arXiv subjects

Jiten C. Kalita

Publications and source records attributed to Jiten C. Kalita.

10 recordsLinked to original sources

arXiv2026

Fractal Scaling of Moffatt Vortices in Triangular Cavity Flow

This study examines the formation, quantification, and fractal characterization of corner vortices in slow viscous incompressible flow within a triangular cavity. The governing Navier-Stokes equations are solved numerically using a pressure-based coupled solver, and the resulting vortex cascade is analyzed through the size and intensity ratios of successive eddies in the spirit of Moffatt's theory of corner vortices. The fractal properties of the vortex sequence are then investigated using the area-perimeter method. An empirical relation is proposed to estimate the fractal dimension of any successive vortex in the cascade for arbitrary grid resolution. The results demonstrate that the corner vortices possess non-integer fractal dimensions between 1 and 2, and that this dimension is systematically linked to vortex size and intensity. The influence of Reynolds number on the fractal scaling is also examined. Finally, a comparative analysis of self-similarity in triangular and square cavities confirms that the observed corner-vortex cascade exhibits robust fractal behavior across geometries and flow regimes.

physics.flu-dyn↗

arXiv2026

HOC simulations of miscible viscous fingering of a finite slice: A new insight

We investigate the dynamics of viscous fingering (VF) in miscible slices in homogeneous, isotropic porous media. The fluid flow is governed by incompressible Darcy's law, whereas the solute transport is described using an advection-diffusion equation. The viscosity of the miscible system depends on the solute concentration, creating a viscosity contrast between the displacing fluid and the finite sample. When expressed in terms of stream function, the flow is described by a system of nonlinear, two-way coupled advection-diffusion type equations. We consider three types of boundary conditions: (a) periodic, (b) impermeable (zero normal velocity) and no-flux (solute), and (c) permeable (allowing non-zero normal velocity) and no diffusive flux (solute) transverse boundaries. This initial boundary value problem is solved numerically using a fourth-order compact finite difference method, while the Crank-Nicolson technique is used for time integration. Although the onset of viscous fingering and early time behavior are independent of the choice of boundary types, long-time behavior, solute mixing and spreading depend on the boundary conditions. In particular, it is observed that the permeable boundaries allow solute mass to increase, leading to stronger fingering instabilities, larger mixing lengths and non-trivial evolution of interfacial lengths. The findings of this study have implications in chromatography separation.

physics.flu-dyn↗

arXiv2025

Dissolution-driven transport in a rotating horizontal cylinder

We study the combined effects of natural convection and rotation on the dissolution of a solute in a solvent-filled circular cylinder. The density of the fluid increases with the increasing concentration of the dissolved solute, and we model this using the Oberbeck-Boussinesq approximation. The underlying moving-boundary problem has been modelled by combining the Navier-Stokes equations with the advection-diffusion equation and a Stefan condition for the evolving solute-fluid interface. We use highly resolved numerical simulations to investigate the flow regimes, dissolution rates, and mixing of the dissolved solute for $Sc = 1$, $Ra \in [10^5, 10^8]$ and $Ω\in [0, 2.5]$. In the absence of rotation and buoyancy, the distance of the interface from its initial position follows a square root relationship with time ($r_d \propto \sqrt{t}$), which ceases to exist at a later time due to the finite-size effect of the liquid domain. We then explore the rotation parameter, considering a range of rotation frequency -- from smaller to larger, relative to the inverse of the buoyancy-induced timescale -- and Rayleigh number. We show that the area of the dissolved solute varies nonlinearly with time depending on $Ra$ and $Ω$. The symmetry breaking of the interface is best described in terms of $Ra/Ω^2$.

physics.flu-dyn↗

arXiv2025

Towards enhanced mixing of a high viscous miscible blob in porous media

In this study, we investigate the rectilinear displacement and deformation of a highly viscous, miscible circular blob influenced by a less viscous fluid within a homogeneous porous medium featuring physically realistic no-flux boundaries. We utilize a fourth-order accurate compact finite difference scheme for the spatial discretization of the nonlinear partial differential equations that govern this phenomenon. The resulting semi-discrete equations are then integrated using the second-order Crank-Nicolson (CN) method. We conduct numerical simulations for a Péclet number ($Pe \leq 3000$) and a log-mobility ratio $0 \leq R \leq 7$, which reveal three distinct pattern formations: comet-shape, lump-shape, and viscous fingering instability. Our results demonstrate that the deformation, spreading, and mixing of the blob vary non-ideally with both $Pe$ and $R$, a behavior attributed to the blob's initial curvature. Consequently, enhanced mixing can be achieved at intermediate values of $Pe$ and $R$, suggesting the existence of an optimal mixing condition. These findings have significant implications for fields such as oil recovery, CO$_2$ sequestration, pollution remediation, and chromatography separation.

physics.flu-dyn↗

arXiv2025

Coherent Structure Dynamics of Heat Transfer in Wakes of an Inclined Elliptical Cylinder: A Novel Lagrangian Framework

