arXiv subjects

Rama Govindarajan

Publications and source records attributed to Rama Govindarajan.

At least 19 recordsLinked to original sources

arXiv2026

Caustics of finitely dense inertial particles

Estimating collision rates is of immense importance in particle-laden flows. An economical way of doing this is to directly identify incidences of caustics, or extreme clustering, by tracking particle velocity gradients in the neighborhoods of individual particles. The objective of this work is two-fold. (i) We find conditions under which caustics form, in point-vortex flow and in two-dimensional turbulence. While caustics are known to form in regions of strain, we show that the velocity alignment with strain directions is key. Particles must remain in compressional strain throughout the process to form caustics, whereas survivor particles: which visit high strain but do not form caustics, briefly go through extensional strain during the early part of the process. This enables survivor particles to attain significantly straighter paths, and to move faster, whereas caustics particles follow paths of high curvature and move slower. As a result, caustics particles stay longer in high-strain regions than survivors. (ii) We ask about the effect of finite particle density, where the particle is denser than the background fluid. We show that finite-density particles need to sample stronger background strain than infinite-density ones to trigger caustics, but our other findings are universal across particle density.

physics.flu-dyn↗

arXiv2026

Viscous Settling of Bravais Unit-Cells

We study experimentally and theoretically the Stokesian settling of a well-known class of porous shapes: Bravais lattice unit-cells, whose porosity we vary controllably by changing their lattice spacing. In our experiments, conducted in a square cuboidal container with its long-axis aligned along gravity, we find that the settling speed U and the solid fraction ϕ of these lattice units obey a power-law relationship U $\propto$ ϕ^γ , with an exponent γ = 0.43 independent of their shape. To understand the observed scaling exponent, we analytically and numerically investigate the settling of the simple cubic structure under different approximations. We find that the walls of the container, though far from the sinking object, have a defining effect. Our Stokesian boundary integral simulations show that the Faxen's boundary correction captures the wall-effects accurately and enables us to discount the wall-effect from the experimental data, yielding a power-law exponent γ = 0.30 for settling in an unbounded domain. The power-law relating sinking speed and porosity is a step towards predictively understanding the sedimentation fluxes of complex objects in the clouds and the oceans. However, the applicability of this universal scaling to irregular and biologically richer aggregates found in nature remains an open direction.

cond-mat.soft↗

arXiv2026

Turbulence is ineffective in causing raindrop growth in polluted clouds

Aerosol-cloud interactions represent the largest uncertainty in climate-change assessment, and while cloud turbulence is considered crucial for droplet growth, its precise role remains unclear. Our laboratory-controlled studies show that turbulence does not always enhance collision and coalescence; instead, its influence emerges only when droplets have a sufficiently broad size distribution. The dissipative-scale droplet behaviour underscores the importance of improved parameterisations to accurately model cloud microphysics.

physics.ao-ph↗

arXiv2025

Active Caustics

Inertial particles (IPs) in vortical fluid flow cluster strongly, forming singular structures termed caustics for their resemblance to focal surfaces in optics. Here we show that such extreme aggregation onto low-dimensional submanifolds can arise without mechanical inertia for self-propelled particles (SPPs), through a formal correspondence between the dynamics of IPs and SPPs in a generic background flow. We establish that a singular perturbation underlies caustics formation by SPPs around a single vortex, and numerical studies of SPPs in two-dimensional Navier-Stokes turbulence reveal intense caustics in straining regions of the flow, peaking at intermediate levels of self-propulsion. Our work offers a route to singularly high local concentrations in a macroscopically dilute suspension of zero-Reynolds-number swimmers. Caustics generate burst-like encounters through large relative velocities between neighboring swimmers, with potentially significant implications for communication and sexual reproduction. An intriguing open direction is whether the active turbulence of a suspension of swimming microbes could serve to generate caustics in its own concentration

cond-mat.soft↗

arXiv2025

Streak generation in viscosity-stratified wall-bounded flows

Streamwise elongated flow structures, or streaks, dominate wall-bounded flows. We show that the renowned lift-up mechanism, that generates streaks, is significantly altered by viscosity stratification. We additionally identify a novel pathway for streak generation: the viscosity-stratified lift-up mechanism. The competition and cooperation of the streaks generated by these mechanisms provides an explanation for trends in viscosity-stratified Poiseuille flows, and remarkably, the opposing trends in Couette flows as well. Our theoretical observations are substantiated by numerical experiments.

