arXiv subjects

Piyush Garg

Publications and source records attributed to Piyush Garg.

15 recordsLinked to original sources

arXiv2026

The ultimate state of elastic turbulence

The asymptotic properties, with vanishing viscosity, of inertial turbulence in Newtonian fluids have been of intense scrutiny over the years. Much less is known about elastic turbulence - a distinct spatio-temporally chaotic state exhibited by viscoelastic fluids. In this work, using direct numerical simulations of turbulence in a triperiodic box, we show that elastic turbulence achieves an ultimate state with increasing polymer relaxation time, i.e., the Deborah number, for two different constitutive models (Oldroyd-B and FENE-P). In the limiting state, various bulk quantities - the fluid dissipation, the polymeric energy transfer, as well as the elastic stresses - are shown to become independent of the polymer relaxation time scale, notwithstanding the microstructure deformation scales distinctly depending on the model.

physics.flu-dyn↗

arXiv2026

Waves dictate the yo-yoing decay of a viscoelastic mixing layer

We find that waves develop in a time-decaying mixing layer of viscoelastic fluid, leading the mean-flow to yo-yo. This is in sharp contrast with Newtonian fluids, where laminar mixing layers evolve monotonically. We combine direct numerical simulations with a theoretical analysis of the energy budget for the flow to uncover the underlying physical mechanism. The yo-yoing of the mean-flow is shown to be driven by the elastic polymers injecting energy into the fluid and, in turn, being rotated by the large-scale mean shear. We then provide the mathematical model of the problem and solve it analytically, finding wave solutions with non-linear dispersion predicting the period of the yo-yoing and the parameter range where it occurs. As decaying mixing layers are one of the simplest and canonical examples of unsteady flows, the phenomenon identified here explains the anomalies recently observed in experiments of unsteady viscoelastic flows in complex geometries.

physics.flu-dyn↗

arXiv2026

The Recipe Matters More Than the Kitchen:Mathematical Foundations of the AI Weather Prediction Pipeline

AI weather prediction has advanced rapidly, yet no unified mathematical framework explains what determines forecast skill. Existing theory addresses specific architectural choices rather than the learning pipeline as a whole, while operational evidence from 2023-2026 demonstrates that training methodology, loss function design, and data diversity matter at least as much as architecture selection. This paper makes two interleaved contributions. Theoretically, we construct a framework rooted in approximation theory on the sphere, dynamical systems theory, information theory, and statistical learning theory that treats the complete learning pipeline (architecture, loss function, training strategy, data distribution) rather than architecture alone. We establish a Learning Pipeline Error Decomposition showing that estimation error (loss- and data-dependent) dominates approximation error (architecture-dependent) at current scales. We develop a Loss Function Spectral Theory formalizing MSE-induced spectral blurring in spherical harmonic coordinates, and derive Out-of-Distribution Extrapolation Bounds proving that data-driven models systematically underestimate record-breaking extremes with bias growing linearly in record exceedance. Empirically, we validate these predictions via inference across ten architecturally diverse AI weather models using NVIDIA Earth2Studio with ERA5 initial conditions, evaluating six metrics across 30 initialization dates spanning all seasons. Results confirm universal spectral energy loss at high wavenumbers for MSE-trained models, rising Error Consensus Ratios showing that the majority of forecast error is shared across architectures, and linear negative bias during extreme events. A Holistic Model Assessment Score provides unified multi-dimensional evaluation, and a prescriptive framework enables mathematical evaluation of proposed pipelines before training.

cs.LG↗

arXiv2025

Elastic turbulence hides in the small scales of inertial polymeric turbulence

Gaining a fundamental understanding of turbulent flows of dilute polymer solutions has been a challenging and outstanding problem for a long time. In this letter, we examine homogeneous, isotropic polymeric turbulence at large Reynolds and Deborah numbers through direct numerical simulations. While at the largest scales of the flow inertial turbulence exists, we find that the flow is fundamentally altered from Newtonian turbulence below the Kolmogorov scale. We demonstrate that `Elastic Turbulence' exists at the smallest scales of polymeric turbulence by quantifying multiple statistical properties of the flow - energy spectrum and flux in Fourier space as well as the spatial statistics of the velocity field - the structure functions and kurtosis, and energy dissipation. Our results show the coexistence of two fundamentally distinct types of turbulence in polymeric fluids and point to the ubiquity of elastic turbulence, which was hitherto only known to exist for negligible inertia.

physics.flu-dyn↗

arXiv2025

Orientation dynamics of a spheroid in the simple shear flow of a weakly elastic fluid

