arXiv subjects

Nadia Bihari Padhan

Publications and source records attributed to Nadia Bihari Padhan.

16 recordsLinked to original sources

arXiv2026

First observation of turbulence-like state in dense algal suspensions

Active turbulence arises typically in systems ranging from microorganisms and biopolymers to synthetic colloids, where chaotic flows are closely associated with motile topological defects in collectively swarming suspensions. Here, we report the first experimental observation of turbulence-like dynamics in a fundamentally different class of systems: dense monolayers of motile unicellular alga Chlamydomonas reinhardtii that exhibit neither orientational order nor topological defects. Nevertheless, the system displays rich spatiotemporal flow patterns with pronounced small-scale intermittency. We uncover strongly non-Gaussian velocity distribution, a feature distinct from both bacterial and classical fluid turbulence. Furthermore, we observe power-law regimes in the kinetic energy spectra, characterized by unique scaling exponents. Not only do our results provide compelling evidence for active spatiotemporal chaos in systems devoid of nematic or polar structures, but they also challenge current theoretical models. Our work opens new avenues for understanding emergent dynamics in active-matter systems and suggests intriguing biological implications, including enhanced mixing and transport in dense cell suspensions.

cond-mat.soft↗

arXiv2026

Obstacle-aware navigation of smart microswimmers in a turbulent flow

Microswimmers in turbulent flows often navigate complex, heterogeneous, and obstacle-rich environments, where they exhibit intricate behaviors such as trapping at and escape from obstacles. We generalize recent $\mathcal{Q}-$learning methods of J.K. Alageshan \textit{et al.} [Phys.Rev.E \textbf{101}, 043110 (2020)] and A. Gupta \textit{et al.} [Physics of Fluids \textbf{37}, 045107 (2025)] developed for non-interacting microswimmers that aim to move optimally from an initial position to a target, to account for the additional complication of an obstacle in the flow. We begin by considering one circular obstacle in forced two-dimensional (2D) Navier-Stokes turbulence in which the energy spectrum displays a forward cascade. We employ the volume-penalization method to introduce this obstacle within our doubly periodic simulation domain. We augment our adversarial $\mathcal{Q}-$learning Refs.~\cite{Alageshan_2020,Akanksha_2025} by suppressing the tendency of microswimmers to get trapped in stagnation points in the vicinity of the obstacle. We demonstrate that smart microswimmers ($SS$), which adopt our obstacle-aware adversarial $\mathcal{Q}-$learning strategy, outperform both naïve swimmers ($NS$) and surfers ($SuS$).

physics.flu-dyn↗

arXiv2026

Non-reciprocal Binary-fluid Turbulence

Although effective non-reciprocal interactions have been investigated in a variety of fields, their consequences have not been explored in hydrodynamical turbulence. We initiate such an exploration by introducing non-reciprocal binary-fluid tubulence and uncover its properties by developing a two-dimensional (2D) Non-Reciprocal Cahn-Hilliard-Navier-Stokes (NRCHNS) model. We show that, as we increase the strength of the non-reciprocal terms, this model displays a hitherto unanticipated type of turbulence, with an inverse cascade of energy and an energy spectrum $E(k)\sim k^{-5/3}$, reminiscent of the well-known inverse cascade in forced, 2D fluid turbulence, but distinct from it, in so far as it develops a non-reciprocal flux $\mathbf J$. We demonstrate how NRCHNS turbulence suppresses $J(t) = |\mathbf J|$, as the Reynolds number increases. We compare and contrast 2D NRCHNS turbulence with its fluid-turbulence counterpart by examining spectra, fluxes, spectral balances, flow topologies, and signatures of multifractality.

physics.flu-dyn↗

arXiv2025

Vortex triplets, symmetry breaking, and emergent nonequilibrium plastic crystals in an active-spinner fluid

