arXiv subjects

Siddhartha Mukherjee

Publications and source records attributed to Siddhartha Mukherjee.

At least 19 recordsLinked to original sources

arXiv2026

Disentangling intermittent flow structure contributions to anomalous scaling and multifractality in turbulence

Intermittency in turbulence manifests as intense vortices and sharp peaks of dissipation. Causing the breakdown of Kolmogorov's simple self-similar theory, it leads to anomalous scaling, multifractality and so far remains beyond the scope of a complete theoretical description. How intermittent flow structures influence these different measurements is not known quantitatively. With a simple filtering procedure-thresholding vorticity and inverting the Biot-Savart law to generate filtered velocity fields-we show the effects of intermittent flow structures can be disentangled. As extreme vorticity contributions to the velocity field are filtered out, the energy spectrum scaling persists, while the bottleneck is flattened, and structure function scalings tend towards their Kolmogorov values. The approach is more rapid for transverse exponents, revealing the selective importance of intensely swirling flow regions. Similarly, the extent of multifractality reduces as intermittency is filtered, shrinking the range of roughness singularity exponents. The residual fields are curiously more multifractal, but their structure begins to break away from an underlying turbulence skeleton. The effects on vortex stretching and strain self-amplification are quantified. Our work shows that a Biot-Savart approach can selectively remove the effects of intermittency from turbulence, and hence from its scalings.

physics.flu-dyn↗

arXiv2026

Time-Symmetry of Lagrangian Coherent Structures in Active Turbulence

Active flows are central to mixing and transport across living systems. While Newtonian fluids remain laminar, diffusive and predictable at the microscale, living fluids like dense bacterial suspensions can exhibit highly chaotic flows like active turbulence, with anomalous transport capabilities. The underlying spatiotemporally persistent structures that drive mixing in active flows, however, remain uncharted. Using Lagrangian Coherent Structures, we now uncover networks of attracting and repelling hyperbolic surfaces. We study changes in the distribution and spectra of Finite-Time Lyapunov Exponent fields in response to increasing activity. Despite the dominance of vorticity in the flow, extreme forward and backward time chaotic mixing is found to originate from straining regions, emphasizing the role of saddles. Fractal dimensions of ridges reveal a morphological simplification of LCS networks with increasing activity, while retaining isotropic crossing. Throughout our work, we also probe a hitherto unasked question-Are signatures of Lagrangian irreversibility manifest in attracting and repelling LCS? To the contrary, we find there is a striking time-symmetry. Our work takes the first steps towards linking flow structures in active turbulence to invariant mixing surfaces. These findings will crucially help in designing activity modulation protocols to seed or inhibit flow structures, and thence mixing, in a bid to tame active turbulence for varied applications.

physics.flu-dyn↗

arXiv2026

Turbulence-Induced Fluctuating Interfaces in Heterogeneously-Active Suspensions

We investigate the effects of heterogeneous (spatially varying) activity in a hydrodynamical model for dense bacterial suspensions, confining ourselves to experimentally realizable, simple, quenched, activity patterns. We show that the evolution of the bacterial velocity field under such activity patterning leads to the emergence of hydrodynamic interfaces separating spatially localized turbulence from jammed frictional surroundings. We characterise the intermittent and multiscale fluctuations of this interface and also investigate how heterogeneity influences mixing via the residence times of Lagrangian tracers. This work reveals how naturally occurring heterogeneities could decisively steer active flows into more complex configurations than those typically studied, opening up parallels to droplet dynamics, front propagation and turbulent mixing layers.

cond-mat.soft↗

arXiv2026

Hydrodynamics of Dense Active Fluids: Turbulence-Like States and the Role of Advected Activity

Dense suspensions of self-propelled bacteria and related active fluids exhibit spontaneous flow generation, vortex formation, and spatiotemporally chaotic dynamics despite operating at vanishingly small Reynolds numbers. These phenomena, commonly referred to as active turbulence, display striking visual and statistical similarities to classical inertial turbulence while arising from fundamentally different nonequilibrium mechanisms. In this article, we present a combined review and theoretical study of hydrodynamic models for dense active fluids, with particular emphasis on bacterial suspensions described by the Toner--Tu--Swift--Hohenberg (TTSH) framework. We review key experimental and theoretical developments underlying the analogy between active and inertial turbulence, highlighting the emergence of multiple dynamical regimes and the conditions under which universal spectral and intermittent behavior arises in homogeneous systems. Moving beyond the conventional assumption of spatially uniform activity, we introduce a minimal model in which the activity field is heterogeneous and dynamically advected by the flow it generates. Thus treating activity as a spatiotemporally evolving field coupled to the TTSH dynamics, we investigate how advection and diffusion lead to sharp activity fronts, confinement of turbulent motion, and complex interfacial morphologies. Our numerical results demonstrate that spatial variations in activity can induce transient coexistence of distinct spectral regimes and that universality in active turbulence is inherently local and time-dependent in heterogeneous systems. These findings underscore the importance of treating activity as a dynamical field in its own right and provide a framework for studying active turbulence in more realistic, spatially structured biological and synthetic active matter systems.

