arXiv subjects

Akshay Bhatnagar

Publications and source records attributed to Akshay Bhatnagar.

17 recordsLinked to original sources

arXiv2026

Orientation Dynamics of Gyrotactic Microswimmers in Turbulent Flows

We study the dynamics of gyrotactic microswimmers suspended in homogeneous and isotropic turbulence by using direct numerical simulations (DNS). The swimmers are characterized by three non-dimensional parameters: their aspect ratio ($\gamma$), a dimensionless swimming speed ($\phi$), and a dimensionless reorientation time ($\psi$). Strong gyrotaxis (smaller $\psi$) promotes vertical alignment of the swimmers, while weak gyrotaxis leads to nearly isotropic orientations. At low swimming numbers, the orientation distribution is largely shape-independent with spheres and spheroids showing marginally greater vertical alignment than rods, whereas at higher activity the peaks of the distributions exhibit largely shape-independent behavior and the tails show a clear dependence on particle shape. However, at large $\psi$ rods exhibit a stronger alignment along the vertical. We observe that at small $\psi$ the rod-shaped swimmers respond to shear by aligning with the stretching direction of the strain-rate tensor, while at large $\psi$ the alignment with the vorticity vector is preferred. The orientation autocorrelation is found to decay exponentially, with a decay rate that scales as $1/(2\psi)$. Analysis of the mean-squared displacement (MSD) reveals a transition from a ballistic motion at short times to a diffusive regime at longer times. To assess the efficiency of vertical migration, we compute the probability distributions of vertical displacement over a fixed time interval and the time taken to migrate a specific vertical distance. Furthermore, we use a simplified two-dimensional model for spherical swimmers that qualitatively reproduces the key trends observed in the full three-dimensional (3D) simulations.

cond-mat.soft↗

arXiv2025

Flow-Induced Phase Separation for Active Brownian Particles in Four-Roll-Mill Flow

We investigate the collective dynamics of active Brownian particles (ABPs) subjected to a steady two-dimensional four-roll-mill flow using numerical simulations. By varying the packing fraction ($\phi$), we uncover a novel flow-induced phase separation (FIPS) that emerges beyond a critical density ($\phi \geq 0.6$). The mean-square displacement (MSD) exhibits an intermediate bump between ballistic and diffusive regimes, indicating transient trapping and flow-guided clustering. The effective diffusivity decreases quadratically with $\phi$, while the drift velocity remains nearly constant, demonstrating that large-scale transport is primarily dictated by the background flow. Number fluctuations show a crossover from normal to giant scaling, signaling the onset of long-range density inhomogeneities in the FIPS regime. Our findings provide new insights into the coupling between activity, crowding, and flow, offering a unified framework for understanding phase behavior in driven active matter systems.

cond-mat.soft↗

arXiv2024

Effect of the background flow on the motility induced phase separation

We simulate active Brownian particles (ABPs) with soft-repulsive interactions subjected to a four-roll-mill flow. In the absence of flow, this system exhibits motility-induced phase separation (MIPS). To investigate the interplay between MIPS and flow-induced mixing, we introduce dimensionless parameters: a scaled time, $\tau$, and a scaled velocity, ${\rm v}$, characterizing the ratio of ABP to fluid time and velocity scales, respectively. The parameter space defined by $\tau$ and ${\rm v}$ reveals three distinct ABP distribution regimes. At low velocities ${\rm v} \ll 1$, flow dominates, leading to a homogeneous mixture. Conversely, at high velocities ${\rm v} \gg 1$, motility prevails, resulting in MIPS. In the intermediate regime (${\rm v} \sim 1$), the system's behavior depends on $\tau$. For $\tau <1$, a moderately mixed homogeneous phase emerges, while for $\tau >1$, a novel phase, termed flow-induced phase separation (FIPS), arises due to the combined effects of flow topology and ABP motility and size. To characterize these phases, we analyze drift velocity, diffusivity, mean-squared displacement, giant number fluctuations, radial distribution function, and cluster-size distribution.

