arXiv subjects

Prasad Perlekar

Publications and source records attributed to Prasad Perlekar.

At least 19 recordsLinked to original sources

arXiv2026

Gappy Reconstruction of Bubbly Flows by Guided Diffusion Models

Experiments in multiphase flows are often limited in their ability to simultaneously obtain velocity measurements in different phases. At the same time, flow reconstruction from phase-limited measurements is a challenging problem due to the substantially different velocity statistics across the phases. We address this problem for buoyancy-driven bubbly flows in the pseudo-turbulence regime by using a guided diffusion model. We train the model using two-dimensional slices of the velocity field extracted from fully resolved three-dimensional direct numerical simulations. The model generates physically realistic velocity fields both unconditionally and when conditioned on the surrounding liquid flow. The reconstructed bubble-phase velocity field accurately reproduces key statistical features of the flow. We further show that a simple patching procedure for adjacent two-dimensional slices enables a reasonable reconstruction of the three-dimensional flow inside a bubble. These results establish the potential of diffusion models to serve as generative priors for three-dimensional turbulent multiphase flows, opening a route toward the reconstruction of unobserved or experimentally inaccessible velocity fields from sparse, partial, or phase-limited measurements.

physics.flu-dyn↗

arXiv2026

Flocking and mesoscale turbulence in three-dimensional active fluids

We numerically study the three-dimensional turbulence in a minimal model of an active fluid--the Toner-Tu-Swift-Hohenburg equation. For small activity, we observe bacterial turbulence, while for large activity, we uncover hitherto unexplored regime of a turbulent flock where a global order coexists with turbulence. We present a simple closure model that predicts the turbulent flock and also qualitatively explains the transition to the bacterial turbulence regime via a transcritical bifurcation.

physics.flu-dyn↗

arXiv2026

Bridging Filtering and Point-Splitting Approaches for Variable-Density Flows

Energy transfer in turbulent flows is typically described either through correlation functions, via the K\'arm\'an-Howarth-Monin relation, or through a scale-by-scale budget of the filtered energy (Frisch 1995). For constant-density homogeneous and isotropic turbulence, the equivalence between these two descriptions is well understood. In compressible turbulence, however, several definitions of filtered energy exist, and for most definitions the associated formulation in terms of correlation functions is unclear. We develop a general empirical framework, supported by theoretical arguments and numerical simulations, to determine the multipoint correlation functions corresponding to any filtered energy. We then show that the Favre filtered energy -- defined as the ratio of the squared filtered momentum to the filtered density -- corresponds to an infinite series of multipoint correlation functions. This is achieved by expanding the Favre velocity as a power series in local density fluctuations. The expansion reveals the contributions of the subgrid-scale fluctuations of velocity and density to the Favre velocity. We verify the proposed expansion for the buoyancy and pressure contributions for three-dimensional buoyancy-driven bubbly flows with a large density contrast ($10^2$) between the liquid and the bubble phase.

physics.flu-dyn↗

arXiv2025

Instabilities and turbulence in extensile swimmer suspensions

We study low Reynolds number turbulence in a suspension of polar, extensile, self-propelled inertial swimmers. We review the bend and splay mechanisms that destabilize an ordered flock. The suspension is always unstable to bend perturbations. Using a minimal 1D model, we show that the splay-stable to splay-unstable transition occurs via a supercritical Hopf bifurcation. We perform high-resolution numerical simulations in 2D to study the varieties of turbulence present in this system transitioning from defect turbulence to concentration-wave turbulence depending on a single non-dimensional number, denoting the ratio of the splay-concentration wavespeed to the swimmer motility.

cond-mat.soft↗

arXiv2025

Scale-by-scale energy transfers in bubbly flows

Buoyancy-driven bubbly flows naturally have spatially-dependent density fields, which allow for multiple definitions of the scale-dependent (or filtered) energy. A priori, it is not obvious which of these provide the most physically apt scale-by-scale budget. In the present study, we compare two such definitions, based on (a) filtered momentum and filtered velocity (Pandey et al. 2020), and (b) Favre filtered energy (Aluie 2013; Pandey et al. 2023). We also derive a K\'arm\'an-Howarth-Monin (KHM) relation using the momentum-velocity correlation function and contrast it with the scale-by-scale energy budget obtained in (a). We find that for the volume fraction and Atwood number explored, irrespective of the definition, energy transfers due to the advective nonlinearity and surface tension are identical. However, discrepancies arise for the buoyancy and pressure contributions. We show that the Favre filtered definition is the more appropriate choice, within which buoyancy injects energy, pressure transfers energy to large scales, and both advective nonlinearity and surface tension transfer energy downscales where it is dissipated by viscosity.