physics.flu-dyn↗

arXiv2025

Viscosity variation in fluid flows across scale

A wide range of natural and engineered fluid flows exhibit spatial or temporal viscosity variations, spanning scales from microbial locomotion to planetary mantle convection. These variations introduce qualitatively new physical mechanisms absent in constant-viscosity flows. This review surveys such phenomena across scales. In low Reynolds number (Stokes) flows, viscosity gradients couple translation and rotation, enabling novel particle responses to uniform forcing-- mechanisms that microorganisms may exploit. In shear flows, viscosity variation alters base flow profiles and breaks symmetries, modifying stability and transition dynamics. At high Reynolds numbers, stratification fundamentally changes the singular perturbation structure governing energy production, enhancing or suppressing canonical instabilities and introducing new ones. Viscosity variation also affects nonnormal growth and nonlinear interactions that drive transition to turbulence. While laminar and fully developed turbulence have been extensively studied, transitional processes remain poorly understood in variable-viscosity flows. In turbulent regimes, viscosity variation impacts jets, wall-bounded flows, and mixing layers. At geophysical scales, incorporating eddy viscosity stratification in climate models may improve predictions, while in Earth's mantle, viscosity contrasts drive large-scale convection and geological evolution. Particle-laden flows, common across contexts, can generate effective viscosity stratification through inhomogeneous loading. Throughout, we highlight cases where viscosity variation alters flow behavior qualitatively, and point to open questions. This review aims to guide graduate students and researchers toward tractable, cross-disciplinary problems.

physics.flu-dyn↗

arXiv2025

Preliminary experimental investigation on the interaction of a subaqueous dune like granular structure with a turbulent open channel flow

We study the interaction of a subaqueous dune like granular structure with a turbulent open channel flow experimentally using optical diagnostics in the Shields and Froude parameter space ($0.05{\leq}θ{\leq}0.32$, $0.1{\leq}Fr{\leq}0.4$). Interactions between the turbulent flow and the granular structure give rise to transient erosion-deposition dynamics leading to various types of particle transport. The subaqueous structures in the channel bed evolves due to shear-stress-induced erosion, gravity-driven deposition, and subsequent particle transport. We study the centroid motion and the granular structure shape evolution. At lower end of our $θ-Fr$ parameter space, we observe no erosion and the structure remains at rest. We show that the critical Shields number ($θ_{cr}$) is of the order of $0.1$ beyond which erosion starts to occur. At intermediate values of $θ$ and $Fr$ we observe slow erosion, resulting in a rigid body motion of the granular structure without significant shape deformation. Higher values of $θ$ and $Fr$ causes vortex formation at the upstream of the dune resulting in stronger erosion, rapid shape deformation and relatively higher translation velocity of the centroid.

cond-mat.soft↗

arXiv2025

Sedimentation and shear-induced dynamics of spheroids in fluids with spatial viscosity variations

A generalized reciprocal theorem is used to relate the force and torque induced on a particle in an inertia-less fluid with small variation in viscosity to integrals involving Stokes flow fields and the spatial dependence of viscosity. These resistivity expressions are analytically evaluated using spheroidal harmonics and then used to obtain the mobility of the spheroid during sedimentation, and in linear flows, of a fluid with linear viscosity stratification. The coupling between the rotational and translational motion induced by stratification rotates the spheroid's centerline, creating a variety of rotational and translational dynamics dependent upon the particle's aspect ratio, $κ$, and the component of the stratification unit vector in the gravity direction, $d_g$. Spheroids with $0.55\lessapproxκ\lessapprox2.0$ exhibit the largest variety of settling behaviors. Interestingly, this range covers most microplastics and typical microorganisms. One of the modes include a stable orientation dependent only on $κ$ and $d_g$, but independent of initial orientation, thus allowing for the potential control of settling angles and sedimentation rates. In a simple shear flow, cross-streamline migration occurs due to the stratification-induced force generated on the particle. Similarly, a particle no longer stays at the stagnation point of a uniaxial extensional flow. While fully analytical results are obtained for spheroids, numerical simulations provide a source of validation. These simulations also provide additional insights into the stratification-induced force- and torque-producing mechanisms through the stratification-induced stress, which is not accessed in the reciprocal theorem-based analytical calculations.