The formation of patterns and exotic nonequilibrium steady states in active-fluid systems continues to pose challenging problems -- theoretical, numerical, and experimental -- for statistical physicists and fluid dynamicists. We combine theoretical ideas from statistical mechanics and fluid mechanics to uncover a new type of self-assembled crystal of vortex triplets in an active-spinner fluid. We begin with the two-dimensional Cahn-Hilliard-Navier-Stokes (CHNS) model for a binary-fluid system of active rotors that has two important ingredients: a scalar order parameter field phi that distinguishes regions with clockwise (CW) and counter-clockwise (CCW) spinners; and an incompressible velocity field u. In addition to the conventional CHNS coupling between phi and u, this model has a torque-induced activity term, with coefficient tau, whose consequences we explore. We demonstrate that, if we increase the activity tau, it overcomes dissipation and this system displays a hitherto unanticipated emergent triangular crystal, with spinning vortex triplets at its vertices. We show that this is a nonequilibrium counterpart of an equilibrium plastic crystal. We characterise the statistical properties of this novel crystal and suggest possible experimental realisations of this new state of active matter.

cond-mat.soft↗

arXiv2025

Interface-induced turbulence in viscous binary fluid mixtures

We demonstrate the existence of interface-induced turbulence, an emergent nonequilibrium statistically steady state (NESS) with spatiotemporal chaos, which is induced by interfacial fluctuations in low-Reynolds-number binary-fluid mixtures. We uncover the properties of this NESS via direct numerical simulations (DNSs) of cellular flows in the Cahn-Hilliard-Navier-Stokes (CHNS) equations for binary fluids. We show that, in this NESS, the shell-averaged energy spectrum $E(k)$ is spread over more than one decade in the wavenumber $k$ and it exhibits a power-law region, indicative of turbulence \textit{but without a conventional inertial cascade}. To characterize the statistical properties of this turbulence, we compute, in addition to $E(k)$, the time series $e(t)$ of the kinetic energy and its power spectrum, scale-by-scale energy transfer as a function of $k$, and the energy dissipation resulting from interfacial stresses. Furthermore, we analyze the mixing properties of this low-Reynolds-number turbulence via the mean-square displacement (MSD) of Lagrangian tracer particles, for which we demonstrate diffusive behavior at long times, a hallmark of strong mixing in turbulent flows.

physics.flu-dyn↗

arXiv2025

Hyperuniformity in ternary fluid mixtures: the role of wetting and hydrodynamics

Phase separation in multicomponent fluids is central to understanding the organization of complex materials and biological structures. The Cahn-Hilliard-Navier-Stokes (CHNS) equations offer a robust framework for modeling such systems, capturing both diffusive dynamics and hydrodynamic interactions. In this work, we investigate hyperuniformity, characterized by suppressed large-scale density fluctuations, in ternary fluid mixtures governed by the ternary CHNS equations. Using large-scale direct numerical simulations, we systematically explore the influence of wetting conditions and hydrodynamic effects on emergent hyperuniformity. Similar to binary systems we observe that the presence of hydrodynamics weakens the hyperuniform characteristics. However, also the wetting properties have an effect. We find that in partial wetting regimes, all three components exhibit comparable degrees of hyperuniformity. In contrast, for complete wetting scenarios, where one component preferentially wets the other two, the wetting component displays a significant reduction in hyperuniformity relative to the others. These findings suggest that wetting asymmetry can act as a control parameter for spatial order in multicomponent fluids.

cond-mat.soft↗

arXiv2025

Emergent turbulence and coarsening arrest in active-spinner fluids

We uncover activity-driven crossover from phase separation to a new turbulent state in a two-dimensional system of counter-rotating spinners. We study the statistical properties of this active-rotor turbulence using the active-rotor Cahn-Hilliard-Navier-Stokes model, and show that the vorticity $ω\propto ϕ$, the scalar field that distinguishes regions with different rotating states. We explain this intriguing proportionality theoretically, and we characterize power-law energy and concentration spectra, intermittency, and flow-topology statistics. We suggest biological implications of such turbulence.

