In many natural and industrial environments, small droplets are irradiated with visible and infrared light, affecting how they evaporate. Without external heating, droplets usually shrink faster as they become smaller. The simplest description of this is the $D^2$ law, where the shrinking rate $dR/dt$ is proportional to $t^{-1/2}$ or $R^{-1}$. However, modeling this becomes more complicated when irradiation-driven volumetric heating is considered, and only few studies have investigated the evaporation behavior of levitating droplets under strong irradiation. Here we show the effects of weak and strong irradiation on single, optically levitated, micrometer-sized water droplets. We find that the droplets shrink following distinct accelerating and decelerating regimes, that we characterize through two power laws. Under weak irradiation, the shrinking rate accelerates, similar to the $D^2$ law. Under strong irradiation, however, the shrinking decelerates following the power law $dR/dt\sim R$, i.e., inverse of the $D^2$ law. Between these two regimes, at radii of 3–5 $\mu \mathrm{m}$, a turnover occurs from decelerating shrinking back to accelerating shrinking. Our findings shed new light on droplet evaporation under weak and strong irradiative heating, such as mists under sunshine or fuel droplets irradiated by flames in rocket engines or internal combustion.

The interaction between low-order roughness and large-scale topography is experimentally investigated using high-resolution particle image velocimetry in a refractive-index-matched channel at two bulk Reynolds numbers differing by an order of magnitude, $\text{Re}=4.0\times {10}^3$ and $4.0\times {10}^4$. A two-dimensional sinusoidal roughness is superimposed on a two-dimensional wavy wall to isolate the effects of multiscale surface modulation on near-wall turbulence. The added roughness reorganizes the flow by inducing larger coherent structures near the surface. Two-point correlations and integral length scales confirm enhanced near-wall coherence, while quadrant-hole analysis reveals a marked suppression of ejection events. This suppression weakens the local turbulence production term $-\langle u^{\prime }{v}^{\prime }\rangle dU/dy$, leading to attenuation of the separated shear layer that develops downstream from the topographic crest within the adverse-pressure-gradient region. The resulting flow exhibits up to 25% lower peak turbulent kinetic energy and Reynolds shear stress relative to the smooth-wavy configuration. Even modest low-order roughness can therefore reorganize the coupling between near-wall and outer-layer motions, a mechanism that persists across an order of magnitude in Reynolds number and offers valuable insight for modeling transport and drag over natural and engineered surfaces.

In this study, we propose closure models for the subgrid turbulent heat flux and drift temperature components. These terms arise as unresolved contributions in the filtered two-fluid model (TFM) for heat transport equations of turbulent gas-particle flows. In the context of moderately dense turbulent fluidization, the drift temperature appears as a correction to the filtered resolved interphase heat transfer component and expressed by a covariance of gas phase temperature and solid concentration. The derived models are mainly motivated by our findings showing that the most commonly used subgrid heat flux models associated linearly with the gradient resolved temperature are invalid in this kind of multiphase turbulence. They reveal a clear misalignment with the actual gas and solid phase turbulent heat flux vectors. Thus, the proposed models are principally based on Taylor development of the subfilter terms, identified as Clark's gradient model [Clark et al., J. Fluid Mech. 91, 1 (1979)]. They differ only in the dynamic formation of model coefficient using the test filters. We find that the conventional dynamic Smagorinsky-type model leads to large errors in predicting the subfilter turbulent heat flux and solid concentration variance, and our dynamic procedure based on a Taylor series expansion of test-filtered resolved terms (Leonard term) [Balarac et al., Phys. Fluids 20, 035114 (2008)] substantially improves the predictive accuracy. This last approach was originally assessed based on the optimal estimator concept, i.e., conditional expectations and statistical minimization of modeling errors; thus we use this terminology in referring to all of our models adopting this dynamic procedure. Two dynamic drift temperature closures are accordingly presented based on optimal estimator dynamic procedure coefficient. They basically approximate the covariance of gas phase temperature and solid concentration by the product of its variances or the gradient Clark's expansion. All of our models are examined in a framework of an a priori study, where filtering fine-grid TFM simulation data of laboratory-scale wall-bounded turbulent fluidization of Geldart B group particles is employed. The presented models provide more accurate and robust tools for heat transfer TFM simulations of industrial-scale fluidized bed reactors.

