arXiv subjects

Prasad Perlekar

Publications and source records attributed to Prasad Perlekar.

At least 37 records · Page 2Linked to original sources

arXiv2021

Pattern stabilisation in swarms of programmable active matter: a probe for turbulence at large length scales

We propose an algorithm for creating stable, ordered, swarms of active robotic agents arranged in any given pattern. The strategy involves suppressing a class of fluctuations known as "non-affine" displacements, viz. those involving non-linear deformations of a reference pattern, while all (or most) affine deformations are allowed. We show that this can be achieved using precisely calculated, fluctuating, thrust forces associated with a vanishing average power input. A surprising outcome of our study is that once the structure of the swarm is maintained at steady state, the statistics of the underlying flow field is determined solely from the statistics of the forces needed to stabilize the swarm.

cond-mat.soft↗

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↗

arXiv2021

Phase ordering, topological defects, and turbulence in the 3D incompressible Toner-Tu equation

We investigate phase ordering dynamics of the incompressible Toner-Tu equation in three dimensions. We show that the phase ordering proceeds via defect merger events and the dynamics is controlled by the Reynolds number Re. At low Re, the dynamics is similar to that of the Ginzburg-Landau equation. At high Re, turbulence controls phase ordering. In particular, we observe a forward energy cascade from the coarsening length scale to the dissipation scale.

cond-mat.soft↗

arXiv2021

Ephemeral Antibubbles: Spatiotemporal Evolution from Direct Numerical Simulations

Antibubbles, which consist of a shell of a low-density fluid inside a high-density fluid, have several promising applications. We show, via extensive direct numerical simulations (DNSs), in both two and three dimensions (2D and 3D), that the spatiotemporal evolution of antibubbles can be described naturally by the coupled Cahn-Hilliard-Navier-Stokes (CHNS) equations for a binary fluid. Our DNSs capture elegantly the gravity-induced thinning and breakup of an antibubble via the time evolution of the Cahn-Hilliard scalar order parameter field $ϕ$, which varies continuously across interfaces, so we do not have to enforce complicated boundary conditions at the moving antibubble interfaces. To ensure that our results are robust, we supplement our CHNS simulations with sharp-interface Volume-of-Fluid (VoF) DNSs. We track the thickness of the antibubble and calculate the dependence of the lifetime of an antibubble on several parameters; we show that our DNS results agree with various experimental results; in particular, the velocity with which the arms of the antibubble retract after breakup scales as $σ^{1/2}$, where $σ$ is the surface tension.

physics.flu-dyn↗

arXiv2021

Surface tension as the destabiliser of a vortical interface

We study the dynamics of an initially flat interface between two immiscible fluids, with a vortex situated on it. We show how surface tension causes vorticity generation at a general curved interface. This creates a velocity jump across the interface which increases quadratically in time, and causes the Kelvin-Helmholtz instability. Surface tension thus acts as a destabiliser by vorticity creation, winning over its own tendency to stabilize by smoothing out interfacial perturbations to reduce surface energy. We further show that this instability is manifested within the vortex core at times larger than $\sim (k We)^{1/4}$ for a Weber number $We$ and perturbation wavenumber $k$, destroying the flow structure. The vorticity peels off into small-scale structures away from the interface. Using energy balance we provide the growth with time in total interface length. A density difference between the fluids produces additional instabilities outside the vortex core due to centrifugal effects. We demonstrate the importance of this mechanism in two-dimensional turbulence simulations with a prescribed initial interface. We show an increase in kinetic energy at large wave numbers due to the creation of small-scale vortices by the action of surface tension.

physics.flu-dyn↗

arXiv2020

Pseudo-turbulence in two-dimensional buoyancy driven bubbly flows: a DNS study

We present a direct numerical simulation (DNS) study of buoyancy driven bubbly flows in two-dimensions. We employ volume of fluid (VOF) method to track the bubble interface. To investigate spectral properties of the flow, we derive the scale-by-scale energy budget equation. We show that the Galilei number (Ga) controls different scaling regimes in the energy spectrum. For high Galilei numbers, we find the presence of an inverse energy cascade. Our study indicates that the density ratio of the bubble with the ambient fluid or the presence of coalescence between the bubbles does not alter the scaling behaviour.

physics.flu-dyn↗

arXiv2020

Coarsening in the two-dimensional incompressible Toner-Tu equation: Signatures of turbulence

We investigate coarsening dynamics in the two-dimensional, incompressible Toner-Tu equation. We show that coarsening proceeds via vortex merger events, and the dynamics crucially depend on the Reynolds number Re. For low Re, the coarsening process has similarities to Ginzburg-Landau dynamics. On the other hand, for high Re, coarsening shows signatures of turbulence. In particular, we show the presence of an enstrophy cascade from the intervortex separation scale to the dissipation scale.

