arXiv subjects

Amitabh Bhattacharya

Publications and source records attributed to Amitabh Bhattacharya.

6 recordsLinked to original sources

arXiv2026

Baroclinic wave dynamics in the Ekman-free rotating rectangular annulus with localized forced plume

We report numerical simulations of a rotating rectangular annulus that isolates the Ekman-free bulk of the cylindrical baroclinic annulus, subjected to bi-directional temperature gradients imposed by a uniformly cooled inner wall and a localized forced heated plume at the outer bottom. The finite-volume OpenFOAM solver is employed across combinations of source Richardson number $Ri_0 = 99, 4, 1$ and Rossby number $Ro = 0.3, 0.1, 0.07$. A non-dimensional scaling of the governing equations identifies geostrophic-hydrostatic balance as the leading-order bulk state, a result confirmed a posteriori by the $x$ and $z-$momentum budgets. Baroclinic waves of mode $m=2$ at $Ro=0.3$ transition to $m=3$ as $Ro$ decreases, consistent with the contraction of the Eady deformation radius $L_ρ= NH/f$; Complex Empirical Orthogonal Function (CEOF) analysis characterizes the wave regime and detects a Hopf-bifurcated vacillating state at $Ri_0 = 99,~Ro = 0.1$. The plume morphology, classified through the Morton length scale and source flux-balance parameter, transitions from weak, laterally-swept structures at $Ri_0 = 99$ to sustained columnar plumes traversing the full baroclinic depth at $Ri_0 \leq 4$. The plume entrainment coefficient $Γ(z)$ shows opposite rotational sensitivities at low and high $Ri_0$, which we organize through a local plume Rossby number $Ro_p = w/(2Ωb)$. A mixing-length argument predicts a bulk turbulent heat flux $\overline{u'T'} \propto Ri_0^{-1/2}$, anticipating an order-of-magnitude enhancement from $Ri_0 = 99$ to $Ri_0 = 1$, in agreement with the simulations. A regime map in the $(Ri_0, Ro)$ plane reveals that, within the explored range, the plume-regime and wave-selection problems are approximately separable: $Ri_0$ sets the plume regime while $Ro$ selects the dominant baroclinic wave mode.

physics.flu-dyn↗

arXiv2026

Scalar mixing in non-Markovian homogeneous isotropic synthetic turbulence

We show that non-Markovianity of the velocity field is an essential property of turbulent mixing. We demonstrate this via passive scalar mixing by synthetically generated stochastic velocity fields. Including a separate velocity decorrelation time scale for each spatial scale (random sweeping) yields an essentially non-Markovian velocity field with a finite time memory decaying as -5 (for a decaying spectrum) instead of an exponential decay (Markovian), which is obtained by including a constant time scale for all spatial scales, irrespective of the filtering function. We characterize the Lagrangian mixing statistics of both the Markovian and non-Markovian synthetic fields and compare them against a corresponding incompressible direct numerical simulation (DNS). We also study diffusive passive scalar mixing in the Schmidt number range Sc<1 using the DNS and the synthetic fields. While both the synthetic fields recover the -17/3 scalar spectrum for low Schmidt numbers, the mean gradients in a decaying simulation, as well as the production and dissipation of scalar variance in a statistically stationary simulation, are severely underpredicted by the Markovian fields compared to the non-Markovian fields. Throughout, we compare our results with companion 3D DNS to show the necessity of non-Markovianity in synthetic fields to capture mixing dynamics.

physics.flu-dyn↗

arXiv2025

A three-dimensional numerical scheme for modeling three-phase contact line pinning using Smoothed Particle Hydrodynamics

In several capillary dynamics experiments, the liquid domain is confined by pinning the three-phase contact line along a sharp edge or a discontinuity on the substrate. Simulating the dynamics of pinned droplets can offer valuable insights into capillary flow phenomena involving wetting of inhomogeneous substrates. However, Eulerian multi-phase flow solvers are usually not able to directly implement pinning of three-phase contact lines. We present the implementation of a model for pinning the contact line of a liquid along an arbitrary pinning curve on the substrate, in an updated Lagrangian, meshless flow solver based on the smoothed particle hydrodynamics (SPH) method. We develop the pinning model for a continuum surface force scheme and assume a free surface for the liquid-gas interface. We validate the model against several capillary dynamics experiments involving pinned three phase contact lines with fixed and dynamic substrates to demonstrate the robustness and accuracy of the solver.