physics.flu-dyn↗

arXiv2025

Dynamics and clustering of sedimenting disc lattices

Uniform arrays of particles tend to cluster as they sediment in viscous fluids. Shape anisotropy of the particles enriches these dynamics by modifying the mode-structure and the resulting instabilities of the array. A one-dimensional lattice of sedimenting spheroids in the Stokesian regime displays either an exponential or an algebraic rate of clustering depending on the initial lattice spacing (Chajwa et al. 2020). This is caused by an interplay between the Crowley mechanism which promotes clumping, and a shape-induced drift mechanism which subdues it. We theoretically and experimentally investigate the sedimentation dynamics of one-dimensional lattices of oblate spheroids or discs and show a stark difference in clustering behaviour: the Crowley mechanism results in clumps comprised of several spheroids, whereas the drift mechanism results in pairs of spheroids whose asymptotic behavior is determined by pair-hydrodynamic interactions. We find that a Stokeslet, or point-particle, approximation is insufficient to accurately describe the instability and that the corrections provided by the first-reflection are necessary for obtaining some crucial dynamical features. As opposed to a sharp boundary between exponential growth and neutral eigenvalues under the Stokeslet approximation, the first-reflection correction leads to exponential growth for all initial perturbations, but far more rapid algebraic growth than exponential growth at large lattice spacing $d$. For discs with aspect ratio 0.125, corresponding to the experimental value, the instability growth rate is found to decrease with increasing lattice spacing $d$, approximately as $d^{-4.5}$, which is faster than the $d^{-2}$ for spheres (Crowley, 1971). Sedimenting pairs predominantly come together to form '$\perp$', which our theory accounts for through an analysis that builds on Koch & Shaqfeh (1989).

cond-mat.soft↗

arXiv2025

Emergence of capillary waves in miscible co-flowing fluids

We show that capillary waves can exist at the the boundary between miscible co-flowing fluids. We unveil that the interplay between transient interfacial stresses and confinement drives the progressive transition from the well-known inertial regime, characterized by a frequency independent wavenumber, $k\simω^{0}$, to a capillary wave scaling, $k\simω^{2/3}$, unexpected for miscible fluids. This allows us to measure the effective interfacial tension between miscible fluids and its rapid decay on time scales never probed so far, which we rationalize with a model going beyond square-gradient theories. Our work potentially opens a new avenue to measure transient interfacial tensions at the millisecond scale in a controlled manner.

physics.flu-dyn↗

arXiv2025

Sedimentation Dynamics of Bodies with Two Planes of Symmetry

We show that bodies with two planes of symmetry can display a range of behaviors even without inertia. Any such body supports a conserved quantity in its dynamics, and is either a settler, a drifter or a flutterer, depending only on its shape. At large time, settlers and drifters, respectively, fall vertically and obliquely, while flutterers rotate forever while executing intricate patterns. The dynamics of flutterers decouples into a periodic and a Floquet part with different timescales, giving periodicity or quasiperiodicity. We design a set of bodies and use the boundary integral method to show that settlers, drifters, and flutterers, all lie in this set.

physics.flu-dyn↗

arXiv2024

Basset-Boussinesq history force and inertia are relevant for unsteady particle settling dynamics

Our experiments on a sphere falling under gravity in Stokes flow show significant history effects. We observe an algebraic, not exponential, relaxation rate to the terminal velocity, validating the solution to the Basset-Boussinesq-Oseen equation. Unlike in steady Stokes theory, our experiments and theory reveal a vortex ring forming around the sphere and drifting away. As the Reynolds number nears unity, the vortex ring lags behind the sphere, departing from Stokesian theory, though the sphere's algebraic response persists. These findings are critical for interactions in the Stokes limit.

physics.flu-dyn↗

arXiv2024

Mechanism of instability in non-uniform dusty channel flow

Particles in pressure-driven channel flow are often inhomogeneously distributed. Two modes of low-Reynolds number instability, absent in Poiseuille flow of clean fluid, are created by inhomogeneous particle loading, and their mechanism is worked out here. Two distinct classes of behaviour are seen: when the critical layer of the dominant perturbation overlaps with variations in particle concentration, the new instabilities arise, which we term overlap modes. But when the layers are distinct, only the traditional Tollmien-Schlichting mode of instability occurs. We derive the dominant critical layer balance equations in this flow along the lines done classically for clean fluid. These reveal how concentration variations within the critical layer cause two the particle-driven instabilities. As a result of these variations, disturbance kinetic energy production is qualitatively and majorly altered. Surprisingly the two overlap modes, though completely different in the symmetry of the eigenstructure and regime of exponential growth, show practically identical energy budgets, highlighting the relevance of variations within the critical layer. The wall layer is shown to be unimportant. We derive a minimal composite theory comprising all terms in the complete equation which are dominant somewhere in the flow, and show that it contains the essential physics. When particles are infinitely dense relative to the fluid, the volume fraction is negligible. But for finite density ratios, the volume fraction of particles causes a profile of effective viscosity. This is shown to be uniformly stabilizing in the present flow. Gravity is neglected here, and will be important to study in future. So will transient growth of perturbations due to non-normality of the stability operator, in a quest for the mechanism of transition to turbulence.

physics.flu-dyn↗

arXiv2024

Trapping and extreme clustering of finitely-dense inertial particles near a rotating vortex pair