cond-mat.soft↗

arXiv2025

Geometric Intermittency in Turbulence

Equal-time scaling exponents in fully developed turbulence typically exhibit non anomalous scaling in the inverse cascade of two-dimensional (2D) turbulence and anomalous scaling in three dimensions. We demonstrate that multiscaling is not confined to longitudinal, scalar velocity increments, but also emerges in increments associated with the magnitude and orientation of the velocity vector. This decomposition uncovers a multiscaling in the 2D inverse cascade, which remains obscured when using conventional structure functions. Our results highlight a decoupling between velocity amplitude and flow geometry, offering new insight into the statistical structure of turbulent cascades as well as showing how different classes of multiscaling emerge.

physics.flu-dyn↗

arXiv2025

Dynamical Response of Deformable Microchannels under Pressure-Driven Flow of Aqueous Polymer Solutions

Microfluidic channels are integral to biomedical technology and process engineering, offering versatility in handling fluids with complex properties, often a combination of viscous and elastic attributes. Despite significant advancements in understanding small-scale fluid-structure interactions, however, experimental insights on the flow of complex fluids in deformable microchannels remain limited. Here, we present controlled experiments using polymer solutions as model viscoelastic fluids to examine the effects of polymer concentration on the elasto-mechanical characteristics of slender cylindrical microchannels. The findings indicate significant differences in fluid-structure interactions between dilute and semi-dilute polymer solutions with varying molecular weights. At higher polymer concentrations, these interactions intensify, leading to reduced pressure drops in high-shear regions and increased pressure drops in low-shear areas, linked to local wall deformation. The increased elasticity of higher concentration solutions further enhances local deformation, disrupts flow, and dissipates energy, resulting in a non-linear rise in pressure drop. This behaviour is aggravated by the solutions increased apparent viscosity due to the entangled polymer network. A theoretical model of flow-induced deformation is also developed, accounting for polymer chain extensibility. These insights highlight the importance of polymer constitution in optimizing the flow characteristics, advancing the development of adaptive microfluidic devices in biological and industrial applications for optimal performance.

cond-mat.soft↗

arXiv2023

Turbulent flows are not uniformly multifractal

The Frisch-Parisi multifractal formalism remains the most compelling rationalisation for anomalous scaling in fully developed turbulence. We now show that this formalism can be adapted locally to reveal the spatial distribution of generalized dimensions and of how multifractal the energy dissipation field is. In particular, we show that most regions of the flow are close to being mono-fractal and these are interspersed with islands of multifractality corresponding to the most singular structures in the flow. By defining a suitable measure $Φ({\bf x})$ of the spatial variation of multifractality, we show that this grows logarithmically with the extent to which the energy dissipation varies locally around ${\bf x}$. These results suggest ways to understand how singularities could arise in disparate regions of a flow and provides new directions in understanding anomalous dissipation and intermittency. We then employ the same technique to a non-intermittent, model turbulent flow to check the robustness of our conclusions.

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

Lagrangian Manifestation of Anomalies in Active Turbulence

We show that Lagrangian measurements in active turbulence bear imprints of turbulent and anomalous streaky hydrodynamics leading to a self-selection of persistent trajectories - Levy walks - over diffusive ones. This emergent dynamical heterogeneity results in a super-diffusive first passage distribution which could lead to biologically advantageous motility. We then go beyond single-particle statistics to show that for the pair-dispersion problem as well, active flows are at odds with inertial turbulence. Our study, we believe, will readily inform experiments in establishing the extent of universality of anomalous behaviour across a variety of active flows.

physics.flu-dyn↗

arXiv2022

Intermittency, fluctuations and maximal chaos in an emergent universal state of active turbulence

A hydrodynamic model of active, low Reynolds number suspensions, shows the emergence of an asymptotic state with a universal spectral scaling and non-Gaussian (intermittent) fluctuations in the velocity field. Such states arise when these systems are pushed beyond a critical level of activity and show features akin to high Reynolds number, inertial turbulence. We provide compelling numerical and analytical evidence for the existence of such a transition at a critical value of activity and further show that the maximally chaotic states are tied to this transition.