physics.flu-dyn↗

arXiv2025

The Cahn-Hilliard-Navier-Stokes Framework for Multiphase Fluid Flows: Laminar, Turbulent, and Active

The Cahn-Hilliard-Navier-Stokes (CHNS) partial differential equations (PDEs) provide a powerful framework for the study of the statistical mechanics and fluid dynamics of multiphase fluids. We provide an introduction to the equilibrium and nonequilibrium statistical mechanics of systems in which coexisting phases, distinguished from each other by scalar order parameters, are separated by an interface. We then introduce the coupled Cahn-Hilliard-Navier-Stokes (CHNS) PDEs for two immiscible fluids and generalisations for (a) coexisting phases with different viscosities, (b) CHNS with gravity, (c) the three-component fluids (CHNS3), and (d) the CHNS for active fluids. We discuss mathematical issues of the regularity of solutions of the CHNS PDEs. Finally we provide a survey of the rich variety of results that have been obtained by numerical studies of CHNS-type PDEs for diverse systems, including bubbles in turbulent flows, antibubbles, droplet and liquid-lens mergers, turbulence in the active-CHNS model, and its generalisation that can lead to a self-propelled droplet.

physics.flu-dyn↗

arXiv2024

Suppression of hyperuniformity in hydrodynamic scalar active field theories

The coarsening dynamics at late times in phase-separating systems lead to universally hyperuniform patterns. This is well known for scalar field theories, such as the Cahn-Hilliard equation, but has also been shown for dry scalar active field theories. We demonstrate the role of hydrodynamic interactions in influencing hyperuniformity in a wet active system described by active model H. Our direct numerical simulations reveal that, while (passive) model H shows hyperuniformity in the coarsening regime, the interplay of activity and hydrodynamic interactions suppresses hyperuniformity in active model H, especially when the activity generates contractile stress in the fluid.

cond-mat.soft↗

arXiv2024

Liquid-Droplet Coalescence: CNN-based Reconstruction of Flow Fields from Concentration Fields

Liquid-droplet coalescence and the mergers of liquid lenses are problems of great practical and theoretical interest in fluid dynamics and the statistical mechanics of multi-phase flows. During such mergers, there is an interesting and intricate interplay between the shapes of the interfaces, separating two phases, and the background flow field. In experiments, it is easier to visualize concentration fields than to obtain the flow field. We demonstrate that two-dimensional (2D) encoder-decoder CNNs, 2D U-Nets, and three-dimensional (3D) U-Nets can be used to obtain flow fields from concentration fields here. To train these networks, we use concentration and flow fields, which we obtain from extensive direct numerical simulations (DNSs) of (a) the coalescence of two circular droplets in the two-component 2D Cahn-Hilliard-Navier-Stokes (CHNS) partial differential equations (PDEs), (b) liquid-lens mergers in the three-component 2D CHNS PDEs, and (c) spherical-droplet coalescence in the two-component 3D CHNS PDEs. We then show that, given test images of concentration fields, our trained models accurately predict the flow fields at both high and low Ohnesorge numbers $Oh$ (a dimensionless ratio of viscous stresses to the inertial and surface-tension forces). Using autoencoders and fully connected neural networks, we also investigate the mapping between the concentration and vorticity fields via low-dimensional latent variables for droplet mergers in the 2D CHNS system. We compare the accuracies of flow-field reconstruction based on the two approaches we employ. Finally, we use data from recent experiments on droplet coalescence to show how our method can be used to obtain the flow field from measurements of the concentration field.

physics.flu-dyn↗

arXiv2024

Interfaces as transport barriers in two-dimensional Cahn-Hilliard-Navier-Stokes turbulence