physics.flu-dyn↗

arXiv2025

Diffusive noise controls early stages of genetic demixing

Theoretical descriptions of the stepping-stone model, a cornerstone of spatial population genetics, have long overlooked diffusive noise arising from migration dynamics. We derive an exact fluctuating hydrodynamic description of this model from microscopic rules, which we then use to demonstrate that diffusive noise significantly alters early-time genetic demixing, which we characterize through heterozygosity, a key measure of diversity. Combining macroscopic fluctuation theory and microscopic simulations, we demonstrate that the scaling of density fluctuations in a spatial domain displays an early-time behaviour dominated by diffusive noise. Our exact results underscore the need for additional terms in existing continuum theories and highlight the necessity of including diffusive noise in models of spatially structured populations.

cond-mat.stat-mech↗

arXiv2024

Emergent asymmetry in confined bioconvection

Bioconvection is the prototypical active matter system for hydrodynamic instabilities and pattern formation in suspensions of biased swimming microorganisms, particularly at the dilute end of the concentration spectrum where cell-cell interactions typically are neglected. Confinement is an inherent characteristic of such systems, including those that are naturally-occurring or industrially-exploited, so it is important to understand the impact of boundaries on the hydrodynamic instabilities. Despite recent interest in this area we note that commonly-adopted symmetry assumptions in the literature, such as for a vertical channel or pipe, are uncorroborated and potentially unjustified. Therefore, by employing a combination of analytical and numerical techniques, we investigate whether confinement itself can drive asymmetric plume formation in a suspension of bottom-heavy swimming microorganisms (gyrotactic cells). For a class of solutions in a vertical channel we establish the existence of a first integral of motion, and reveal that asymptotic asymmetry is plausible. Furthermore, numerical simulations from both Lagrangian and Eulerian perspectives demonstrate with remarkable agreement that asymmetric solutions can indeed be more stable than symmetric; asymmetric solutions are in fact dominant for a large, practically-important region of parameter space. In addition, we verify the presence of blip and varicose instabilities for an experimentally accessible parameter range. Finally, we extend our study to a vertical Hele-Shaw geometry to explore whether a simple linear drag approximation can be justified. We find that although two-dimensional bioconvective structures and associated bulk properties have some similarities with experimental observations, approximating near wall physics in even the simplest confined systems remains challenging.

cond-mat.soft↗

arXiv2024

Inertia drives concentration-wave turbulence in swimmer suspensions

We discover an instability mechanism in suspensions of self-propelled particles that does not involve active stress. Instead, it is driven by a subtle interplay of inertia, swimmer motility, and concentration fluctuations, through a crucial time lag between the velocity and the concentration field. The resulting time-persistent state seen in our high-resolution numerical simulations consists of self-sustained waves of concentration and orientation, transiting from regular oscillations to wave turbulence. We analyze the statistical features of this active turbulence, including an intriguing connection to the Batchelor spectrum of passive scalars.

cond-mat.soft↗

arXiv2023

Kolmogorov Turbulence Coexists with Pseudo-Turbulence in Buoyancy-Driven Bubbly Flows

We investigate spectral properties of buoyancy driven bubbly flows. Using high-resolution numerical simulations and phenomenology of homogeneous turbulence, we identify the relevant energy transfer mechanisms. We find: (a) At high enough Galilei number (ratio of the buoyancy to viscous forces) the kinetic energy spectrum shows the Kolmogorov scaling with a power law exponent $-5/3$ for the range of scales between the bubble diameter and the dissipation scale ($η$). (b) For scales smaller than $η$, the physics of pseudo-turbulence is recovered.

physics.flu-dyn↗

arXiv2023

Intermittency in the not-so-smooth elastic turbulence

Elastic turbulence is the chaotic fluid motion resulting from elastic instabilities due to the addition of polymers in small concentrations at very small Reynolds ($\mbox{Re}$) numbers. Our direct numerical simulations show that elastic turbulence, though a low $\mbox{Re}$ phenomenon, has more in common with classical, Newtonian turbulence than previously thought. In particular, we find power-law spectra for kinetic energy $E(k) \sim k^{-4}$ and polymeric energy $E_{\rm p}(k) \sim k^{-3/2}$, independent of the Deborah ($\mbox{De}$) number. This is further supported by calculation of scale-by-scale energy budget which shows a balance between the viscous term and the polymeric term in the momentum equation. In real space, as expected, the velocity field is smooth, i.e., the velocity difference across a length scale $r$, $\delta u \sim r$ but, crucially, with a non-trivial sub-leading contribution $r^{3/2}$ which we extract by using the second difference of velocity. The structure functions of second difference of velocity up to order $6$ show clear evidence of intermittency/multifractality. We provide additional evidence in support of this intermittent nature by calculating moments of rate of dissipation of kinetic energy averaged over a ball of radius $r$, $\varepsilon_{r}$, from which we compute the multifractal spectrum.