Under unstable stratification, the Reynolds shear stress $-\overline{u^{\prime }{w}^{\prime }}$ in the atmospheric surface layer (ASL) reflects a multiscale superposition in which large-scale motions can contribute appreciably, motivating a scale-resolved quantification beyond standard similarity scaling. Using multiheight SLTEST velocity measurements under unstable conditions, we obtain an additive scale decomposition of $-\overline{u^{\prime }{w}^{\prime }}$ from momentum-flux cospectra and quantify cumulative contributions with an ogive $C\left(k\right)$, where $k$ is the streamwise wave number. Interpreting $C\left(k\right)$ as an empirical cumulative distribution in $lnk$, we parametrize it with a lognormal cumulative distribution function, yielding a compact two-parameter description $(\mu ,\sigma )$ of the dominant contributing scale and the breadth of scale allocation. Two indicators isolate the key mechanisms: the cumulative contribution from large scales and a counterstress fraction ${\eta }_{\mathrm{neg},1}$ that measures cospectral contributions opposite in sign to the net stress. Under weakly unstable conditions, normalized premultiplied cospectra collapse when plotted against the nondimensional wave number $kz$, where $z$ is the measurement height, with a peak at $kz\approx 0.5$, and the large-scale contribution increases with relative height, indicating enhanced large-scale influence aloft. For weak-cancellation records (${\eta }_{\mathrm{neg},1}<0.1$), ogives are accurately captured by the lognormal form, and $(\mu ,\sigma )$ reproduce the observed cospectral morphology across heights. With increasing instability, the dominant contribution shifts to larger wavelengths, the large-scale flux fraction increases, and scale-domain cancellation strengthens, with larger magnitudes and stronger sensitivity at higher relative heights. A variable-interval time-averaging-based burst analysis provides a consistent time-domain counterpart: events become sparser while the stress magnitude concentrates within fewer intervals, and a time-domain cancellation metric increases concurrently. These results establish a low-dimensional height-stability parametrization of momentum-flux scale allocation and show that unstable ASL transport is organized by coupled large-scale enhancement, strengthened cancellation, and increased intermittency.

The turbulent von Kármán flow in a cylinder has been studied by helical-wave decomposition (HWD) based on direct numerical simulations. HWD provides a powerful tool for analyzing wall-bounded flows by decomposing the flow field into global orthogonal eigenmodes with different scales. The flow visualizations show that the flow field exhibits significant spatial inhomogeneity and anisotropy, characterized by laminar boundary-layer near the endwalls, turbulent boundary-layers on the sidewall adjacent to the endwalls, jetlike flow in the middle of the sidewall, and a central mixing region. The numerical results indicate that the global helical-wave energy spectra of the fluctuating flow in the whole domain show a scaling range of ${\lambda }^{-5/4}$ with wave number $\lambda$. At the same time, the second-order structure functions in physical space are found to exhibit a 2/3 scaling. The finding suggests that the direct relationship between the energy spectrum and the second-order structure function observed in homogeneous isotropic turbulence (HIT) no longer holds. Furthermore, we investigated the nonlinear inter-scale energy transfer in the fluctuating flows. Within the $-5/4$ scaling range of the energy spectrum, the energy transfer function of fluctuating modes remains nonzero; this range is termed the scaling range to distinguish it from the inertial subrange in HIT where the transfer function is zero. This finding reveals the impact of the moving boundary on the energy cascade dynamics at small scales.

Mach reflection (MR) of axisymmetric internal shocks in a steady supersonic flow is studied analytically and numerically in this paper. An analytical model, developed from a recent planar model and based on the curved shock theory and the method of curved shock characteristics, is utilized in the investigation. The presence of a center body as the unique geometry component in axisymmetric internal flow has been included. The comparison with numerical simulations shows that the primary flow configurations of axisymmetric internal shock MRs can be accurately predicted. By utilizing the analytical model, the shape of the slip line and the size of the Mach disk are studied. An in-depth analysis was conducted on the phenomenon where, at a specific wedge angle and with a sufficiently small outlet radius, the interference between the trailing-edge expansion fan and the slip line occurs downstream of the sonic throat, resulting in the size of the Mach disk being independent of the outlet radius. It is indicated that the formation of the sonic throat without relying on the trailing edge expansion fan is attributed to the negative pressure gradient that arises behind the reflection shock. Such pressure gradients are related to slip line deflection, with flatter slip lines implying greater negative pressure gradients being generated. Thus, the independent formation of the sonic throat is more feasible when the wedge angle is small enough, where the triple point is close to the von Neumann criterion and the deflection of the slip line is slight.

