We investigate the near-wake flow of an Ahmed body which is characterized by switches between two asymmetric states that are mirrors of each other in the spanwise direction. The work focuses on the relationship between the base pressure distribution and the near-wake velocity field. Using direct numerical simulation obtained at a Reynolds number of ${10}^4$ based on incoming velocity and body height as well as Bonnavion and Cadot's experiment [G. Bonnavion and O. Cadot, J. Fluid Mech. 854, 196 (2018)], we perform proper orthogonal decomposition (POD) of the base pressure field. The signature of the switches is given by the amplitude of the most energetic, antisymmetric POD mode. However, switches are also characterized by a global base suction decrease, as well as deformations in both vertical and lateral directions, which all correspond to large-scale symmetric modes. Most of the base suction reduction is due to the two most energetic symmetric modes. Using the linear stochastic estimation technique of Podvin et al. [Exp. Fluids 59, 58 (2018)], we show that the large scales of the near-wake velocity field can be recovered to some extent from the base pressure modes. Conversely, it is found that the dominant pressure modes and the base suction fluctuation can be well estimated from the POD velocity modes of the near-wake.

Reynolds stresses transport in a turbulent channel flow under streamwise traveling waves is analyzed in detail using direct numerical simulations to gain physical insights into the mechanism of drag reduction. Streamwise traveling waves are known to produce larger drag reduction margins compared to simple homogeneous wall oscillations. The aim of the current investigation is to identify and analyze the direct effects arising from streamwise traveling waves that leads to larger drag reduction margins compared to simple homogeneous wall oscillations. Several cases were considered, with amplitudes ranging from 0.15 to 1.25 (in outer units) at fixed angular frequency and wave number of 0.16 and 1.66 (in outer units), respectively, to yield drag reduction margins ranging from 26% to 58%, respectively. Streamwise traveling waves of large amplitudes were found to block the intercomponent energy transfer, resulting in shut off of the near-wall buffer layer dynamics. The analyses here suggest that the combined effect of loss of communication between low and high buffer layers with damping in the wall-normal Reynolds stress component is associated to the traveling wave effect and results in larger drag reduction margins.

Cilia and flagella are organelles that play central roles in unicellular locomotion, embryonic development, and fluid transport around tissues. In these examples, multiple cilia are often found in close proximity and exhibit coordinated motion. Inspired by the flagellar motion of biflagellate cells, we examine the synchrony exhibited by a filament pair surrounded by a viscous fluid and tethered to a rigid planar surface. A geometrically switching base moment drives filament motion, and we characterize how the stability of synchonized states depends on the base torque magnitude. In particular, we study the emergence of bistability that occurs when the antiphase, breast-stroke branch becomes unstable. Using a bisection algorithm, we find the unstable edge state that exists between the two basins of attraction when the system exhibits bistability. We establish a bifurcation diagram, study the nature of the bifurcation points, and find that the observed dynamical system can be captured by a modified version of Adler's equation. The bifurcation diagram and presence of bistability reveal a simple mechanism by which the antiphase breast stroke can be modulated, or switched entirely to in-phase undulations through the variation of a single bifurcation parameter.

In this work we study the fingering double diffusive convection, namely, the buoyancy-driven convection flow within a fluid layer experiencing an unstable salinity gradient and a stable thermal gradient. In particular, we investigate the influences from a background shear with uniform strength. Linear stability analysis indicates that the unstable modes shift from a circular shape to a sheetlike shape as the shear becomes stronger. Three-dimensional direct numerical simulations are conducted for five groups of cases, each of which has the same combination of thermal and salinity gradients (measured by corresponding Rayleigh numbers) and gradually increasing shear strength. The same properties of seawater are used for all simulations, i.e., the Prandtl number $\text{Pr}=7$ (the ratio of kinematic viscosity to thermal diffusivity) and the Schmidt number $\text{Sc}=700$ (the ratio of kinematic viscosity to salinity diffusivity). Numerical results reveal that a very weak shear organizes the salt fingers into a very regular pattern, which enhances the salinity flux. This enhancement effect, however, reduces as the Rayleigh number increases. For stronger shear the dominant structures shift from salt fingers to salt sheets, and the coherence length scale increases in the streamwise direction. Meanwhile, salinity and heat fluxes decrease. These findings suggest that even a weak shear can notably alter the morphology and transport properties of fingering double diffusive convection.