We investigate the orientation dynamics of a neutrally buoyant spheroid, of an arbitrary aspect ratio ($\kappa$), freely rotating in a weakly viscoelastic fluid undergoing simple shear flow. Weak elasticity is characterized by a small but finite Deborah number ($De$), and the suspending fluid rheology is therefore modeled as a second-order fluid, with the constitutive equation involving a material parameter $\epsilon$ related to the ratio of the first and second normal stress differences; polymer solutions correspond to $\epsilon\in[-0.7,-0.5]$. Employing a reciprocal theorem formulation, along with expressions for the relevant disturbance fields in terms of vector spheroidal harmonics, we obtain the spheroid angular velocity to $O(De)$. In the Newtonian limit, a spheroid rotates along Jeffery orbits parametrized by an orbit constant $C$, although this closed-trajectory topology is structurally unstable, being susceptible to weak perturbations. For $De$ well below a threshold, $De_c(\kappa)$, weak viscoelasticity transforms the closed-trajectory topology into a tightly spiralling one. A multiple-scales analysis is used to interpret the resulting orientation dynamics in terms of an $O(De)$ orbital drift. The drift in orbit constant over a Jeffery period $\Delta C$, when plotted as a function of $C$, identifies four different orientation dynamics regimes on the $\kappa-\epsilon$ plane. For $\epsilon$ in the polymeric range, prolate spheroids always drift towards the spinning mode. Oblate spheroids drift towards the tumbling mode for $\kappa > \kappa_c(\epsilon)$, but towards an intermediate kayaking mode for $\kappa < \kappa_c(\epsilon)$. The rotation of spheroids of extreme aspect ratios, either slender prolate spheroids ($\kappa \gg 1$) or thin oblate ones ($\kappa \ll 1$), about the vorticity axis, is arrested for $De \geq De_c(\kappa)$

physics.flu-dyn↗

arXiv2024

Kilometer-Scale Convection Allowing Model Emulation using Generative Diffusion Modeling

Storm-scale convection-allowing models (CAMs) are an important tool for predicting the evolution of thunderstorms and mesoscale convective systems that result in damaging extreme weather. By explicitly resolving convective dynamics within the atmosphere they afford meteorologists the nuance needed to provide outlook on hazard. Deep learning models have thus far not proven skilful at km-scale atmospheric simulation, despite being competitive at coarser resolution with state-of-the-art global, medium-range weather forecasting. We present a generative diffusion model called StormCast, which emulates the high-resolution rapid refresh (HRRR) model-NOAA's state-of-the-art 3km operational CAM. StormCast autoregressively predicts 99 state variables at km scale using a 1-hour time step, with dense vertical resolution in the atmospheric boundary layer, conditioned on 26 synoptic variables. We present evidence of successfully learnt km-scale dynamics including competitive 1-6 hour forecast skill for composite radar reflectivity alongside physically realistic convective cluster evolution, moist updrafts, and cold pool morphology. StormCast predictions maintain realistic power spectra for multiple predicted variables across multi-hour forecasts. Together, these results establish the potential for autoregressive ML to emulate CAMs -- opening up new km-scale frontiers for regional ML weather prediction and future climate hazard dynamical downscaling.

physics.ao-ph↗

arXiv2024

Generative Data Assimilation of Sparse Weather Station Observations at Kilometer Scales

Data assimilation of observational data into full atmospheric states is essential for weather forecast model initialization. Recently, methods for deep generative data assimilation have been proposed which allow for using new input data without retraining the model. They could also dramatically accelerate the costly data assimilation process used in operational regional weather models. Here, in a central US testbed, we demonstrate the viability of score-based data assimilation in the context of realistically complex km-scale weather. We train an unconditional diffusion model to generate snapshots of a state-of-the-art km-scale analysis product, the High Resolution Rapid Refresh. Then, using score-based data assimilation to incorporate sparse weather station data, the model produces maps of precipitation and surface winds. The generated fields display physically plausible structures, such as gust fronts, and sensitivity tests confirm learnt physics through multivariate relationships. Preliminary skill analysis shows the approach already outperforms a naive baseline of the High-Resolution Rapid Refresh system itself. By incorporating observations from 40 weather stations, 10% lower RMSEs on left-out stations are attained. Despite some lingering imperfections such as insufficiently disperse ensemble DA estimates, we find the results overall an encouraging proof of concept, and the first at km-scale. It is a ripe time to explore extensions that combine increasingly ambitious regional state generators with an increasing set of in situ, ground-based, and satellite remote sensing data streams.

