arXiv subjects

Dhrubaditya Mitra

Publications and source records attributed to Dhrubaditya Mitra.

At least 37 records · Page 2Linked to original sources

arXiv2022

Exact analytical solutions in inhomogeneous magnetic fields for linear asteroseismic waves

We solve for waves in an isothermal, stratified medium with a magnetic field that points along a direction perpendicular to that of gravity and varies exponentially in the direction of gravity. We find exact analytical solutions for two different cases: (a) waves propagating along the direction of the magnetic field and (b) waves propagating along the direction of the gravity. In each case, we find solutions in terms of either the hypergeometric functions or their confluent cousins. We solve the resultant transcendental dispersion relation numerically. The changes in the eigenfrequencies due to a spatially inhomogeneous Alfvén wave speed are significant -- there are more oscillations or leaking of nodes of the eigenfunctions in regions of lower Alfvén speed and wave reflection from regions of larger Alfvén speed. Such changes in the dispersion relation and the mode structures may allow detection of magnetic fields buried in the stellar interior.

astro-ph.SR↗

arXiv2022

Dynamic multiscaling in stochastically forced Burgers turbulence

We carry out a detailed study of dynamic multiscaling in the turbulent nonequilibrium, but statistically steady, state of the stochastically forced one-dimensional Burgers equation. We introduce the concept of $\textit{interval collapse times}$ $τ_{\rm col}$, the time taken for an interval of length $\ell$, demarcated by a pair of Lagrangian tracers, to collapse at a shock. By calculating the dynamic scaling exponent of the order-$p$ moment of $τ_{\rm col}$, we show that (a) there is $\textit{not one but an infinity of characteristic time scales}$ and (b) the probability distribution function of $τ_{\rm col}$ is non-Gaussian and has a power-law tail. Our study is based on (a) a theoretical framework that allows us to obtain dynamic-multiscaling exponents analytically, (b) extensive direct numerical simulations, and (c) a careful comparison of the results of (a) and (b). We discuss possible generalizations of our work to dimensions $d >1 $, for the stochastically forced Burgers equation, and to other compressible flows that exhibit turbulence with shocks.

cond-mat.stat-mech↗

arXiv2022

MeMC: A package for monte-carlo simulations of spherical shells

The MeMC is an open-source software package for monte-carlo simulation of elastic shells. It is designed as a tool to interpret the force-distance data generated by indentation of biological nano-vesicles by atomic force microscopes. The code is written in c++ and python. The code is customizable -- new modules can be added in a straightforward manner.

physics.comp-ph↗

arXiv2021

Turbulence modulation in buoyancy-driven bubbly flows

We present a Direct Numerical Simulation (DNS) study of buoyancy-driven bubbly flows in the presence of large scale driving that generates turbulence. On increasing the turbulence intensity: (a) the bubble trajectories become more curved, and (b) the average rise velocity of the bubbles decreases. We find that the energy spectrum of the flow shows a pseudo-turbulence scaling for length scales smaller than the bubble diameter and a Kolmogorov scaling for scales larger than the bubble diameter. We conduct a scale-by-scale energy budget analysis to understand the scaling behaviour observed in the spectrum. Although our bubbles are weakly buoyant, the statistical properties of our DNS are consistent with the experiments that investigate turbulence modulation by air bubbles in water.

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

Quantitative analysis of non-equilibrium systems from short-time experimental data

We provide a minimal strategy for the quantitative analysis of a large class of non-equilibrium systems in a {statistically} steady state using the short-time Thermodynamic Uncertainty Relation (TUR). From short-time trajectory data obtained from experiments, we demonstrate how we can simultaneously infer quantitatively, both the thermodynamic force field acting on the system, as well as the (potentially exact) rate of entropy production. We benchmark this scheme first for an experimental study of a colloidal particle system where exact analytical results are known, before applying it to the case of a colloidal particle in a hydrodynamical flow field, where neither analytical nor numerical results are available. In this latter case, we build an effective model of the system based on our results. In both cases, we also demonstrate that our results match with those obtained from another recently introduced scheme [Phys. Rev. X 10, 021009].

cond-mat.soft↗

arXiv2021

Planetesimals on eccentric orbits erode rapidly

We investigate the possibility of erosion of planetesimals in a protoplanetary disk. We use theory and direct numerical simulations (Lattice Boltzmann Method) to calculate the erosion of large -- much larger than the mean-free-path of gas molecules -- bodies of different shapes in flows. We find that erosion follows a universal power-law in time, at intermediate times, independent of the Reynolds number of the flow and the initial shape of the body. Consequently, we estimate that planetesimals in eccentric orbits, of even very small eccentricity, rapidly (in about hundred years) erodes away if the semi-major axis of their orbit lies in the inner disk -- less than about $10$ au. Even planetesimals in circular orbits erode away in approximately ten thousand years if the semi-major axis of their orbits are $\lessapprox 0.6$au.

