Prasad Perlekar

Theoretical descriptions of the stepping-stone model, a cornerstone of spatial population genetics, have long overlooked diffusive noise arising from migration dynamics. We derive a 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 allele-number fluctuations in a spatial domain displays an early-time behavior dominated by diffusive noise. Our 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.

Energy transfer in turbulent flows is typically described either through correlation functions, via the Kármán-Howarth-Monin relation, or through a scale-by-scale budget of the filtered energy (Frisch U., Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press) 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.

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 (i) filtered momentum and filtered velocity (Pandey et al., J. Fluid Mech ., 2020, vol. 884, p. R6), and (ii) Favre-filtered energy (Aluie, Phys. D: Nonlinear Phenom. , 2013, vol. 247, pp. 54–65; Pandey et al., Phys. Rev. Lett. , 2023, vol. 131, p. 114002). We also derive a Kármán–Howarth–Monin relation using the momentum–velocity correlation function and contrast it with the scale-by-scale energy budget obtained in (i). 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.

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.

Energy transfer in turbulent flows is typically described either through correlation functions, via the Kármán-Howarth-Monin relation, or through a scale-by-scale budget of filtered energy (Frisch 1995). For constant-density turbulence, the equivalence between these two descriptions is well understood. In compressible turbulence, however, several definitions of filtered energy exist, and for most of them the associated formulation in terms of correlation functions is unclear. We develop a general framework to determine the multi-point correlation functions corresponding to any specified filtered energy. As a demonstration, we show that the Favre filtered energy--defined as the ratio of the squared filtered momentum to the filtered density--and the terms in its budget can be written as an infinite series of multi-point correlation functions. We validate the framework numerically using three-dimensional buoyancy-driven bubbly flows.

The ordered state of microswimmers can be destroyed by an instability created by their swimming stresses. This leads to chaotic flows that resemble turbulence characterized by the presence of topological defects, a phenomenon known as active turbulence. We show that for pushers, the defect turbulent state transitions to a novel concentration-wave turbulent state reported earlier, where defects coexist along with concentration waves. This state emerges from an instability where fluctuations in the concentration of swimmers play a dominant role. Our study aims to provide a comprehensive understanding of the instabilities and turbulence in weakly inertial suspensions of pushers.

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 direct cell–cell interactions are less relevant. 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.