In this paper, we perform an asymptotic study of the effect of local surface temperature (heating or cooling) strips on oncoming inviscid Mack instability in supersonic or hypersonic boundary layers, which is presented for a canonic problem to shed light on the physical mechanisms by which surface imperfections impact on boundary-layer transition to turbulence. Assuming the Reynolds number to be sufficiently large, the change of the Mack amplitude due to interaction with the temperature strip is quantified by an explicit model developed by the multiscale analysis. It is revealed that the temperature strip plays an equivalent role as a roughness element by producing mean-flow distortions described by the triple-deck structure. However, the former renders a more complicated interaction with the Mack modes since the lower deck is compressible to leading-order accuracy. Based on this model, a systematic study for different control parameters is conducted. A heating strip enhances (or suppresses) the Mack modes with frequencies below (or above) a critical value, whereas a cooling strip plays the opposite role. The critical frequency is found to be the most unstable frequency of the second mode, instead of the synchronization frequency as was found in some previous works for both roughness and temperature-strip configurations. A few phenomena in contrast to the roughness configuration are observed and readily explained by the asymptotic model. The asymptotic predictions agree favorably with the Harmonic linearized Navier-Stokes calculations and the direct numerical simulations, especially when the wall temperature is low.

We use the recently developed macroscopic forcing method [A. Mani and D. Park, Phys. Rev. Fluids 6, 054607 (2021).] to compute the scale-dependent eddy diffusivity characterizing ensemble-averaged scalar and momentum transport in incompressible homogeneous isotropic turbulence. For scales larger than the energy containing eddies, eddy diffusivity is found to be constant and consistent with the Boussinesq approximation. However, for small scales eddy diffusivity is found to vanish inversely proportional to the wave number. Behavior at all scales is reasonably captured by a nonlocal eddy diffusivity operator modeled as $D/\sqrt{\mathcal{I}-l^2{\nabla }^2}$, where $D$ is the eddy diffusivity in the Boussinesq limit, and $l$ is a constant on the order of the large-eddy length. These results present a direct measurement of eddy diffusivity in turbulence with implications in turbulence modeling.

The Peregrine soliton (PS) is widely regarded as a prototype nonlinear structure capturing properties of rogue waves that emerge in the nonlinear propagation of unidirectional wave trains. It has been recently demonstrated that the PS can emerge locally, as an asymptotic structure arising from the propagation of an arbitrary large decaying pulse, independently of its solitonic content. This mathematical discovery has changed the widely accepted paradigm of the solitonic nature of rogue waves by enabling the PS to emerge from partially radiative or even completely solitonless initial data. In this work, we realize this scenario in a water tank experiment with a particular aim to control the point of the PS occurrence in space-time by imposing an appropriately chosen initial chirp. By employing the inverse scattering transform for the synthesis of the initial data, we are able to engineer a localized wave packet with a prescribed solitonic and radiative content. This enables us to control the position of the emergence of the rogue wave by adjusting the inverse scattering spectrum. The proposed method of nonlinear spectral engineering is found to be robust to higher-order nonlinear effects, preceding the wave breaking dynamics, that are inevitable in realistic wave propagation conditions.