cond-mat.soft↗

arXiv2023

Inertial Particles in Superfluid Turbulence: Coflow and Counterflow

We use pseudospectral direct numerical simulations (DNSs) to solve the three-dimensional (3D) Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model of superfluid Helium. We then explore the statistical properties of inertial particles, in both coflow and counterflow superfluid turbulence (ST) in the 3D HVBK system; particle motion is governed by a generalization of the Maxey-Riley-Gatignol equations. We first characterize the anisotropy of counterflow ST by showing that there exist large vortical columns. The light particles show confined motion as they are attracted towards these columns and they form large clusters; by contrast, heavy particles are expelled from these vortical regions. We characterise the statistics of such inertial particles in 3D HVBK ST: (1) The mean angle $Θ(τ)$, between particle positions, separated by the time lag $τ$, exhibits two different scaling regions in (a) dissipation and (b) inertial ranges, for different values of the parameters in our model; in particular, the value of $Θ(τ)$, at large $τ$, depends on the magnitude of ${\bf U}_{ns}$. (2) The irreversibility of 3D HVBK turbulence is quantified by computing the statistics of energy increments for inertial particles. (3) The probability distribution function (PDF) of energy increments is of direct relevance to recent experimental studies of irreversibility in superfluid turbulence; we find, in agreement with these experiments, that, for counterflow ST, the skewness of this PDF is less pronounced than its counterparts for coflow ST or for classical-fluid turbulence.

physics.flu-dyn↗

arXiv2021

Rate of formation of caustics in heavy particles advected by turbulence

The rate of collision and the relative velocities of the colliding particles in turbulent flows is a crucial part of several natural phenomena, e.g., rain formation in warm clouds and planetesimal formation in a protoplanetary disks. The particles are often modeled as passive, but heavy and inertial. Within this model, large relative velocities emerge due to formation of singularities (caustics) of in the gradient matrix of the velocities of the particles. Using extensive direct numerical simulations of heavy particles in both two (direct and inverse cascade) and three dimensional turbulent flows we calculate the rate of formation of caustics, $J$ as a function of the Stokes number (${\rm St}$).The best approximation to our data is $J \sim \exp(-C/{\rm St})$, in the limit ${\rm St} \to 0 $ where $C$ is a non-universal constant.

physics.flu-dyn↗

arXiv2021

Coagulation drives turbulence in binary fluid mixtures

We use direct numerical simulations and scaling arguments to study coarsening in binary fluid mixtures with a conserved order parameter in the droplet-spinodal regime -- the volume fraction of the droplets is neither too small nor symmetric -- for small diffusivity and viscosity. Coagulation of droplets drives a turbulent flow that eventually decays. We uncover a novel coarsening mechanism, driven by turbulence where the characteristic length scale of the flow is different from the characteristic length scale of droplets, giving rise to a domain growth law of $t^{1/2}$, where $t$ is time. At intermediate times, both the flow and the droplets form self-similar structures: the structure factor $S(q) \sim q^{-2}$ and the kinetic energy spectra $E(q) \sim q^{-5/3}$ for an intermediate range of $q$, the wavenumber.

cond-mat.stat-mech↗

arXiv2021

Paths to caustic formation in turbulent aerosols

The dynamics of small, yet heavy, identical particles in turbulence exhibits singularities, called caustics, that lead to large fluctuations in the spatial particle-number density, and in collision velocities. For large particle, inertia the fluid velocity at the particle position is essentially a white-noise signal and caustic formation is analogous to Kramers escape. Here we show that caustic formation at small particle inertia is different. Caustics tend to form in the vicinity of particle trajectories that experience a specific history of fluid-velocity gradients, characterised by low vorticity and a violent strain exceeding a large threshold. We develop a theory that explains our findings in terms of an optimal path to caustic formation that is approached in the small inertia limit.