cs.LG↗

arXiv2024

DiffObs: Generative Diffusion for Global Forecasting of Satellite Observations

This work presents an autoregressive generative diffusion model (DiffObs) to predict the global evolution of daily precipitation, trained on a satellite observational product, and assessed with domain-specific diagnostics. The model is trained to probabilistically forecast day-ahead precipitation. Nonetheless, it is stable for multi-month rollouts, which reveal a qualitatively realistic superposition of convectively coupled wave modes in the tropics. Cross-spectral analysis confirms successful generation of low frequency variations associated with the Madden--Julian oscillation, which regulates most subseasonal to seasonal predictability in the observed atmosphere, and convectively coupled moist Kelvin waves with approximately correct dispersion relationships. Despite secondary issues and biases, the results affirm the potential for a next generation of global diffusion models trained on increasingly sparse, and increasingly direct and differentiated observations of the world, for practical applications in subseasonal and climate prediction.

physics.comp-ph↗

arXiv2022

Anomalous dispersion of microswimmer populations

We examine the longitudinal dispersion of spheroidal microswimmers in pressure-driven channel flow. When time scales corresponding to swimmer orientation relaxation, and diffusion in the gradient and flow directions, are well separated, a multiple scales analysis leads to the shear-enhanced diffusivity governing the long-time spread of the swimmer population along the flow\,(longitudinal) direction. For large $Pe_r$, $Pe_r$ being the rotary Peclet number, this diffusivity scales as $O(Pe_r^4D_t)$ for $1 \leq κ\lesssim 2$, and as $O(Pe_r^{\frac{10}{3}}D_t)$ for $κ= \infty$, $D_t$ being the (bare)\,swimmer translational diffusivity and $κ$ the swimmer aspect ratio. For $2 \lesssim κ< \infty$, swimmers collapse onto the centerline with increasing $Pe_r$, leading to an anomalously reduced diffusivity of $O(Pe_r^{5+C(κ)}D_t)$. Here, $C(κ)\!<\!-1$ characterizes the algebraic decay of swimmer concentration outside an $O(Pe_r^{-1})$ central core, with the anomalous exponent governed by large velocity variations sampled by the few swimmers outside this core. $C(κ)$ dips below $-5$ for $κ\gtrsim 10$, leading to a flow-independent bound of $O(κ^{10}D_t)$ for the dispersion of sufficiently slender swimmers.

physics.flu-dyn↗

arXiv2021

Inertio-elastic instability of a vortex column

We analyze the instability of a vortex column in a dilute polymer solution at large $\textit{Re}$ and $\textit{De}$ with $\textit{El} = \textit{De}/\textit{Re}$, the elasticity number, being finite. Here, $\textit{Re} = Ω_0 a^2/ν_s$ and $\textit{De} = Ω_0 τ$ are, respectively, the Reynolds and Deborah numbers based on the core angular velocity ($Ω_0$), the radius of the column ($a$), the solvent-based kinematic viscosity ($ν_s = μ_s/ρ$), and the polymeric relaxation time ($τ$). The stability of small-amplitude perturbations in this distinguished limit is governed by the elastic Rayleigh equation whose spectrum is parameterized by $ \textrm{E} = \textit{El}(1-β)$, $β$ being the ratio of the solvent to the solution viscosity. The neglect of the relaxation terms, in the said limit, implies that the polymer solution supports undamped elastic shear waves propagating relative to the base-state flow. The existence of these shear waves leads to multiple (three) continuous spectra associated with the elastic Rayleigh equation in contrast to just one for the original Rayleigh equation. Further, unlike the neutrally stable inviscid case, an instability of the vortex column arises for finite E due to a pair of elastic shear waves being driven into a resonant interaction under the differential convection by the irrotational shearing flow outside the core. An asymptotic analysis for the Rankine profile shows the absence of an elastic threshold; although, for small E, the growth rate of the unstable discrete mode is transcendentally small, being O$(\textrm{E}^2e^{-1/\textrm{E}^{\frac{1}{2}}})$. An accompanying numerical investigation shows that the instability persists for smooth vorticity profiles, provided the radial extent of the transition region (from the rotational core to the irrotational exterior) is less than a certain $\textrm{E}$-dependent threshold.