physics.flu-dyn↗

arXiv2020

Fixation in Competing Populations: Diffusion and Strategies for Survival

How should dispersal strategies be chosen to increase the likelihood of survival of a species? We obtain the answer for the spatially extended versions of three well-known models of two competing species with unequal diffusivities. Though identical at the mean-field level, the three models exhibit drastically different behaviour leading to different optimal strategies for survival, with or without a selective advantage for one species. With conserved total particle number, dispersal has no effect on survival probability. With a fluctuating number, faster dispersal is advantageous if intra-species competition is present, while moving slower is the optimal strategy for the disadvantaged species if there is no intra-species competition: it is imperative to include fluctuations to properly formulate survival strategies.

q-bio.PE↗

arXiv2019

Liquid velocity fluctuations and energy spectra in three-dimensional buoyancy driven bubbly flows

We present a direct numerical simulation (DNS) study of pseudo-turbulence in buoyancy driven bubbly flows for a range of Reynolds ($\Rey$) and Atwood ($\At$) numbers. We study the probability distribution function of the horizontal and vertical liquid velocity fluctuations and find them to be in quantitative agreement with the experiments. The energy spectrum shows the $k^{-3}$ scaling at high $\Rey$ and becomes steeper on reducing the $\Rey$. To investigate the spectral transfers in the flow, we derive the scale-by-scale energy budget equation. Our analysis shows that, for scales smaller than the bubble diameter, the net production because of the surface tension and the kinetic energy flux balances viscous dissipation to give the $k^{-3}$ scaling of the energy spectrum for both low and high $\At$.

physics.flu-dyn↗

arXiv2019

Clustering and energy spectra in two-dimensional dusty gas turbulence

We present Direct Numerical Simulation (DNS) of heavy inertial particles (dust) immersed in two-dimensional turbulent flow (gas). The dust are modeled as mono-dispersed heavy particles capable of modifying the flow through two-way coupling. By varying the Stokes number (St) and the mass-loading parameter $(ϕ_{\rm m})$, we study the clustering phenomenon and the gas phase kinetic energy spectra. We find that the dust-dust correlation dimension $(d_2)$ also depends on $ϕ_{\rm m}$. In particular, clustering decreases as mass-loading $(ϕ_{\rm m})$, is increased. In the kinetic energy spectra of gas we show: (i) emergence of a new scaling regime, (ii) the scaling exponent in this regime is not unique but rather a function of both St and $(ϕ_{\rm m} )$. Using a scale-by-scale enstrophy budget analysis we show in the new scaling regime, viscous dissipation due to the gas balances back-reaction from the dust.

physics.flu-dyn↗

arXiv2018

Kinetic energy spectra and flux in turbulent phase-separating symmetric binary-fluid mixtures

We conduct direct numerical simulation (DNS) of the Cahn-Hilliard-Navier-Stokes (CHNS) equations to investigate the statistical properties of the turbulent phase-separating symmetric binary-fluid mixture. Turbulence causes an arrest of the phase-separation which leads to the formation of a statistically steady emulsion. We characterize turbulent velocity fluctuations in an emulsion for different values of the Reynolds number and the Weber number. Our scale-by-scale kinetic energy budget analysis shows that the interfacial terms in the CHNS provide an alternate route for the kinetic energy transfer. By studying the probability distribution function (PDF) of the energy dissipation rate, the vorticity magnitude, and the joint-PDF of the velocity-gradient invariants we show that the statistics of the turbulent fluctuations do not change with the Weber number.

physics.flu-dyn↗

arXiv2017

Topology of two-dimensional turbulent flows of dust and gas

We perform direct numerical simulations (DNS) of passive heavy inertial particles (dust) in homogeneous and isotropic two-dimensional turbulent flows (gas) for a range of Stokes number, ${\rm St} < 1$, using both Lagrangian and Eulerian approach (with a shock-capturing scheme). We find that: The dust-density field in our Eulerian simulations have the same correlation dimension $d_2$ as obtained from the clustering of particles in the Lagrangian simulations for ${\rm St} < 1$; The cumulative probability distribution function of the dust-density coarse-grained over a scale $r$ in the inertial range has a left-tail with a power-law fall-off indicating presence of voids; The energy spectrum of the dust-velocity has a power-law range with an exponent that is same as the gas-velocity spectrum except at very high Fourier modes; The compressibility of the dust-velocity field is proportional to ${\rm St}^2$. We quantify the topological properties of the dust-velocity and the gas-velocity through their gradient matrices, called $\mathcal{A}$ and $\mathcal{B}$, respectively. The topological properties of $\mathcal{B}$ are the same in Eulerian and Lagrangian frames only if the Eulerian data are weighed by the dust-density -- a correspondence that we use to study Lagrangian properties of $\mathcal{A}$. In the Lagrangian frame, the mean value of the trace of $\mathcal{A} \sim - \exp(-C/{\rm St}$, with a constant $C\approx 0.1$. The topology of the dust-velocity fields shows that as ${\rm St} increases the contribution to negative divergence comes mostly from saddles and the contribution to positive divergence comes from both vortices and saddles. Compared to the Eulerian case, the density-weighed Eulerian case has less inward spirals and more converging saddles. Outward spirals are the least probable topological structures in both cases.