physics.flu-dyn↗

arXiv2020

The spreading of viruses by airborne aerosols: lessons from a first-passage-time problem for tracers in turbulent flows

We study the spreading of viruses, such as SARS-CoV-2, by airborne aerosols, via a new first-passage-time problem for Lagrangian tracers that are advected by a turbulent flow: By direct numerical simulations of the three-dimensional (3D) incompressible, Navier-Stokes equation, we obtain the time $t_R$ at which a tracer, initially at the origin of a sphere of radius $R$, crosses the surface of the sphere \textit{for the first time}. We obtain the probability distribution function $\mathcal{P}(R,t_R)$ and show that it displays two qualitatively different behaviors: (a) for $R \ll L_{\rm I}$, $\mathcal{P}(R,t_R)$ has a power-law tail $\sim t_R^{-α}$, with the exponent $α= 4$ and $L_{\rm I}$ the integral scale of the turbulent flow; (b) for $l_{\rm I} \lesssim R $, the tail of $\mathcal{P}(R,t_R)$ decays exponentially. We develop models that allow us to obtain these asymptotic behaviors analytically. We show how to use $\mathcal{P}(R,t_R)$ to develop social-distancing guidelines for the mitigation of the spreading of airborne aerosols with viruses such as SARS-CoV-2.

physics.flu-dyn↗

arXiv2020

Lagrangian Irreversibility and Eulerian Dissipation in Fully-Developed Turbulence

We revisit the issue of Lagrangian irreversibility in the context of recent results [Xu, et al., PNAS, 111, 7558 (2014)] on flight-crash events in turbulent flows and show how extreme events in the Eulerian dissipation statistics are related to the statistics of power-fluctuations for tracer trajectories. Surprisingly, we find that particle trajectories in intense dissipation zones are dominated by energy gains sharper than energy losses, contrary to flight-crashes, through a pressure-gradient driven take-off phenomenon. Our conclusions are rationalised by analysing data from simulations of three-dimensional intermittent turbulence, as well as from non-intermittent decimated flows. Lagrangian irreversibility is found to persist even in the latter case, wherein fluctuations of the dissipation rate are shown to be relatively mild and to follow probability distribution functions with exponential tails.

physics.flu-dyn↗

arXiv2020

Statistics of relative velocity for particles settling under gravity in a turbulent flow

We study the joint probability distributions of separation, $R$, and radial component of the relative velocity, $V_{\rm R}$, of particles settling under gravity in a turbulent flow. We also obtain the moments of these distributions and analyze their anisotropy using spherical harmonics. We find that the qualitative nature of the joint distributions remains the same as no gravity case. Distributions of $V_{\rm R}$ for fixed values of $R$ show a power-law dependence on $V_{\rm R}$ for a range of $V_{\rm R}$, exponent of the power-law depends on the gravity. Effects of gravity are also manifested in the following ways: (a) moments of the distributions are anisotropic; the degree of anisotropy depends on particle's Stokes number, but does not depend on $R$ for small values of $R$. (b) mean velocity of collision between two particles is decreased for particles having equal Stokes numbers but increased for particles having different Stokes numbers. For the later, collision velocity is set by the difference in their settling velocities.

physics.flu-dyn↗

arXiv2018

Relative velocities in bi-disperse turbulent aerosols: simulations and theory

We perform direct numerical simulations of a bi-disperse suspension of heavy spherical particles in forced, homogeneous, and isotropic three-dimensional turbulence. We compute the joint distribution of relative particle distances and longitudinal relative velocities between particles of different sizes, and compare the results with recent theoretical predictions [Meibohm et al. Phys. Rev. E 96 (2017) 061102] for the shape of this distribution. We also compute the moments of relative velocities as a function of particle separation, and compare with the theoretical predictions. We observe good agreement.