physics.flu-dyn↗

arXiv2023

Defect turbulence in a dense suspension of polar, active swimmers

We study the effects of inertia in dense suspensions of polar swimmers. The hydrodynamic velocity field and the polar order parameter field describe the dynamics of the suspension. We show that a dimensionless parameter $R$ (ratio of the swimmer self-advection speed to the active stress invasion speed) controls the stability of an ordered swimmer suspension. For $R$ smaller than a threshold $R_1$, perturbations grow at a rate proportional to their wave number $q$. Beyond $R_1$, we show that the growth rate is $\mathcal{O}(q^2)$ until a second threshold $R=R_2$ is reached. The suspension is stable for $R>R_2$. We perform direct numerical simulations to investigate the steady state properties and observe defect turbulence for $R<R_2$. An investigation of the spatial organisation of defects unravels a hidden transition: for small $R\approx 0$ defects are uniformly distributed and cluster as $R\to R_1$. Beyond $R_1$, clustering saturates and defects are arranged in nearly string-like structures.

cond-mat.soft↗

arXiv2023

Large is different: non-monotonic behaviour of elastic range scaling in polymeric turbulence at large Reynolds and Deborah numbers

We use direct numerical simulations to study homogeneous, and isotropic turbulent flows of dilute polymer solutions at high Reynolds and Deborah numbers. We find that for small wavenumbers $k$, the kinetic energy spectrum shows Kolmogorov--like behavior which crosses over at a larger $k$ to a novel, elastic scaling regime, $E(k) \sim k^{-ξ}$, with $ξ\approx 2.3$. We study the contribution of the polymers to the flux of kinetic energy through scales, and find that it can be decomposed into two parts: one increase in effective viscous dissipation, and a purely elastic contribution that dominates over the nonlinear flux in the range of $k$ over which the elastic scaling is observed. The multiscale balance between the two fluxes determines the crossover wavenumber which depends non-monotically on the Deborah number. Consistently, structure functions also show two scaling ranges, with intermittency present in both of them in equal measure.

physics.flu-dyn↗

arXiv2022

Energy spectra of buoyancy-driven bubbly flow in a vertical Hele-Shaw cell

We present direct numerical simulations (DNS) study of confined buoyancy-driven bubbly flows in a Hele-Shaw setup. We investigate the spectral properties of the flow and make comparisons with experiments. The energy spectrum obtained from the gap-averaged velocity field shows $E(k) \sim k$ for $k < k_d$, $E(k) \sim k^{-5}$ for $k > k_d$, and an intermediate scaling range with $E(k) \sim k^{-3}$ around $k \sim k_d$. We perform an energy budget analysis to understand the dominant balances and explain the observed scaling behavior. We also show that the Navier-Stokes equation with a linear drag can be used to approximate large scale flow properties of bubbly Hele-Shaw flow.

physics.flu-dyn↗

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

Inertia drives a flocking phase transition in viscous active fluids

How fast must an oriented collection of extensile swimmers swim to escape the instability of viscous active suspensions? We show that the answer lies in the dimensionless combination $R=ρv_0^2/2σ_a$, where $ρ$ is the suspension mass density, $v_0$ the swim speed and $σ_a$ the active stress. Linear stability analysis shows that for small $R$ disturbances grow at a rate linear in their wavenumber $q$, and that the dominant instability mode involves twist. The resulting steady state in our numerical studies is isotropic hedgehog-defect turbulence. Past a first threshold $R$ of order unity we find a slower growth rate, of $O(q^2)$; the numerically observed steady state is {\it phase-turbulent}: noisy but {\it aligned} on average. We present numerical evidence in three and two dimensions that this inertia driven flocking transition is continuous, with a correlation length that grows on approaching the transition. For much larger $R$ we find an aligned state linearly stable to perturbations at all $q$. Our predictions should be testable in suspensions of mesoscale swimmers [D Klotsa, Soft Matter \textbf{15}, 8946 (2019)].

cond-mat.soft↗

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

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↗