physics.flu-dyn↗

arXiv2017

Spreading of non-motile bacteria on a hard agar plate: Comparison between agent-based and stochastic simulations

We study spreading of a non-motile bacteria colony on a hard agar plate by using agent-based and continuum models. We show that the spreading dynamics depends on the initial nutrient concentration, the motility and the inherent demographic noise. Population fluctuations are inherent in an agent based model whereas, for the continuum model we model them by using a stochastic Langevin equation. We show that the intrinsic population fluctuations coupled with non-linear diffusivity lead to a transition from Diffusion Limited Aggregation (DLA) type morphology to an Eden-like morphology on decreasing the initial nutrient concentration.

physics.comp-ph↗

arXiv2017

Numerical analysis of the lattice Boltzmann method for simulation of linear acoustic waves

We analyse a linear lattice Boltzmann (LB) formulation for simulation of linear acoustic wave propagation in heterogeneous media. We employ the single-relaxation-time Bhatnagar-Gross-Krook (BGK) as well as the general multi-relaxation-time (MRT) collision operators. By calculating the dispersion relation for various 2D lattices, we show that the D2Q5 lattice is the most suitable model for the linear acoustic problem. We also implement a grid-refinement algorithm for the LB scheme to simulate waves propagating in a heterogeneous medium with velocity contrasts. Our results show that the LB scheme performance is comparable to the classical second-order finite-difference schemes. Given its efficiency for parallel computation, the LB method can be a cost effective tool for the simulation of linear acoustic waves in complex geometries and multiphase media.

physics.comp-ph↗

arXiv2016

Coherent structures and extreme events in rotating multiphase turbulent flows

By using direct numerical simulations (DNS) at unprecedented resolution we study turbulence under rotation in the presence of simultaneous direct and inverse cascades. The accumulation of energy at large scale leads to the formation of vertical coherent regions with high vorticity oriented along the rotation axis. By seeding the flow with millions of inertial particles, we quantify -for the first time- the effects of those coherent vertical structures on the preferential concentration of light and heavy particles. Furthermore, we quantitatively show that extreme fluctuations, leading to deviations from a normal-distributed statistics, result from the entangled interaction of the vertical structures with the turbulent background. Finally, we present the first-ever measurement of the relative importance between Stokes drag, Coriolis force and centripetal forces along the trajectories of inertial particles. We discover that vortical coherent structures lead to unexpected diffusion properties for heavy and light particles in the directions parallel and perpendicular to the rotation axis.

physics.flu-dyn↗

arXiv2016

Two-dimensional, homogeneous, isotropic fluid turbulence with polymer additives

We present the most extensive direct numerical simulations, attempted so far, of statistically steady, homogeneous, isotropic turbulence in two-dimensional fluid films with air-drag-induced friction and with polymer additives. Our study reveals that the polymers (a) reduce the total fluid energy, enstrophy, and palinstrophy, (b) modify the fluid energy spectrum both in inverse- and forward-cascade regimes, (c) reduce small-scale intermittency, (d) suppress regions of large vorticity and strain rate, and (e) stretch in strain-dominated regions. We compare our results with earlier experimental studies; and we propose new experiments.

physics.flu-dyn↗

arXiv2016

Binary-Fluid Turbulence: Signatures of Multifractal Droplet Dynamics and Dissipation Reduction

We present an extensive direct numerical simulation of statistically steady, homogeneous, isotropic turbulence in two-dimensional, binary-fluid mixtures with air-drag-induced friction by using the Cahn-Hilliard-Navier-Stokes equations. We choose parameters, e.g., the surface tension, such that we have a droplet of the minority phase moving inside a turbulent background of the majority phase. We characterize the deformation of the droplet and show that it displays multifractal dynamics. The probability distribution functions of the components of the acceleration of the center of mass of the droplet exhibit wide, non-Gaussian tails. Our study reveals that the droplet enhances the energy spectrum $E(k)$ when the wavenumber $k$ is large; this enhancement leads to dissipation reduction.

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↗