This work introduces a novel Lagrangian-based framework to analyze forced convective heat transfer in the unsteady wake of a heated elliptical cylinder inclined at angles ranging from $θ= 0^\circ$ to $90^\circ$, in $15^\circ$ increments with $Pr = 0.71$ at a fixed Reynolds number of $Re = 100$. The framework correlates the temporal evolution of the surface-averaged Nusselt number with the dynamic behavior of Lagrangian saddle points, formed at the intersection of repelling and attracting Lagrangian Coherent Structures (LCSs) extracted via Finite-Time Lyapunov Exponent (FTLE) fields.The study is carried out within a precisely constructed observational domain, a previously unreported influential region in the near-wake, where the trajectory analysis of the newly defined key saddle points (active saddle points) consistently aligns with the trends in surface heat transfer. This domain enables predictive identification of key transitional events in the Nusselt number profile, including local extrema and slope inflections, across all inclination angles. The analysis reveals that oblique displacement of active saddle points enhances heat transfer by promoting the shedding of repelling LCSs, while parallel displacement leads to weakened heat transfer due to the delayed detachment of repelling coherent structures. The proposed framework enables the construction of a temporal function that closely replicates the monotonicity and transitional features of the Nusselt number evolution. Furthermore, threshold displacement metrics are defined for dominant repelling LCSs to correspond with peak heat transfer efficiency. The proposed methodology not only generalizes across a wide range of inclination angles but also provides a physically interpretable framework for predicting heat transfer enhancement based on coherent structure evolution in unsteady flows.

physics.flu-dyn↗

arXiv2023

Comprehensive study of forced convection over a heated elliptical cylinder with varying angle of incidences to uniform free stream

In this paper we carry out a numerical investigation of forced convection heat transfer from a heated elliptical cylinder in a uniform free stream with angle of inclination $θ^{\circ}$. Numerical simulations were carried out for $10 \leq Re \leq 120$, $0^{\circ} \leq θ\leq 180^{\circ}$, and $Pr = 0.71$. Results are reported for both steady and unsteady state regime in terms of streamlines, vorticity contours, isotherms, drag and lift coefficients, Strouhal number, and Nusselt number. In the process, we also propose a novel method of computing the Nusselt number by merely gathering flow information along the normal to the ellipse boundary. The critical $Re$ at which which flow becomes unsteady, $Re_c$ is reported for all the values of $θ$ considered and found to be the same for $θ$ and $180^\circ -θ$ for $0^\circ \leq θ\leq 90^\circ$. In the steady regime, the $Re$ at which flow separation occurs progressively decreases as $θ$ increases. The surface averaged Nusselt number ($Nu_{\text{av}}$) increases with $Re$, whereas the drag force experienced by the cylinder decreases with $Re$. The transient regime is characterized by periodic vortex shedding, which is quantified by the Strouhal number ($St$). Vortex shedding frequency increases with $Re$ and decreases with $θ$ for a given $Re$. $Nu_{\text{av}}$ also exhibits a time-varying oscillatory behaviour with a time period which is half the time period of vortex shedding. The amplitude of oscillation of $Nu_{\text{av}}$ increases with $θ$.

physics.flu-dyn↗

arXiv2017

HOC simulation of Moffatt eddies and its flow topology in the triangular cavity flow

In this work, we present HOC simulation of vortices in the triangular cavity for slow viscous incompressible flows by using a recently proposed new paradigm approach for solving Navier-Stokes (N-S) equations. These vortices qualify as Moffatt vortices which are characterized by the computation of common ratios of their sizes and intensities. We further explore topological structures of Moffatt eddies by using crtical point theory which is one of the key concept in the field of topological fluid dynamics.

physics.comp-ph↗

arXiv2017

Moffatt vortices: Concerns and Finiteness

Till date, the sequence of vortices present in the solid corners of steady internal viscous incompressible flows, widely known as Moffatt vortices was thought to be infinite. However, the already existing and most recent geometric theories on incompressible viscous flows that express vortical structures in terms of critical points in bounded domains, indicate a strong opposition to this notion of infiniteness. In this study, we endeavor to bridge the gap between the two opposing stream of thoughts by addressing what might have gone wrong and pinpoint the shortcomings on the assumptions of the existing theorems on Moffatt vortices. We provide our own set of proofs for establishing the finiteness of the sequence of Moffatt vortices by making use of the continuum hypothesis and Kolmogorov scale, which guarantee a non-zero scale for the smallest vortex structure possible in incompressible viscous flows. We point out that the notion of infiniteness resulting from discrete self-similarity of the vortex structures is not physically feasible. The centers of these vortices have been quantified by us as fixed points through Brouwer fixed-point theorem and boundary of a vortex as circle cell. With the aid of these new developments and making use of some existing theorems in topology along with some elementary concept of mathematical analysis, we provide several approaches to delve into this issue. All these approaches converge to the same conclusion that the sequence of Moffatt vortices cannot be infinite; in fact, it is at most finite.

physics.flu-dyn↗

arXiv2016

The Finiteness of vortices in steady incompressible viscous fluid flow

In this work, we provide two novel approaches to show that incompressible fluid flow in a finite domain contains at most a finite number vortices. We use a recently developed geometric theory of incompressible viscous flows along with an existing mathematical analysis concept to establish the finiteness. We also offer a second proof of finiteness by roping in the Kolmogorov's length scale criterion in conjunction with the notion of diametric disks.

physics.flu-dyn↗

arXiv2016

Moffatt vortices in the lid-driven cavity flow

In incompressible viscous flows in a confined domain, vortices are known to form at the corners and in the vicinity of separation points. The existence of a sequence of vortices (known as Moffatt vortices) at the corner with diminishing size and rapidly decreasing intensity has been indicated by physical experiments as well as mathematical asymptotics. In this work, we establish the existence of Moffatt vortices for the flow in the famous Lid-driven square cavity at moderate Reynolds numbers by using an efficient Navier-Stokes solver on non-uniform space grids. We establish that Moffatt vortices in succession follow fixed geometric ratios in size and intensities for a particular Reynolds number. In order to eliminate the possibility of spurious solutions, we confirm the physical presence of the small scales by pressure gradient computation along the walls.

physics.comp-ph↗