Small heavy particles cannot get attracted into a region of closed streamlines in a non-accelerating frame (Sapsis & Haller 2010). In a rotating system, however, particles can get trapped (Angilella 2010) near vortices. We perform numerical simulations examining trapping of inertial particles in a prototypical rotating flow: an identical pair of rotating Lamb-Oseen vortices, without gravity. Our parameter space includes the particle Stokes number $St$, measuring the particle's inertia, and a density parameter $R$, measuring the particle-to-fluid relative density. We focus on inertial particles that are finitely denser than the fluid. Particles can get indefinitely trapped near the vortices and display extreme clustering into smaller dimensional objects: attracting fixed-points, limit cycles and chaotic attractors. As $St$ increases for a given $R$, we may have an incomplete or complete period-doubling route to chaos, as well as an unusual period-halving route back to a fixed-point attractor. The fraction of trapped particles can vary non-monotonically with $St$. We may even have windows in $St$ for which no particle trapping occurs. At $St$ larger than a critical value, beyond no trapping occurs, significant fractions of particles can spend long but finite times in the vortex vicinity. The inclusion of the Basset-Boussinesq history (BBH) force is imperative in our study due to particle's finite density. BBH force significantly increases the basin of attraction as well as the range of $St$ where trapping can occur. Extreme clustering can be physically significant in planetesimal formation by dust aggregation in protoplanetary disks, phytoplankton aggregation in oceans, etc.

physics.flu-dyn↗

arXiv2023

Explicit Runge-Kutta algorithm to solve non-local equations with memory effects: case of the Maxey-Riley-Gatignol equation

A standard approach to solve ordinary differential equations, when they describe dynamical systems, is to adopt a Runge-Kutta or related scheme. Such schemes, however, are not applicable to the large class of equations which do not constitute dynamical systems. In several physical systems, we encounter integro-differential equations with memory terms where the time derivative of a state variable at a given time depends on all past states of the system. Secondly, there are equations whose solutions do not have well-defined Taylor series expansion. The Maxey-Riley-Gatignol equation, which describes the dynamics of an inertial particle in nonuniform and unsteady flow, displays both challenges. We use it as a test bed to address the questions we raise, but our method may be applied to all equations of this class. We show that the Maxey-Riley-Gatignol equation can be embedded into an extended Markovian system which is constructed by introducing a new dynamical co-evolving state variable that encodes memory of past states. We develop a Runge-Kutta algorithm for the resultant Markovian system. The form of the kernels involved in deriving the Runge-Kutta scheme necessitates the use of an expansion in powers of $t^{1/2}$. Our approach naturally inherits the benefits of standard time-integrators, namely a constant memory storage cost, a linear growth of operational effort with simulation time, and the ability to restart a simulation with the final state as the new initial condition.

physics.flu-dyn↗

arXiv2023

Irregular dependence on Stokes number and non-ergodic transport of heavy inertial particles in steady laminar flows

Small heavy particles in a fluid flow respond to the flow on a time-scale proportional to their inertia, or Stokes number St. Their behaviour is thought to be gradually modified as St increases. We show, in the steady spatially-periodic laminar Taylor-Green flow, that particle dynamics, and their effective diffusivity, actually change in an irregular, non-monotonic and sometimes discontinuous manner, with increasing St. At Stokes of order one, we show chaotic particle motion, contrasting earlier conclusions for heavy particles in the same flow (Wang et al. 1992). Particles may display trapped orbits, or unbounded diffusive or ballistic dispersion, with the vortices behaving like scatterers in a soft Lorentz gas (Klages et al. 2019). The dynamics is non-ergodic. We discuss the possible consequences of our findings for particulate turbulent flows.

physics.flu-dyn↗

arXiv2023

Geometric characterization of vortex lines in turbulence

Vorticity in turbulent flows is often organized into complex geometries that influence the dynamics. We use a relatively novel approach to describe these geometries: that of obtaining segments of vortex lines embedded in the flow. This enables us to quantify the geometric features of these objects. Vortex lines differ widely in their behaviour but we find some unifying features. The decay from high levels of vorticity is shown to happen over a short fraction of the vortex length. The local curvature is inversely related with the vorticity magnitude. Strong parts of vortex lines bundle together. It is hoped that this first work will generate interest in such quantification and the physics of vortex dynamics in turbulence.

physics.flu-dyn↗

arXiv2022

The waltz of tiny droplets and the flow they live in

This article describes the dynamics of small inertial particles centrifuging out of a single vortex. It shows the importance of caustics formation in the vicinity of a single vortex: both for particle collisions and void formation. From these single-vortex studies we provide estimates of the role of caustics in high Reynolds number turbulence, and in the case of clouds, estimate how they may help in rain initiation by bridging the droplet-growth bottleneck. We briefly describe how the Basset- Boussinesq history force may be calculated by a method which does not involve huge memory costs, and provide arguments for its possible importance for droplets in turbulence. We discuss how phase change could render cloud turbulence fundamentally different from turbulence in other situations.

physics.flu-dyn↗