physics.flu-dyn↗

arXiv2018

Clustering and dynamic decoupling of dust grains in turbulent molecular clouds

We present high resolution ($1024^3$) simulations of super-/hyper-sonic isothermal hydrodynamic turbulence inside an interstellar molecular cloud (resolving scales of typically 20 -- 100 AU), including a multi-disperse population of dust grains, i.e., a range of grain sizes is considered. Due to inertia, large grains (typical radius $a \gtrsim 1.0\,μ$m) will decouple from the gas flow, while small grains ($a\lesssim 0.1\,μ$m) will tend to better trace the motions of the gas. We note that simulations with purely solenoidal forcing show somewhat more pronounced decoupling and less clustering compared to simulations with purely compressive forcing. Overall, small and large grains tend to cluster, while intermediate-size grains show essentially a random isotropic distribution. As a consequence of increased clustering, the grain-grain interaction rate is locally elevated; but since small and large grains are often not spatially correlated, it is unclear what effect this clustering would have on the coagulation rate. Due to spatial separation of dust and gas, a diffuse upper limit to the grain sizes obtained by condensational growth is also expected, since large (decoupled) grains are not necessarily located where the growth species in the molecular gas is.

astro-ph.GA↗

arXiv2017

Heavy inertial particles in turbulent flows gain energy slowly but lose it rapidly

We present an extensive numerical study of the time irreversibility of the dynamics of heavy inertial particles in three-dimensional, statistically homogeneous and isotropic turbulent flows. We show that the probability density function (PDF) of the increment, $W(τ)$, of a particle's energy over a time-scale $τ$ is non-Gaussian, and skewed towards negative values. This implies that, on average, particles gain energy over a period of time that is longer than the duration over which they lose energy. We call this $\textit{slow gain}$ and $\textit{fast loss}$. We find that the third moment of $W(τ)$ scales as $τ^3$, for small values of $τ$. We show that the PDF of power-input $p$ is negatively skewed too; we use this skewness ${\rm Ir}$ as a measure of the time-irreversibility and we demonstrate that it increases sharply with the Stokes number ${\rm St}$, for small ${\rm St}$; this increase slows down at ${\rm St} \simeq 1$. Furthermore, we obtain the PDFs of $t^+$ and $t^-$, the times over which $p$ has, respectively, positive or negative signs, i.e., the particle gains or loses energy. We obtain from these PDFs a direct and natural quantification of the the slow-gain and fast-loss of the particles, because these PDFs possess exponential tails, whence we infer the characteristic loss and gain times $t_{\rm loss}$ and $t_{\rm gain}$, respectively; and we obtain $t_{\rm loss} < t_{\rm gain}$, for all the cases we have considered. Finally, we show that the slow-gain in energy of the particles is equally likely in vortical or strain-dominated regions of the flow; in contrast, the fast-loss of energy occurs with greater probability in the latter than in the former.

physics.flu-dyn↗

arXiv2017

Statistics of the relative velocity of particles in turbulent flows : monodisperse particles

We use direct numerical simulations to calculate the joint probability density function of the relative distance $R$ and relative radial velocity component $V_R$ for a pair of heavy inertial particles suspended in homogeneous and isotropic turbulent flows. At small scales the distribution is scale invariant, with a scaling exponent that is related to the particle-particle correlation dimension in phase space, $D_2$. It was argued [1, 2] that the scale invariant part of the distribution has two asymptotic regimes: (1) $|V_R| \ll R$ where the distribution depends solely on $R$; and (2) $|V_R| \gg R$ where the distribution is a function of $|V_R|$ alone. The probability distributions in these two regimes are matched along a straight line $|V_R| = z^\ast R$. Our simulations confirm that this is indeed correct. We further obtain $D_2$ and $z^\ast$ as a function of the Stokes number, ${\rm St}$. The former depends non-monotonically on ${\rm St}$ with a minimum at about ${\rm St} \approx 0.7$ and the latter has only a weak dependence on ${\rm St}$.

