arXiv subjects

Vinod Narayanan

Publications and source records attributed to Vinod Narayanan.

4 recordsLinked to original sources

arXiv2025

Rethinking Pipe Flow Stability: Insights from a Meshless Global Analysis

Despite extensive experimental evidence of turbulence in Hagen Poiseuille flow, linear stability analysis has not yet confirmed its instability. One challenge is the singularity introduced by the term 1/r in the center of the pipe, which complicates traditional stability approaches. In this study, we explore a global stability analysis using a meshless framework. Although this approach did not recover the expected unstable modes, it revealed a new set of modes with distinct characteristics from those observed in local stability analysis. We analyze these modes and their impact on transient energy growth, demonstrating the effectiveness of the global approach in capturing localized instabilities without requiring multiple simulations.

physics.flu-dyn↗

arXiv2024

Bifurcation in narrow gap spherical Couette flow

Incompressible Navier-Stokes equations in the spherical coordinates are solved using a pseudo-spectral method to simulate the problem of spherical Couette flow. The flow is investigated for a narrow gap ratio with only the inner sphere rotating. We find that the flow is sensitive to the initial conditions and have used various initial conditions to obtain di!erent branches of the bifurcation curve of the flow. We have identified three di!erent branches dominated respectively by axisymmetric flow, traveling wave instability, and equatorial instability. The axisymmetric branch shows unsteadiness at large Reynolds numbers. The traveling wave instability branch shows spiral instability and is prominent near poles. The traveling wave instability branch further exhibits a reversal in the propagation direction of the spiral instability as the Reynolds number is increased. This branch also exhibits a multi-mode equatorial instability at larger Reynolds numbers. The equatorial instability branch exhibits twin jet streams on either side of the equator, which becomes unstable at larger Reynolds numbers. The flow topology on the three branches are also investigated in their phase space and the found to exhibit a chaotic behavior at large Reynolds numbers on the traveling wave instability branch.

physics.flu-dyn↗

arXiv2024

High-order meshless global stability analysis of Taylor-Couette flows in complex domains

Recently, meshless methods have become popular in numerically solving partial differential equations and have been employed to solve equations governing fluid flows, heat transfer, and species transport. In the present study, a numerical solver is developed employing the meshless framework to efficiently compute the hydrodynamic stability of fluid flows in complex geometries. The developed method is tested on two cases of Taylor-Couette flows. The concentric case represents the parallel flow assumption incorporated in the Orr-Sommerfeld model and the eccentric Taylor-Couette flow incorporates a non-parallel base flow with separation bubbles. The method was validated against earlier works by Marcus [1], Oikawa et al. [2], Leclercq et al. [3], and Mittal et al. [4]. The results for the two cases and the effectiveness of the method are discussed in detail. The method is then applied to Taylor-Couette flow in an elliptical enclosure and the stability of the flow is investigated.

physics.flu-dyn↗

arXiv2022

Shear-Driven Flow in an Elliptical Enclosure Generated by an Inner Rotating Circular Cylinder

Shear-driven flow between a rotating cylinder and a stationary elliptical enclosure is studied in this paper. Two-dimensional time-dependent Navier Stokes equations are solved using a meshless method where interpolations are done with Polyharmonic Spline Radial Basis Functions. The fluid flow is analyzed for various aspect ratios of the ellipse and eccentric placements of the inner cylinder. Contour plots of vorticity with streamlines, plots of non-dimensional torque, and the angle of eye of the primary vortex are presented in the paper for Reynolds numbers between 200 and 2000. Formation of Moffatt like vortices in the wide-gap region of the model is observed and some benchmark data are provided for various cases that are simulated.

physics.flu-dyn↗