We investigate the role of interfaces as transport barriers in binary-fluid turbulence by employing Lagrangian tracer particles. The Cahn-Hilliard-Navier-Stokes (CHNS) system of partial differential equations provides a natural theoretical framework for our investigations. For specificity, we utilize the two-dimensional (2D) CHNS system. We capture efficiently interfaces and their fluctuations in 2D binary-fluid turbulence by using extensive pseudospectral direct numerical simulations (DNSs) of the 2D CHNS equations. We begin with $n$ tracers within a droplet of one phase and examine their dispersal into the second phase. The tracers remain within the droplet for a long time before emerging from it, so interfaces act as transport barriers in binary-fluid turbulence. We show that the fraction of the number of particles inside the droplet decays exponentially and is characterized by a decay time $τ_ξ\sim R_0^{3/2}$ that increases with $R_0$, the radius of the initially circular droplet. Furthermore, we demonstrate that the average first-passage time $\langle τ\rangle$ for tracers inside a droplet is orders of magnitude larger than it is for transport out of a hypothetical circle with the same radius as the initially circular droplet. We examine the roles of the Okubo-Weiss parameter $Λ$, the fluctuations of the droplet perimeter, and the probability distribution function of $\cos(θ)$, with $θ$ the angle between the fluid velocity and the normal to a droplet interface, in trapping tracers inside droplets. We mention possible generalisations of our study.

physics.flu-dyn↗

arXiv2024

Novel turbulence and coarsening arrest in active-scalar fluids

We uncover a new type of turbulence -- activity-induced homogeneous and isotropic turbulence in a model that has been employed to investigate motility-induced phase separation (MIPS) in a system of microswimmers. The active Cahn-Hilliard-Navier-Stokes equations (CHNS), also called active model H, provides a natural theoretical framework for our study. In this CHNS model, a single scalar order parameter $ϕ$, positive (negative) in regions of high (low) microswimmer density, is coupled with the velocity field $\bm u$. The activity of the microswimmers is governed by an activity parameter $ζ$ that is positive for \textit{extensile} swimmers and negative for \textit{contractile} swimmers. With extensile swimmers, this system undergoes complete phase separation, which is similar to that in binary-fluid mixtures. By carrying out pseudospectral direct numerical simulations (DNSs), we show, for the first time, that this model (a) develops an emergent nonequilibrium, but statistically steady, state (NESS) of active turbulence, for the case of contractile swimmers, if $ζ$ is sufficiently large and negative and (b) this turbulence arrests the phase separation. We quantify this suppression by showing how the coarsening-arrest length scale does not grow indefinitely, with time $t$, but saturates at a finite value at large times. We characterise the statistical properties of this active-scalar turbulence by employing energy spectra and fluxes and the spectrum of $ϕ$. For sufficiently high Reynolds numbers, the energy spectrum $\mathcal E(k)$ displays an inertial range, with a power-law dependence on the wavenumber $k$. We demonstrate that, in this range, the flux $Π(k)$ assumes a nearly constant, negative value, which indicates that the system shows an inverse cascade of energy, even though energy injection occurs over a wide range of wavenumbers in our active-CHNS model.

physics.flu-dyn↗

arXiv2023

Unveiling the Spatiotemporal Evolution of Liquid-Lens Coalescence: Self-Similarity, Vortex Quadrupoles, and Turbulence in a Three-Phase Fluid System

We demonstrate that the three-phase Cahn-Hilliard-Navier-Stokes (CHNS3) system provides a natural theoretical framework for studying liquid-lens coalescence, which has been investigated in recent experiments. Our extensive direct numerical simulations (DNSs) of lens coalescence, in the two and three dimensional (2D and 3D) CHNS3, uncover the rich spatiotemporal evolution of the fluid velocity $\bf u$ and vorticity $ω$, the concentration fields $c_1, \, c_2,$ and $c_3$ of the three liquids, and a generalized Laplace pressure $P^G_\mathcal{L}$, which we define in terms of these concentrations via a Poisson equation. We find, in agreement with experiments, that as the lenses coalesce, their neck height $h(t) \sim t^{α_v}$, with $α_v \simeq 1$ in the viscous regime, and $h(t) \sim t^{α_i}$, with $α_i \simeq 2/3$ in the inertial regime. We obtain the crossover from the viscous to the inertial regimes as a function of the Ohnesorge number $Oh$, a dimensionless combination of viscous stresses and inertial and surface tension forces. We show that a vortex quadrupole, which straddles the neck of the merging lenses, and $P^G_\mathcal{L}$ play crucial roles in distinguishing between the viscous- and inertial-regime growths of the merging lenses. In the inertial regime we find signatures of turbulence, which we quantify via kinetic-energy and concentration spectra. Finally, we examine the merger of asymmetric lenses, in which the initial stages of coalescence occur along the circular parts of the lens interfaces; in this case, we obtain power-law forms for the $h(t)$ with inertial-regime exponents that lie between their droplet-coalescence and lens-merger counterparts.