We study the coupled hydrodynamics between a motile slender microswimmer and a deformable interface that separates two Newtonian fluid regions. From the disturbance field generated by the swimming motion, we quantitatively characterize the interface deformation and the manner in which the coupling modifies the microswimmer translation itself. We treat the role of the swimmer type (pushers and pullers), size and model an interface that can deform due to both surface tension and bending elasticity. Our analysis reveals a strong dependence of the hydrodynamics on the swimmer orientation and position. Given the viscosities of the two fluid media, the interface properties and the swimmer type, a swimmer can either migrate toward or away from the interface depending on its configurations. When the swimmer is oriented parallel to the interface, a pusher-type swimmer is repelled from the interface at short times if it is swimming in the more viscous fluid. At long times, however, pushers are always attracted to the interface, and pullers are always repelled from it. However, swimmers oriented orthogonal to the interface exhibit a migration pattern opposite to the parallel swimmers. In consequence, a host of complex migration trajectories emerge for swimmers arbitrarily oriented to the interface. We find that confining a swimmer between a rigid boundary and a deformable interface results in regimes of attraction toward both surfaces depending on the swimmer location in the channel, irrespective viscosity ratio. The differing migration patterns are most prominent in a region of order the swimmer size from the interface, where the slender swimmer model yields a better approximation to the coupled hydrodynamics.

Temporally evolving convective boundary layers that develop on the external surface of an isothermally heated vertical circular cylinder are investigated with scale analysis in this study. Large variation of cylinder aspect ratio, $1\le A\le 100$, is considered. The Rayleigh number ranges from $1\times {10}^6$ to $5\times {10}^8$, and the Prandtl number varies from 10 to 100. The present numerical simulations suggest that the curved boundary layer experiences a transient and a steady state. Our study demonstrates that the key to correctly scaling the curvature effect is the determination of an appropriate estimation of the diffusion term. One set of scale laws quantifying the flow is obtained by assuming $\left(1/r\right)\left(\partial /\partial r\right)\sim 1/\left[\left(R+\delta /2\right)\delta \right]$, where $r$ is the radial coordinate, and $R$ and δ denote cylinder radius and boundary layer thickness, respectively. It is demonstrated that if the boundary layer is much thinner than the cylinder radius, the proposed scale laws are reduced to the well-known flat boundary layer ones. However, with reducing the cylinder radius or the governing Rayleigh number, the curvature effect gradually differentiates the present boundary layer flow from the flat ones. The corresponding flow behaviors are reasonably described by the various ${\left(R+N{\delta }_{\mathrm{t}}\right)}^{\mathrm{m}}$ terms of the present scale laws, where $N$ and $m$ are the corresponding scale-law constants. Numerical validations indicate that the proposed scale laws are capable of precisely describing from flat boundary layers at $\xi =0$ to remarkably curved ones at $\xi =26$ (almost a line heat source), where $\xi$ is the ratio of boundary layer thickness to cylinder radius. Therefore, the proposed scale relations are considered as unified laws.

We seek to develop a closure model to enable scale-resolving simulation (SRS) of a turbulent flow to optimally switchover from a Reynolds-averaged Navier-Stokes (RANS) calculation at the wall to a specified degree of resolution in the wake or free-stream region. The closure model is derived by (i) using the physical principle that the total energy of resolved and unresolved scales should be conserved in the switchover region and (ii) establishing consistency with equilibrium boundary layer scaling of the partially resolved field. The model development is performed in the context of a partially averaged Navier-Stokes (PANS) scale-resolving method by quantifying and modeling the commutation terms resulting from varying resolutions in the wall-normal direction. The resulting wall-modeled PANS (WM-PANS) is used to compute the turbulent channel flow in the ${\text{Re}}_{\tau }$ range $180-8000$. The influence of the RANS-SRS switchover location on the computed flow field is examined. It is then demonstrated that the mean flow is reproduced with reasonable accuracy at modest computational effort without discernible log-layer mismatch even at the highest Reynolds number considered. While the Reynolds stresses are also recovered accurately over most of the flow domain, a noticeable computational transition from RANS to unsteady SRS flow behavior is observed and the underlying physics is examined. Irrespective of the location of computational transition, the unsteady features of the flow away from the wall are well captured. It is demonstrated that the proposed closure is able to inject the appropriate amount of resolved turbulence without the need for artificially generated synthetic turbulence. Overall, WM-PANS presents an accurate and computationally viable option for scale-resolving computations of near-wall high-Reynolds number flows.