physics.flu-dyn↗

arXiv2017

Lagrangian Statistics for Navier-Stokes Turbulence under Fourier-mode reduction: Fractal and Homogeneous Decimations

We study small-scale and high-frequency turbulent fluctuations in three-dimensional flows under Fourier-mode reduction. The Navier-Stokes equations are evolved on a restricted set of modes, obtained as a projection on a fractal or homogeneous Fourier set. We find a strong sensitivity (reduction) of the high-frequency variability of the Lagrangian velocity fluctuations on the degree of mode decimation, similarly to what is already reported for Eulerian statistics. This is quantified by a tendency towards a quasi-Gaussian statistics, i.e., to a reduction of intermittency, at all scales and frequencies. This can be attributed to a strong depletion of vortex filaments and of the vortex stretching mechanism. Nevertheless, we found that Eulerian and Lagrangian ensembles are still connected by a dimensional bridge-relation which is independent of the degree of Fourier-mode decimation.

physics.flu-dyn↗

arXiv2016

How long do particles spend in vortical regions in turbulent flows?

We obtain the probability distribution functions (PDFs) of the time that a Lagrangian tracer or a heavy inertial particle spends in vortical or strain-dominated regions of a turbulent flow, by carrying out direct numerical simulation (DNS) of such particles advected by statistically steady, homogeneous and isotropic turbulence in the forced, three-dimensional, incompressible Navier-Stokes equation. We use the two invariants, $Q$ and $R$, of the velocity-gradient tensor to distinguish between vortical and strain-dominated regions of the flow and partition the $Q-R$ plane into four different regions depending on the topology of the flow; out of these four regions two correspond to vorticity-dominated regions of the flow and two correspond to strain-dominated ones. We obtain $Q$ and $R$ along the trajectories of tracers and heavy inertial particles and find out the time $\mathrm{t_{pers}}$ for which they remain in one of the four regions of the $Q-R$ plane. We find that the PDFs of $\mathrm{t_{pers}}$ display exponentially decaying tails for all four regions for tracers and heavy inertial particles. From these PDFs we extract characteristic times scales, which help us to quantify the time that such particles spend in vortical or strain-dominated regions of the flow.

physics.flu-dyn↗

arXiv2014

Universal Statistical Properties of Inertial-particle Trajectories in Three-dimensional, Homogeneous, Isotropic, Fluid Turbulence

We uncover universal statistical properties of the trajectories of heavy inertial particles in three-dimensional, statistically steady, homogeneous, and isotropic turbulent flows by extensive direct numerical simulations. We show that the probability distribution functions (PDFs) $P(ϕ)$, of the angle $ϕ$ between the Eulerian velocity ${\bf u}$ and the particle velocity ${\bf v}$, at this point and time, shows a power-law region in which $P(ϕ) \sim ϕ^{-γ}$, with a new universal exponent $γ\simeq 4$. Furthermore, the PDFs of the trajectory curvature $κ$ and modulus $θ$ of the torsion $\vartheta$ have power-law tails that scale, respectively, as $P(κ) \sim κ^{-h_κ}$, as $κ\to \infty$, and $P(θ) \sim θ^{-h_θ}$, as $θ\to \infty$, with exponents $h_κ\simeq 2.5$ and $h_θ\simeq 3$ that are universal to the extent that they do not depend on the Stokes number ${\rm St}$ (given our error bars). We also show that $γ$, $h_κ$ and $h_θ$ can be obtained by using simple stochastic models. We characterize the complexity of heavy-particle trajectories by the number $N_{\rm I}(t,{\rm St})$ of points (up until time $t$) at which $\vartheta$ changes sign. We show that $n_{\rm I}({\rm St}) \equiv \lim_{t\to\infty} \frac{N_{\rm I}(t,{\rm St})}{t} \sim {\rm St}^{-Δ}$, with $Δ\simeq 0.4$ a universal exponent.

physics.flu-dyn↗