physics.flu-dyn↗

arXiv2024

Machine Learning-Based Estimation of Superdroplet Growth Rates Using DNS Data

Droplet growth and size spectra play a crucial role in the microphysics of atmospheric clouds. However, it is challenging to represent droplet growth rate accurately in cloud-resolving models such as Large Eddy Simulations (LESs). The assumption of "well-mixed" condition within each grid cell, often made by traditional LES solvers, typically falls short near the edges of clouds, where sharp gradients in water vapor supersaturation occur. This under-resolution of supersaturation gradients can lead to significant errors in prediction of droplet growth rate, which in turn affects the prediction of buoyancy at cloud edges, as well as forecast of precipitation. In "superdroplet" based LES model, a Lagrangian coarse-graining approach groups multiple droplets into superdroplets, each encompassing a specific number and size of actual droplets. The superdroplets are advected by the underlying LES velocity field, and the growth rate of these superdroplets is based on the filtered supersaturation field represented by the LES. To overcome the limitations of the "well-mixed" assumption, we propose a parameterization for superdroplet growth using high-fidelity Direct Numerical Simulation (DNS) data. We introduce a novel clustering algorithm to map droplets in DNS fields to superdroplets. The effective supersaturation at each superdroplet location is computed by averaging the unfiltered supersaturation of the associated droplets, which may differ from the value of filtered supersaturation at the superdroplet location. We then develop a machine learning-based parameterization to relate the effective growth rate of superdroplets to other filtered DNS flow variables. Preliminary results show a promising $R^2$ value of nearly 0.9 between the predicted and true effective supersaturation values for the superdroplets, for a range of superdroplet multiplicities.

physics.flu-dyn↗

arXiv2021

Numerical Simulation of Vortex-Induced Vibration With Bistable Springs : Consistency with the Equilibrium Constraint

We present results from 2-D numerical simulations based on Immersed Boundary Method of a cylinder in uniform fluid flow attached to bistable springs undergoing Vortex-Induced Vibrations (VIV). The elastic spring potential for the bistable springs, consisting of 2 potential wells, is defined by the spacing between the potential minima and the depth of the potential wells. We perform simulations of VIV with linear spring, as well as bistable springs with two different inter-well separations, over a wide range of reduced velocity. As expected, large oscillation amplitudes correspond to lock-in of the lift force with the natural frequency of the spring-mass system. The range of reduced velocity over which lock-in occurs is significantly higher for VIV with bistable springs compared to VIV with linear springs, although the maximum possible amplitude appears to be independent of the spring type. For VIV with bistable springs, the cylinder undergoes double-well oscillations in the lock-in regime. Range of reduced velocity over which lock-in occurs increases when the inter-well distance is reduced. The vortex shedding patterns and amplitude trends look similar at the same equivalent reduced velocity for the different springs. The results here are consistent with our prior theory, in which we propose a new "Equilibrium-Constraint (EC)" based on average kinetic energy budget of the structure. For a given spring potential, the intersection of natural frequency curves with the EC curve yields the possible range of reduced velocities over which lock-in should occur. Our numerical simulations show a collapse of the amplitude-versus-structure frequency data for all the simulations onto roughly the same curve, thus supporting the existence of the EC, and providing an explanation for the trends in the VIV oscillations.

physics.flu-dyn↗

arXiv2016

Convection in rotating flows with simultaneous imposition of radial and vertical temperature gradients

Laboratory experiments were conducted to study heat transport characteristics in a nonhomogeneously heated fluid annulus subjected to rotation along the vertical axis (z). The nonhomogeneous heating was obtained by imposing radial and vertical temperature gradient (ΔT). The parameter range for this study was Rayleigh number, Ra=2.43x10^8-3.66x10^8, and Taylor number, Ta=6.45x10^8-27x10^8. The working fluid was water with a Prandtl number, Pr=7. Heat transport was measured for varying rotation rates (Ω) for fixed values of ΔT. The Nusselt number, Nu, plotted as a function of Ta distinctly showed the effect of rotation on heat transport. In general, Nu was found to have a larger value for non-rotating convection. This could mean an interplay of columnar plumes and baroclinic wave in our system as also evident from temperature measurements. Laser based imaging at a single vertical plane also showed evidence of such flow structure.

physics.flu-dyn↗