As one of the canonical flow problems in compressible wall-bounded turbulence, compressible turbulent channel flow (CTCF) with symmetric isothermal boundaries has been studied a lot in the past. In the present work, an empirical scaling for the central mean temperature in CTCFs is proposed. The scaling originates from the generalized Reynolds analogy (GRA) theory, and it depends on the Mach number, Prandtl number, and ratio of the central mean velocity to the bulk mean velocity. The available direct numerical simulation data with the bulk Reynolds number ranging from 3000 to 34 000 and Mach number ranging from 0.5 to 4.0 are used to assess the proposed scaling. It is found that the empirical scaling is quite accurate and most of the relative errors are below $1.5\%$. With the scaling of the central mean temperature and the GRA theory, the mean temperature profile can be quantitatively obtained through the mean velocity in CTCFs.

In this paper, we present three-dimensional direct numerical simulations (3D DNS) of vortex-induced vibrations of an elastically mounted circular cylinder near a stationary wall at a subcritical Reynolds number of 500. The circular cylinder can oscillate in both the streamwise and transverse directions. A typical gap of 0.$8D$ between the cylinder surface and the stationary wall was selected to evaluate the characteristics of the responses and vortex dynamics in the presence of a stationary wall and boundary layer. We observe that the vibration response is two-branched, with two desynchronization regions lying at the ends of the simulated $U_r$ range. Because of the wall proximity, the dominant vibration frequencies in the two directions are generally identical, and the trajectories of the displacement significantly differ in each branch. Figure-eight, combined figure-eight and raindrop, raindrop, and chaotic trajectories appear successively with increasing $U_r$, dominating the first desynchronization region, initial branch, lower branch (LB), and second desynchronization region (DS-II), respectively. In addition, the phase lag between the lift and displacement jumps from 0° to 180° at the transition between the LB and DS-II. Furthermore, we evaluated the three-dimensionality of the wake through the instantaneous vortical structures, spanwise-averaged vorticity contours, and statistics of the enstrophies. We found that the three-dimensionality increases linearly with the amplitude, leading to substantial variations in the vortex dynamics. The statistics of the gap flow indicates that the mean gap flow velocity is determined by only the time-averaged gap, whereas the fluctuating gap flow velocity is governed by the amplitude. Finally, the flow physics behind the response was analyzed using the time histories of the displacement, gap flow velocity, drag and lift coefficients, and vorticity contours in one vibration period. We observed that the interactions of the vortices with the wall-generated boundary layer play significant roles in altering the cylinder vibration. In the small-amplitude case, the boundary layer merges with the freestream-side vortex of the cylinder, forcing the gap-side vortex to pair with the freestream-side vortex. In contrast, in the large-amplitude case, the gap-side shear layer collides with the boundary layer and disintegrates into small parts, resulting in negative vortices in the wake.

A numerical study of convection with stress-free boundary conditions in the presence of an imposed magnetic field that is tilted with respect to the direction of gravity is carried out in the limit of small magnetic Reynolds number. The dynamics are investigated over a range of Rayleigh number Ra and Chandrasekhar numbers up to $Q=2\times {10}^6$, with the tilt angle of the imposed magnetic field vector fixed at ${45}^{\circ }$ relative to vertical. For a fixed value of $Q$ and increasing Ra, the convection dynamics can be broadly characterized by three primary flow regimes: (1) quasi-two-dimensional convection rolls near the onset of convection, (2) isolated convection columns aligned with the imposed magnetic field, and (3) unconstrained convection reminiscent of nonmagnetic convection. The influence of varying $Q$ and Ra on the various fields is analyzed. Heat and momentum transport, as characterized by the Nusselt and Reynolds numbers, are quantified and compared with the vertical field case. Ohmic dissipation dominates over viscous dissipation in all cases investigated. Various mean fields are investigated and their scaling behavior is analyzed. Provided Ra is sufficiently large, all investigated values of $Q$ exhibit an inverse kinetic energy cascade that yields strong “zonal” flows with an amplitude that scales as $Q^{1/3}$. Relaxation oscillations, as characterized by a quasiperiodic shift in the predominance of either the zonal or nonzonal component of the mean flow, occur when Ra and $Q$ are sufficiently large.