physics.flu-dyn↗

arXiv2021

Anomalous diffusion and Lévy walks distinguish active from inertial turbulence

Bacterial swarms display intriguing dynamical states like active turbulence. Using a hydrodynamic model we now show that such dense active suspensions manifest super-diffusion, via Lévy walks, which masquerades as a crossover from ballistic to diffusive scaling in measurements of mean-squared-displacements, and is tied to the emergence of hitherto undetected oscillatory streaks in the flow. Thus, while laying the theoretical framework of an emergent advantageous strategy in the collective behaviour of microorganisms, our study underlines the essential differences between active and inertial turbulence.

cond-mat.soft↗

arXiv2021

Electroosmotic flow of viscoelastic fluids in deformable microchannels

The electroosmotic flow of non-Newtonian fluids in deformable microchannels is fundamentally important in the understanding of the hydrodynamics in physiological flows. The performance of these microchannels is governed by the load bearing capacity indicating the maximum amount of load that the device can withstand. While significant research efforts are aimed towards the coupling of electrokinetics with substrate deformability, the corresponding enhancement in the performances still remains elusive. Towards this, employing an intricate coupling between substrate compliance, hydrodynamic, and electrokinetic modulations, we have analyzed the possible sources of alterations in the flow physics in a deformable microchannel under the rheological premises of viscoelastic fluids which have a close resemblance with biological fluids typically used in several bio and micro-fluidic applications. The present study reveals that by operating under favorable regimes of parameters like the concentration and molecular weight of the polymer, the quality of the Newtonian solvent, and the concentration of electrolyte, one can achieve substantial augmentation in the load carrying capacity of a deformable microchannel for viscoelastic fluids as compared to its Newtonian counterpart. We believe that the present theoretical framework can be extremely important in the designing of electro-kinetically modulated bio-mimetic microfluidic devices.

cond-mat.soft↗

arXiv2020

Correlation and decomposition framework for identifying and disentangling flow structures: canonical examples and application to isotropic turbulence

Turbulence organization, long conceptualized in terms of spatial coherent-structures, has resisted clear description. A major limitation has been the lack of tools to identify instantaneous spatial organization, while unravelling the superposition of structures. To address this, we present a generalized correlation framework, using: (i) correlation measures to identify instantaneous vector-field patterns, and (ii) a Helmholtz-decomposition based structure-disentanglement paradigm. After examples using canonical flows, we apply these methods to homogeneous isotropic turbulence fields. We show that high kinetic energy ($E_k$) regions manifest as interspersed, localized, velocity-jets, contrary to the prevalent view of high $E_k$ regions as large swirling structures (eddies). High enstrophy ($ω^2$) regions form small vorticity-jets, invariably surrounded by swirling-velocity. The jet-like and swirling-velocity structures are spatially exclusive. Decomposing the Biot-Savart contributions from different levels and regions of the vorticity-field reveals the organization of velocity-field structures. High $E_k$ jets are neither self-induced (due to their low vorticity contents), nor induced by strong vorticity, being almost entirely induced, non-locally, by the permeating intermediate range (rms level) vorticity. High $ω^2$ swirls, instead, are a superposition of self-induced swirling-velocity along with a background-induced flow. Moreover, intermediate vorticity dominantly induces the velocity-field everywhere. This suggests that turbulence organization could emerge from non-local and non-linear field interactions, dominated by permeating intermediate vorticity, leading to an alternative description of turbulence, contrary to the notion of a strict structural hierarchy. The tools presented can be readily applied to generic vector and scalar fields associated with diverse phenomena.

physics.flu-dyn↗

arXiv2019

Universality in coalescence of polymeric fluid drops

Coalescence of liquid droplets involves an interplay between capillary forces, viscous forces and inertial forces. Here, we unveil a universal temporal evolution of the neck radius during the coalescence of two polymeric drops. Through high speed imaging we demonstrate that drops of polyacrylamide (PAM), poly-vinyl alcohol (PVA), polyethylene oxide (PEO), polyethylene glycol (PEG) and xanthan gum (XG) depict a universal behavior $R/\sqrt(ν_0λ) \sim (t/λ)^{0.36}(C/C^{*})^{-0.83}$ over a dilute, semi-dilute and non-dilute range of concentrations. A linear Phan-Thein-Tanner viscoelastic model captures the temporal aspect of universality.

physics.flu-dyn↗

arXiv2019

Droplet-turbulence interactions and quasi-equilibrium dynamics in turbulent emulsions