physics.flu-dyn↗

arXiv2020

The center-mode instability of viscoelastic plane Poiseuille flow

A modal stability analysis shows that plane Poiseuille flow of an Oldroyd-B fluid becomes unstable to a `center mode' with phase speed close to the maximum base-flow velocity, $U_{max}$. The governing dimensionless groups are the Reynolds number $Re = ρU_{max} H/η$, the elasticity number $E = λη/(H^2ρ)$, and the ratio of solvent to solution viscosity $η_s/η$; here, $λ$ is the polymer relaxation time, $H$ is the channel half-width, and $ρ$ is the fluid density. For experimentally relevant values (e.g., $E \sim 0.1$ and $β\sim 0.9$), the predicted critical Reynolds number, $Re_c$, for the center-mode instability is around $200$, with the associated eigenmodes being spread out across the channel. In the asymptotic limit of $E(1 -β) \ll 1$, with $E$ fixed, corresponding to strongly elastic dilute polymer solutions, $Re_c \propto (E(1-β))^{-\frac{3}{2}}$ and the critical wavenumber $k_c \propto (E(1-β))^{-\frac{1}{2}}$. The unstable eigenmode in this limit is confined in a thin layer near the channel centerline. The above features are largely analogous to the center-mode instability in viscoelastic pipe flow (Garg et al., Phys. Rev. Lett., 121, 024502 (2018)), and suggest a universal linear mechanism underlying the onset of turbulence in both channel and pipe flows of suffciently elastic dilute polymer solutions.

physics.flu-dyn↗

arXiv2020

Linear instability of viscoelastic pipe flow

A modal stability analysis shows that pressure-driven pipe flow of an Oldroyd-B fluid is linearly unstable to axisymmetric perturbations, in stark contrast to its Newtonian counterpart which is linearly stable at all Reynolds numbers. The dimensionless groups that govern stability are the Reynolds number, the elasticity number, and the ratio of solvent to solution viscosity. The unstable mode has a phase speed close to the base-state maximum over the entire unstable region in the relevant parameter space, implying that the unstable mode belongs to a class of viscoelastic center modes. Unlike the Newtonian transition which is dominated by nonlinear processes, the linear instability discussed here could be very relevant to the onset of turbulence in viscoelastic pipe flows. The prediction of an instability is, in fact, consistent with several experimental studies on pipe flow of polymer solutions, ranging from previous reports of early turbulence to the more recent discovery of elasto-inertial turbulence. The instability identified in this study comprehensively dispels the prevailing notion of pipe flow of viscoelastic fluids being linearly stable in the Reynolds-Weissenberg plane, marking a possible paradigm shift in our understanding of transition in rectilinear viscoelastic shearing flows.

physics.flu-dyn↗

arXiv2019

Enhanced velocity fluctuations in interacting swimmer suspensions

A dilute non-interacting suspension of micro-swimmers exhibits a finite velocity variance and short-ranged correlations that decay over a swimmer length. For a suspension of interacting straight swimmers, however, pair-interactions leads to a non-decaying velocity covariance, and a variance that diverges logarithmically with system size. The divergence is arrested on inclusion of orientation decorrelation mechanisms. Results for suspensions of run-and-tumble particles (RTPs) are presented, where the underlying straight-swimmer divergence leads to a broad cross-over between the ballistic and diffusive regimes, of immersed passive tracers, in the limit of long run lengths. Our analysis explains long-standing experimental observations of a volume-fraction dependent crossover time for passive tracer dynamics.

cond-mat.soft↗

arXiv2018

Concentration banding instability of a sheared bacterial suspension

We demonstrate a novel shear-induced mechanism for growth of concentration fluctuations in a bacterial suspension. Using a linear stability analysis, a homogeneously sheared suspension is shown to support exponentially growing layering perturbations in the shear-rate and bacterial concentration. Non-linear simulations show that the instability eventually leads to gradient-banded velocity profiles, with a local depletion of bacteria at the interface between the bands. Our results show that long-ranged hydrodynamic interactions are sufficient to explain recent observations of shear-bands in bacterial suspensions.

physics.flu-dyn↗

arXiv2017

Viscoelastic pipe flow is linearly unstable

Newtonian pipe flow is known to be linearly stable at all Reynolds numbers. We report, for the first time, a linear instability of pressure driven pipe flow of a viscoelastic fluid, obeying the Oldroyd-B constitutive equation commonly used to model dilute polymer solutions. The instability is shown to exist at Reynolds numbers significantly lower than those at which transition to turbulence is typically observed for Newtonian pipe flow. Our results qualitatively explain experimental observations of transition to turbulence in pipe flow of dilute polymer solutions at flow rates where Newtonian turbulence is absent. The instability discussed here should form the first stage in a hitherto unexplored dynamical pathway to turbulence in polymer solutions. An analogous instability exists for plane Poiseuille flow.

physics.flu-dyn↗