Wavelet multiresolution analysis is extended to describe interphase, cross-scale interactions involving turbulence kinetic energy (TKE) of particle-laden turbulence. Homogeneous isotropic turbulence (HIT) suspended with inertial particles at the Stokes number of unity (critical particles) is analyzed. Direct numerical simulation is performed for decaying HIT coupled via the Stokes drag law in two ways with the dispersed phase. The effects of two-way coupling on spectral TKE transfer are examined. Clustering of the critical particles in thin, filamentlike regions is observed, and mean wavelet statistics are similar to those of the Fourier analysis. However, spatially local wavelet analysis demonstrates the complexities of the preferential concentration in interphase, interscale energy transfer and associated challenges in subgrid-scale (SGS) modeling of particle-laden turbulence. Two-way coupling enhances correlations between local particle concentration and local interphase TKE transfer. However, particle concentration alone does not indicate a definite direction of interphase energy transfer. Rather, particle clusters behave as an energy source or sink with similar probabilities. A similar argument is made for correlations between particle concentration and cross-scale energy transfer. Wavelet statistics conditioned on coarse-grained number density support the same conclusions. In addition, the joint statistics show the qualitative consistency of the SGS Stokes number in describing the two-way interactions, which should be considered in the SGS modeling of two-way coupled particle-laden turbulence.

The success of spectroscopy to characterize equilibrium fluids, for example the heat-capacity ratio, suggests a parallel approach for active fluids. Here, we start from a hydrodynamic description of chiral active fluids composed of spinning constituents and derive their low-frequency, long-wavelength response functions using the Kadanoff-Martin formalism. We find that the presence of odd (equivalently, Hall) viscosity leads to mixed density-vorticity response even at linear order. Such response, prohibited in time-reversal-invariant fluids, is a large-scale manifestation of the microscopic breaking of time-reversal symmetry. Our work suggests possible experimental probes that can measure anomalous transport coefficients in active fluids through dynamic light scattering.

Convective dynamics developing below growing sea ice are studied experimentally by freezing salt water from above in a quasi-two-dimensional Hele-Shaw cell. Observations of the convective processes are made with Schlieren and direct imaging systems, allowing visualization both under and within the growing ice. Buoyancy-driven flows are seen to develop under the ice layer via two different mechanisms: On one hand, brine diffuses out from the ice layer creating a denser boundary layer of enhanced salinity, which triggers boundary layer convection resulting in small-scale interfacial fingers. On the other hand, internal flow within brine drainage channels inside the ice is observed flushing out longer-scale convective streamers at given locations at the ice-water interface. Streamers descend in the bulk aqueous layer faster and for longer distances than fingers. Simulations confirm that, despite nonlinear interactions between fingers and streamers, the different speeds observed can be correlated to different density differences between the interfacial or internal rejection and the underlying bulk salt water. Estimates of relative mass fluxes through the interface by the two mechanisms suggest that, when streamers are active, the mass of salt rejected through the streamer pathway can be larger than the one expelled through the finger pathway. However, as fingers are maintained throughout the ice growth while the rejection from brine channels features an intermittent “on-off” behavior, there are certain periods of time when the mass flux of the two mechanisms is similar, but also some time intervals during which the flux due to interfacial short fingers becomes dominant.