physics.flu-dyn↗

arXiv2022

An analytical and computational study of the incompressible Toner-Tu Equations

The incompressible Toner-Tu (ITT) partial differential equations (PDEs) are an important example of a set of active-fluid PDEs. While they share certain properties with the Navier-Stokes equations (NSEs), such as the same scaling invariance, there are also important differences. The NSEs are usually considered in either the decaying or the additively forced cases, whereas the ITT equations have no additive forcing. Instead, they include a linear, activity term $α\bu$ ($\bu$ is the velocity field) which pumps energy into the system, but also a negative $\bu|\bu|^{2}$-term which provides a platform for either frozen or statistically steady states. Taken together, these differences make the ITT equations an intriguing candidate for study using a combination of PDE analysis and pseudo-spectral direct numerical simulations (DNSs). In the $d=2$ case, we have established global regularity of solutions, but we have also shown the existence of bounded hierarchies of weighted, time-averaged norms of both higher derivatives and higher moments of the velocity field. Similar bounded hierarchies for Leray-type weak solutions have also been established in the $d=3$ case. We present results for these norms from our DNSs in both $d=2$ and $d=3$, and contrast them with their Navier-Stokes counterparts.

math.AP↗

arXiv2022

Activity-induced droplet propulsion and multifractality

We develop a minimal hydrodynamic model, without an orientational order parameter, for assemblies of contractile swimmers encapsulated in a droplet of a binary-fluid emulsion. Our model uses two coupled scalar order parameters, $ϕ$ and $ψ$, which capture, respectively, the droplet interface and the activity of the contractile swimmers inside this droplet. These order parameters are also coupled to the velocity field $\bm u$. At low activity, our model yields a self-propelling droplet whose center of mass $(CM)$ displays rectilinear motion, powered by the spatiotemporal evolution of the field $ψ$, which leads to a time-dependent vortex dipole at one end of the droplet. As we increase the activity, this $CM$ shows chaotic super-diffusive motion, which we characterize by its mean-square displacement; and the droplet interface exhibits multifractal fluctuations, whose spectrum of exponents we calculate. We explore the implications of our results for experiments on active droplets of contractile swimmers.

cond-mat.soft↗

arXiv2020

Direct Numerical Simulations of Three-dimensional Magnetohydrodynamic Turbulence with Random, Power-law Forcing

We present pseudospectral direct-numerical-simulation (DNS) studies of the three-dimensional magnetohydrodynamic (MHD) equations (3DRFMHD) with a stochastic force that has zero mean and a variance $\sim k^{-3}$, where $k$ is the wavenumber, because 3DRFMHD is used in field-theoretic studies of the scaling of energy spectra in MHD turbulence. We obtain velocity and magnetic-field spectra and structure functions and, from these, the multiscaling exponent ratios $ζ_p/ζ_3$, by using the extended self similarity (ESS) procedure. These exponent ratios lie within error bars of their counterparts for conventional three-dimensional MHD turbulence (3DMHD). We then carry out a systematic comparison of the statistical properties of 3DMHD and 3DRFMHD turbulence by examining various probability distribution functions (PDFs), joint PDFs, and isosurfaces of of, e.g., the moduli of the vorticity and the current density for three magnetic Prandtl numbers ${\rm Pr_M} = 0.1,~1$, and $10$.

physics.flu-dyn↗