Focusing on simulated dilute polymer solutions, this letter investigates the interactions between flow structures and organized polymer stress sheets for the steady arrowhead coherent structure in a two-dimensional periodic channel flow. Formulating the problem in a frame of reference moving with the arrowhead, in which streamlines are also pathlines, enables the identification of two distinct topological regions linked to two stagnation points. The streamlines help connect the spatial distribution of polymer stress within the sheets and the dynamics of polymers transported by the flow. Using stresslines, lines parallel to the eigenvectors of polymer stress, we propose a formulation of the viscoelastic stress term in the momentum equation, which provides a more intuitive interpretation of the relation between the curvature of the stresslines, and the variation of stress along these lines, with the local flow topology. An approximation of this formulation is shown to explain the pressure jump observed in the arrowhead structure as a function of the local curvature of the polymer stress sheet.

We provide compelling numerical evidence for the development of (potential) finite-time singularities in the three-dimensional axisymmetric, ideal, incompressible magnetohydrodynamic (IMHD) equations, in a wall-bounded cylindrical domain, starting from smooth initial data, for the velocity and magnetic fields. We demonstrate that the nature of the singularity depends crucially on the relative strength $\mathcal{C}$ of the velocity and magnetic fields at the time of initialization: (i) if $\mathcal{C}<1$, then the swirl components, at the wall, evolve toward square profiles that lead to the intensification of shear at the meridional plane $(r=1,z=L/2)$ and the development of a finite-time singularity; (ii) if $\mathcal{C}=1$, there is no temporal evolution; (iii) if $\mathcal{C}>1$, then the swirl components, at the wall, evolve toward a cusp-type singularity. By examining the spatiotemporal evolution of the pressure, we obtain insights into the development of these singularities.

Dense granular flows made of elongated particles exhibit a strong inhibition of particle rotation compared to spherical grains, but the mechanisms responsible for this effect remain unclear. Using three-dimensional discrete element simulations, we investigate the angular dynamics of elongated particles in dense, confined shear flows. We systematically vary particle aspect ratio, interparticle friction, and boundary conditions to elucidate their respective roles. We show that the reduction of the average angular velocity cannot be attributed to particle shape, friction, or solid fraction alone. Instead, it is controlled by the degree of collective alignment developed under shear, quantified by a nematic order parameter. Based on this observation, we propose a simple scaling law linking the average angular velocity to the local shear rate through a hampering parameter that depends solely on the orientational order via the nematic order parameter. This scaling successfully collapses data obtained for different particle properties (shape, friction), different flow patterns, and, remarkably, remains valid for two additional flow configurations.

The displacement of air by a noncolloidal particulate suspension between two parallel plates can trigger interfacial instabilities and two seemingly intertwined patterns: deformation of the fluid-fluid interface and dense particle clusters within the suspension, hereafter referred to as plumes. While prior studies have primarily examined the onset and source of this instability, the emergence and coupling of these patterns remain unresolved. Notably, existing investigations have been limited to radial geometries, where continuous outward expansion of the interface weakens plume-plume interactions. Here, we experimentally displace air with an oil suspension in a rectangular Hele-Shaw cell. Confinement within a constant-width channel amplifies interactions between neighboring plumes, giving rise to previously unreported regimes of pattern formation, including plume merging and plume shedding. Image analysis reveals strong coupling between interfacial deformation and plumes and characterizes the interaction between adjacent plumes. Employing the suspension balance model, we demonstrate how net particle flux toward the interface drives particle accumulation and establishes the conditions for pattern formation. Namely, particle clustering at the interface locally slows the advancing interface and produces concave plume tips that become preferential sites for plume initiation. In addition, we develop a simple scaling for the size of the interfacial deformation based on the interplay between upstream pressure, interface concentration, and plume concentration.