In this work, we experimentally investigate the physics of a strongly oscillating, millimeter-sized, axisymmetric air-water interface with a fixed contact line boundary condition. Many previous studies focused on the regime of small oscillation amplitude, e.g., $R=d/D\ll 1$, where $d$ is the oscillation amplitude and $D$ is the characteristic size of the air-water interface. The current investigation instead focuses on a less-studied oscillation regime with large $R$ that is up to 0.33. The dynamic oscillations induce different steady streaming patterns, such as a low-speed streaming vortex or a fast-speed streaming jet. The steady streaming jet, in particular, was not much studied previously and is the major focus of this work. The streaming jet is only generated when the oscillating interface exhibits the higher-order axisymmetric oscillation modes with a large oscillation amplitude, which correspond to the regime with large $R$ and large Weber number (We). The streaming jet has a larger Reynolds number $[\mathrm{Re}\sim \mathcal{O}(100\left)\right]$ than the typical streaming motions induced by an oscillating interface $[\mathrm{Re}\sim \mathcal{O}(1\left)\right]$. In addition, the streaming jet has a high ratio of the streaming velocity versus the oscillatory velocity, which suggests a high efficiency in generating steady streaming motion. The dynamic velocity and vorticity field of the streaming jet in both the initiation stage and the quasisteady stage are presented, which demonstrates that the streaming jet onset process is a consequence of vorticity generation, transportation, and accumulation happening at the oscillating interface. As a zero-mass-flux jet, the streaming jet is sustained by entraining fluid mass flux from the circumferential regions through a process similar to the classical Stokes drift. It is further found that a streaming jet can be induced by an oscillating elastic no-slip membrane as well, when the oscillation has large $R$ and We. The extraordinary characters of the streaming jet can be employed in many engineering applications.

We study the orientational and translational dynamics of spherical microswimmers trapped at fluid interfaces in terms of the force dipole and source dipole components of their flow field. Using numerical simulations and analytical calculations, we show that the force dipole exerts a torque, orienting pushers parallel to the interface and pullers in the normal direction. The source dipole results in particle rotation only for a finite viscosity contrast between the two fluids, in agreement with previous studies. The superposition of these two contributions leads to a rotational dynamics with a steady-state orientation that depends on the relative magnitudes of the force and source dipoles. In the general case, swimmers with weak force dipoles and strong pullers are observed to align perpendicular to the interface and become stationary, while strong pushers have a finite inclination angle toward the lower viscosity fluid and swim along the interface.

The minimization of dissipation is a general principle in physics. It stipulates that a nonequilibrium system converges toward a state minimizing the energy dissipation. In fluid mechanics, this principle is well known for Newtonian fluids governed by the Stokes equation. It can be formulated as follows: Among all admissible velocity fields, the solution of the Stokes equation is the one that minimizes the total viscous dissipation. In this Letter, we extend these approaches to non-Newtonian fluids in macroscopic heterogeneous porous media or fractures. The flow is then governed by a nonlinear Darcy equation that can vary in space. In this case, a minimization principle can still be written depending on the boundary conditions. Moreover, such a minimization principle can be derived either for the velocity or the pressure field.

The results of six highly resolved direct and large eddy simulations of gravity and conservative turbidity currents are presented to illustrate the point that the rapidly varying evolution of these currents follow a universal cyclic sequence of four states. The demarcation between these four states is determined by the bulk Richardson number and the acceleration/deceleration of the flow. We describe in detail the identification process of these states, together with the associated three-dimensional structure of the current. The exact depth-averaged momentum balance is computed and used to explain the intricate details of the nonmonotonic rapid evolution of the current between the different states. Finally, the balance of turbulent kinetic energy and concentration flux are computed to explain how and why the current evolves through the cyclic sequence of states. We also explore the mechanism by which the current can exit the cyclic sequence and slowly evolve towards self-similar supercritical or subcritical states.