astro-ph.EP↗

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

A model-free, data-based forecast for sunspot cycle 25

The dynamic activity of the Sun, governed by its cycle of sunspots -- strongly magnetized regions that are observed on its surface -- modulate our solar system space environment creating space weather. Severe space weather leads to disruptions in satellite operations, telecommunications, electric power grids and air-traffic on polar routes. Forecasting the cycle of sunspots, however, has remained a challenging problem. We use reservoir computing -- a model-free, neural--network based machine-learning technique -- to forecast the upcoming solar cycle, sunspot cycle 25. The standard algorithm forecasts that solar cycle 25 is going to last about ten years, the maxima is going to appear in the year 2024 and the maximum number of sunspots is going to be 113 ($\pm15$). We also develop a novel variation of the standard algorithm whose forecasts for duration and peak timing matches that of the standard algorithm, but whose peak amplitude forecast is 124 ($\pm2$) -- within the upper bound of the standard reservoir computing algorithm. We conclude that sunspot cycle 25 is likely to be a weak, lower than average solar cycle, somewhat similar in strength to sunspot cycle 24.

astro-ph.SR↗

arXiv2020

Erosion of planetesimals by gas flow

The first stages of planet formation take place in protoplanetary disks that are largely made up of gas. Understanding how the gas affects planetesimals in the protoplanetary disk is therefore essential. In this paper, we discuss whether or not gas flow can erode planetesimals. We estimate how much shear stress is exerted onto the planetesimal surface by the gas as a function of disk and planetesimal properties. To determine whether erosion can take place, we compare this with previous measurements of the critical stress that a pebble-pile planetesimal can withstand before erosion begins. If erosion takes place, we estimate the erosion time of the affected planetesimals. We also illustrate our estimates with two-dimensional numerical simulations of flows around planetesimals using the lattice Boltzmann method. We find that the wall shear stress can overcome the critical stress of planetesimals in an eccentric orbit within the innermost regions of the disk. The high eccentricities needed to reach erosive stresses could be the result of shepherding by migrating planets. We also find that if a planetesimal erodes, it does so on short timescales. For planetesimals residing outside of $1 \ \rm{au}$, we find that they are mainly safe from erosion, even in the case of highly eccentric orbits.

astro-ph.EP↗

arXiv2019

The breakdown of Darcy's law in a soft porous material

We perform direct numerical simulations of the flow through a model of a deformable porous medium. Our model is a two-dimensional hexagonal lattice, with defects, of soft elastic cylindrical pillars, with elastic shear modulus $G$, immersed in a liquid. We use a two-phase approach: the liquid phase is a viscous fluid and the solid phase is modeled as an incompressible viscoelastic material, whose complete nonlinear structural response is considered. We observe that the Darcy flux ($q$) is a nonlinear function -- steeper than linear -- of the pressure-difference ($ΔP$) across the medium. Furthermore, the flux is larger for a softer medium (smaller $G$). We construct a theory of this super-linear behavior by modelling the channels between the solid cylinders as elastic channels whose walls are made of a material with a linear constitutive relation but can undergo large deformation. Our theory further predicts that the flow permeability is a universal function of $ΔP/G$, which is confirmed by the present simulations.

physics.flu-dyn↗

arXiv2019

Kazantsev dynamo in turbulent compressible flows

We consider the kinematic fluctuation dynamo problem in a flow that is random, white-in-time, with both solenoidal and potential components. This model is a generalization of the well-studied Kazantsev model. If both the solenoidal and potential parts have the same scaling exponent, then, as the compressibility of the flow increases, the growth rate decreases but remains positive. If the scaling exponents for the solenoidal and potential parts differ, in particular if they correspond to typical Kolmogorov and Burgers values, we again find that an increase in compressibility slows down the growth rate but does not turn it off. The slow down is, however, weaker and the critical magnetic Reynolds number is lower than when both the solenoidal and potential components display the Kolmogorov scaling. Intriguingly, we find that there exist cases, when the potential part is smoother than the solenoidal part, for which an increase in compressibility increases the growth rate. We also find that the critical value of the scaling exponent above which a dynamo is seen is unity irrespective of the compressibility. Finally, we realize that the dimension $d = 3$ is special, since for all other values of $d$ the critical exponent is higher and depends on the compressibility.

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

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

Rheology of suspensions of viscoelastic spheres: deformability as an effective volume fraction

We study suspensions of deformable (viscoelastic) spheres in a Newtonian solvent in plane Couette geometry, by means of direct numerical simulations. We find that in the limit of vanishing inertia the effective viscosity $μ$ of the suspension increases as the volume-fraction occupied by the spheres $Φ$ increases and decreases as the elastic modulus of the spheres $G$ decreases; the function $μ(Φ,G)$ collapses to an universal function, $μ(Φ_e)$, with a reduced effective volume fraction $Φ_e(Φ,G)$. Remarkably, the function $μ(Φ_e)$ is the well-known Eilers fit that describes the rheology of suspension of rigid spheres at all $Φ$. Our results suggest new ways to interpret macro-rheology of blood.

physics.flu-dyn↗

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↗