We study the motion of columnar ice crystals that form in clouds over a range of low temperature. Our focus here is on elongated ice crystals, which are smaller than the size of the smallest eddies in the flow, with a moderate aspect ratio comprised between 3 and 5. We determine turbulent solutions of the Navier-Stokes equations over a range of turbulent kinetic energy dissipation characteristic of clouds ($4.41{\mathrm{cm}}^2/{\mathrm{s}}^3\le \varepsilon \le 1120{\mathrm{cm}}^2/{\mathrm{s}}^3$) by using direct numerical simulations, and we follow the motion of crystals using simplified but realistic models for the motion of nonspherical, elongated particles. The influence of the fluid inertia leads to a preferential alignment of the crystals perpendicular to the direction of gravity, the alignment effect being opposed by the turbulent fluctuations. Along with the strong alignment of the crystal axis perpendicular to gravity, we observe only a weak alignment with the vorticity, much weaker than in the absence of gravity. The settling velocity depends only weakly on the orientation of the crystals, but is strongly enhanced when $\varepsilon$ increases, an effect that we attribute to preferential concentration in the flow. As the inertia of the columnar ice crystals considered here is significant, we observe a strong spatial clustering. Finally, we discuss the relevance of the effects identified here on the collision frequency between ice crystals in cloud conditions.

The velocity statistics reveal nonuniversality in both three-dimensional (3D) and two-dimensional (2D) turbulence, despite both prototype systems containing an energy inertial range with constant energy flux. Recently, statistics of scale-dependent velocity circulation exhibit universal bifractal behavior in 2D and 3D hydrodynamic turbulence and quantum turbulence, where the circulation scale is defined as the square root of the minimum area enclosed by the loop. This definition of scale that is independent of loop shape is based on the area rule of circulation first proposed by Migdal: the probability density function (PDF) of circulation is only a function of the minimal surface area enclosed by the loop but not the shape of the loop. This paper demonstrates that the derivation of the circulation area rule can be generalized to all scales in 2D instability-driven turbulence without external forcing, not limited to the inertial range. However, the area rule is not the only solution to the loop equation, so it may not be observed. Another necessary condition for the validity of the area rule is that the second-order momentum of circulation is loop-shape independent. By deriving the relationship between the second-order moment of circulation on a rectangular loop and the energy spectrum, we prove that the area rule cannot be satisfied in the classic inertial-range turbulence with $-5/3$ or $-3$ spectral scalings. As in the 3D case [Iyer et al., Proc. Natl. Acad. Sci. USA 118, e2114679118 (2013)], the second-order moment of circulation is size dependent. Compared with the circulation PDFs, the PDFs normalized by the second-order moment of circulation exhibit significantly weaker dependence on loop shape.

This study experimentally investigates the three-dimensional settling process of centimeter-sized spherical particles in still water using convergent binocular vision technology. The results reveal that the number of settling particles significantly influences the settling behavior when particles are released side by side. Individual particles initially settle along nearly straight paths before randomly deflecting and returning after reaching maximum deviation points. In contrast, twin particles settle synchronously in an almost mirror-image manner, with random deflection largely suppressed—a phenomenon referred to as the mutual support phenomenon (MSP) is this study. The outermost two particles in triplet and quadruplet configurations also exhibit a typical MSP during the settling process. However, the middle particle in the triplet configuration behaves similarly to an individual particle, while the middle two particles in the quadruplet configuration display more complicated settling trajectories due to asymmetric influences from neighboring particles. Additionally, particle image velocimetry measurements are conducted in specific cases to explore the possible mechanisms underlying the random deflection of individual particles and the MSP observed in twin particles.

Two-equation models introduce auxiliary transport equations to estimate a velocity scale and a length scale, whose combination yields the eddy viscosity. The velocity scale is typically associated with the variable $k$, often interpreted as the turbulent kinetic energy (TKE). Using high-Reynolds-number data that were not available at the time of model development, we affirm that the modeled $k$ does not, in fact, represent the total TKE. Rather, it exhibits scaling behavior similar to that of the kinetic energy contained in the active motions—those responsible for producing Reynolds shear stress. To separate active and inactive motions, we propose and validate decomposition methods that segregate turbulent motions into active and inactive components across different levels of data availability. The decompositions are shown to obey the expected scalings of active motions. We further derive the energy budgets of the active and inactive components under the attached eddy hypothesis, revealing that the former are governed by the usual balance between production and dissipation, while the latter contains mean convection, viscous diffusion, dissipation, and the energy transferred from active motions. Analysis of the $k$ equation in two-equation models reveals that it admits both the total TKE and the energy in active motions as asymptotic solutions; the fact that two-equation models select the latter arises from the structure of the dissipation equation. Finally, we introduce a transport equation that governs the kinetic energy in the inactive motions in the logarithmic region, providing a path toward reconciling model outputs with physical turbulence quantities.

