerical simulations.

We show that Lagrangian measurements in active turbulence bear imprints of turbulent and anomalous streaky hydrodynamics leading to a self-selection of persistent trajectories—Lévy walks—over diffusive ones. This emergent dynamical heterogeneity results in a super-diffusive first passage distribution which could lead to biologically advantageous motility. We then go beyond single-particle statistics to show that for the pair-dispersion problem as well, active flows are at odds with inertial turbulence. Our study, we believe, will readily inform experiments in establishing the extent of universality of anomalous behaviour across a variety of active flows.

Ocean eddies play an important role in the transport and mixing processes of the ocean due to their ability to transport material, heat, salt, and other tracers across large distances. They exhibit at least two timescales: an Eulerian lifetime associated with persistent identifiable signatures in gridded fields such as vorticity or sea-surface height and multiple Lagrangian or material coherence timescales that are typically much shorter. We propose a method to study the multiple-timescale material transport, leakage, and entrainment by eddies with their surroundings by constructing sequences of finite-time coherent sets, computed as superlevel sets of dominant eigenfunctions of dynamic Laplace operators. The dominant eigenvalues of dynamic Laplace operators defined on time intervals of varying length allows us to identify a maximal coherence timescale that minimizes the rate of mass loss over a domain per unit flow time. We apply the method to examine the persistence and material coherence of an Agulhas ring, an ocean eddy in the South Atlantic ocean, using particle trajectories derived from a $0.1^{\circ }$ global numerical ocean simulation. Using a sequence of sliding windows, the method is able to identify and track a persistent eddy feature for a time much longer than the maximal coherence timescale and with considerably larger material transport than the corresponding eddy feature identified from purely Eulerian information. Furthermore, the median residence times of fluid in the identified feature far exceed the timescale over which fully material motion is guaranteed. Through residence time calculations, we find that this particular eddy does not exhibit a long-lived coherent inner core and that the bulk of material transport is performed by the quasi-coherent outer ring of the eddy.

Bluff body wakes in stratified fluids are known to exhibit a rich range of dynamic behavior that can be categorized into different regimes based on Reynolds number ($\text{Re}$) and Froude number ($\text{Fr}$). Topological differences in wake structure across these different regimes have been clarified recently through the use of dynamic mode decomposition (DMD) on direct numerical simulation (DNS) and laboratory data for a sphere in a stratified fluid for $\text{Re}\in [200,1000]$ and $\text{Fr}\in [0.5,16]$. In this work, we attempt to identify the dynamic regime from limited measurement data in a stratified wake with (nominally) unknown $\text{Re}$ and $\text{Fr}$. A large database of candidate basis functions is compiled by pooling the DMD modes obtained in prior DNS. A sparse model is built using the forward regression with orthogonal least squares (FROLS) algorithm, which sequentially identifies DMD modes that best represent the data and calibrates their amplitude and phase. After calibration, the velocity field can be reconstructed using a weighted combination of the dominant DMD modes. The dynamic regime for the measurements is estimated via a projection-weighted average of $\text{Re}$ and $\text{Fr}$ corresponding to the identified modes. Regime identification is carried out from a limited number of two-dimensional velocity snapshots from numerical and experimental data sets, as well as three point measurements in the wake of the body. A metric to assess confidence is introduced based on the observed predictive capability. This approach holds promise for the implementation of data-driven fluid pattern classifiers.