We perform direct numerical simulations (DNSs) of emulsions in homogeneous, isotropic turbulence using a pseudopotential lattice-Boltzmann (PP-LB) method. Improving on previous literature by minimizing droplet dissolution and spurious currents, we show that the PP-LB technique is capable of long, stable simulations in certain parameter regions. Varying the dispersed phase volume fraction $ϕ$, we demonstrate that droplet breakup extracts kinetic energy from the larger scales while injecting energy into the smaller scales, increasingly with higher $ϕ$, with the Hinze scale dividing the two effects. Droplet size ($d$) distribution was found to follow the $d^{-10/3}$ scaling (Deane & Stokes 2002). We show the need to maintain a separation of the turbulence forcing scale and domain size to prevent the formation of large connected regions of the dispersed phase. For the first time, we show that turbulent emulsions evolve into a quasi-equilibrium cycle of alternating coalescence and breakup dominated processes. Studying the system in its state-space comprising kinetic energy $E_k$, enstrophy $ω^2$ and the droplet number density $N_d$, we find that their dynamics resemble limit-cycles with a time delay. Extreme values in the evolution of $E_k$ manifest in the evolution of $ω^2$ and $N_d$ with a delay of $\sim0.3\mathcal{T}$ and $\sim0.9\mathcal{T}$ respectively (with $\mathcal{T}$ the large eddy timescale). Lastly, we also show that flow topology of turbulence in an emulsion is significantly more different than single-phase turbulence than previously thought. In particular, vortex compression and axial straining mechanisms become dominant in the droplet phase, a consequence of the elastic behaviour of droplet interfaces. Revised and extended version now published in the Journal of Fluid Mechanics: https://doi.org/10.1017/jfm.2019.654

physics.flu-dyn↗

arXiv2019

Temperature-gradient induced massive augmentation of solute dispersion in viscoelastic micro-flows

Enhancing solute dispersion in electrically actuated flows has always been a challenging proposition, as attributed to the inherent uniformity of the flow field in absence of surface patterns. Over the years, researchers have focused their attention towards circumventing this limitation, by employing several fluidic and geometric modulations. However, the corresponding improvements in solute dispersion often turn out to be inconsequential. Here we unveil that by exploiting the interplay between an externally imposed temperature gradient, subsequent electrical charge redistribution and ionic motion, coupled with the rheological complexities of the fluid, one can achieve up to one order of magnitude enhancement of solute dispersion in a pressure-driven flow of an electrolyte solution. Our results demonstrate that the complex coupling between thermal, electrical, hydro-dynamic and rheological parameters over small scales, responsible for such exclusive phenomenon, can be utilitarian in designing novel thermally-actuated micro and bio-microfluidic devices with favorable solute separation and dispersion characteristics.

physics.flu-dyn↗

arXiv2019

Streaming Potential in Bio-mimetic Microvessels Mediated by Capillary Glycocalyx

Implantable medical devices and biosensors are pivotal in revolutionizing the field of medical technology by opening new dimensions in the field of disease detection and cure. These devices need to harness a biocompatible and physiologically sustainable safe power source instead of relying on external stimuli, overcoming the constraints on their applicability in-vivo. Here, by appealing to the interplay of electromechanics and hydrodynamics in physiologically relevant microvessels, we bring out the role of charged Endothelial Glycocalyx layer (EGL) towards establishing a streaming potential across physiological fluidic conduits. We account for the complex rheology of blood-mimicking fluid by appealing to Newtonian fluid model representing the blood plasma and a viscoelastic fluid model representing the whole blood. We model the EGL as a poroelastic layer with volumetric charge distribution. Our results reveal that for physiologically relevant microflows, the streaming potential induced is typically of the order of 0.1 V/mm, which may turn out to be substantial towards energizing biosensors and implantable medical devices whose power requirements are typically in the range of micro to milli Watt. We also bring out the specific implications of the relevant physiological parameters towards establishment of the streaming potential, with a vision of augmenting the same within plausible functional limits. We further unveil that the dependence of streaming potential on EGL thickness might be one of the key aspects in unlocking the mystery behind the angiogenesis pattern. Our results may open up novel bio-sensing and actuating possibilities in medical diagnostics as well as may provide a possible alternative regarding the development of physiologically safe and biocompatible power sources within the human body.

physics.flu-dyn↗

arXiv2018

An electrokinetic route to giant augmentation in load bearing capacity of compliant microfluidic channels

The performances of lubricated systems widely used in natural, biological, and artificial settings are traditionally dictated by their load bearing capacities. Here we unveil that, by exploiting a unique coupling between interfacial electro-mechanics, hydrodynamics and substrate compliance, it is plausible to realize a massive augmentation in the load bearing capacities ofcompliant microfluidic channels. Our analysis demonstrates that the interplay between wettability and charge modulation in association with the solution chemistry and surface compliance results in this remarkable phenomenon. These results are likely to open up novel design paradigms of augmenting the load bearing capacities of miniaturized bio-mimetic units through the realization of a symmetry breaking phenomenon triggered by asymmetries in electromechanical and hydrodynamic transport over interfacial scales.

physics.flu-dyn↗