We numerically investigate turbulent heat transfer in water-in-oil (W/O) and oil-in-water (O/W) emulsions using direct numerical simulations coupled with a phase-field method. Heat is treated as a passive scalar, initially confined within the dispersed phase and subsequently transferred to the carrier fluid. The two emulsions share identical density and thermal diffusivity, while the oil phase is four times more viscous than water. To isolate convective effects, the same Péclet number ($\text{Pe}=2400$) is imposed in both configurations. Viscosity contrast strongly affects local flow and scalar dynamics, producing enhanced velocity fluctuations and mixing in the water phase and reduced activity in the oil phase. Reversing the dispersed and carrier phases redistributes these local mixing mechanisms between the drop interior and the surrounding fluid. This redistribution leads to similar global heat-transfer rates and comparable thermal transient in both emulsions, despite fundamentally different phase-conditioned flow and mixing dynamics.

A laboratory investigation was conducted to quantify the influence of background rotation on nearly zero-mean turbulence generated within an off-axis mounted isotropic box. High-resolution particle image velocimetry measurements were performed at the box center under varying rotation rates to examine the onset and development of anisotropy. In the absence of rotation, the turbulence exhibits nearly isotropic behavior, with radial and azimuthal velocity fluctuations closely matched and energy spectra consistent with Kolmogorov scaling. As the inverse turbulent Rossby number, ${\text{Ro}}_{\varepsilon }^{-1}$, increases, spectral anisotropy becomes increasingly pronounced, and the range of scales over which the radial and azimuthal spectra diverge broadens. The lower bound of this anisotropic range follows the scaling $({\kappa }_L-{\kappa }_{DI})\eta ={\text{Ro}}_{\varepsilon }^{-1}/40$, indicating a progressive influence of the Coriolis effects. A generalized Taylor transformation applied to spatial and temporal spectra yields characteristic convection velocities $U_r^{*}$ and $U_{\theta }^{*}$, which exceed the local rms fluctuations and scale as $U_r^{*}\sim 3u_r^{\prime }$ and $U_{\theta }^{*}\sim 2u_{\theta }^{\prime }$. Direction-specific turbulent rotation numbers exhibit a linear dependence on ${\text{Ro}}_{\varepsilon }^{-1}$, linking integral-scale rotational dynamics to small-scale anisotropy. The results provide experimental support for theoretical predictions of energy redistribution, quasi-two-dimensionalization, and wave-eddy interaction in rotating turbulence. The empirical scalings may offer compact constraints for turbulence closures in noninertial frames and establish a basis for future studies of scalar transport and dispersion in geophysical and astrophysical flows.

This study experimentally investigates water waves generated by the collapse of a partially immersed axisymmetric granular column into water. The experiments reveal the presence of cnoidal-like waves, nonlinear transition waves, and nonlinear oscillatory waves. Two simplified wave-generation mechanisms are proposed and related to the transition between different wave types, which helps explain the connection between the initial conditions and the resulting wave regimes. The relationships between wave amplitude, celerity, wavelength, and period under varying initial conditions are systematically analyzed and an empirical formula is proposed to predict the maximum wave amplitude. Except in shallow-water cases, most of the observed waves exhibit weak nonlinearity and strong dispersive behavior, distinguishing them from wave patterns reported in previous two-dimensional studies.

We develop a perturbation-based frequency-response framework for analyzing amplification mechanisms that are central to subcritical routes to transition in wall-bounded shear flows. By systematically expanding the input-output dynamics of fluctuations about the laminar base flow with respect to forcing amplitude, we establish a rigorous correspondence between linear resolvent analysis and higher-order nonlinear interactions. At second order, quadratic interactions of unsteady oblique waves generate steady streamwise streaks via the lift-up mechanism. We demonstrate that the spatial structure of these streaks is captured by the second output singular function of the streamwise-constant resolvent operator. At higher orders, nonlinear coupling between oblique waves and induced streaks acts as structured forcing of the laminar linearized dynamics, yielding additional streak components whose relative phase governs reinforcement or attenuation of the leading-order streak response. Our analysis identifies a critical forcing amplitude marking the breakdown of the weakly nonlinear regime, beyond which direct numerical simulations exhibit sustained unsteadiness. We show that this breakdown coincides with the onset of secondary instability, revealing that the nonlinear interactions responsible for streak formation also drive the modal growth central to classical transition theory. The resulting framework provides a mechanistically transparent and computationally efficient description of transition that unifies nonmodal amplification, streak formation, and modal instability within a single formulation derived directly from the Navier–Stokes equations.