arXiv subjects

Vikash Pandey

Publications and source records attributed to Vikash Pandey.

22 records · Page 2Linked to original sources

arXiv2019

Clustering and energy spectra in two-dimensional dusty gas turbulence

We present Direct Numerical Simulation (DNS) of heavy inertial particles (dust) immersed in two-dimensional turbulent flow (gas). The dust are modeled as mono-dispersed heavy particles capable of modifying the flow through two-way coupling. By varying the Stokes number (St) and the mass-loading parameter $(ϕ_{\rm m})$, we study the clustering phenomenon and the gas phase kinetic energy spectra. We find that the dust-dust correlation dimension $(d_2)$ also depends on $ϕ_{\rm m}$. In particular, clustering decreases as mass-loading $(ϕ_{\rm m})$, is increased. In the kinetic energy spectra of gas we show: (i) emergence of a new scaling regime, (ii) the scaling exponent in this regime is not unique but rather a function of both St and $(ϕ_{\rm m} )$. Using a scale-by-scale enstrophy budget analysis we show in the new scaling regime, viscous dissipation due to the gas balances back-reaction from the dust.

physics.flu-dyn↗

arXiv2016

Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations

The characteristic time-dependent viscosity of the intergranular pore-fluid in Buckingham's grain-shearing (GS) model [Buckingham, J. Acoust. Soc. Am. 108, 2796-2815 (2000)] is identified as the property of rheopecty. The property corresponds to a rare type of a non-Newtonian fluid in rheology which has largely remained unexplored. The material impulse response function from the GS model is found to be similar to the power-law memory kernel which is inherent in the framework of fractional calculus. The compressional wave equation and the shear wave equation derived from the GS model are shown to take the form of the Kelvin-Voigt fractional-derivative wave equation and the fractional diffusion-wave equation respectively. Therefore, an analogy is drawn between the dispersion relations obtained from the fractional framework and those from the GS model to establish the equivalence of the respective wave equations. Further, a physical interpretation of the characteristic fractional order present in the wave equations is inferred from the GS model. The overall goal is to show that fractional calculus is not just a mathematical framework which can be used to curve-fit the complex behavior of materials. Rather, it can also be derived from real physical processes as illustrated in this work by the example of grain-shearing.

cond-mat.soft↗

arXiv2016

Spatial dispersion of elastic waves in a bar characterized by tempered nonlocal elasticity

We apply the framework of tempered fractional calculus to investigate the spatial dispersion of elastic waves in a one-dimensional elastic bar characterized by range-dependent nonlocal interactions. The measure of the interaction is given by the attenuation kernel present in the constitutive stress-strain relation of the bar, which follows from the Kröner-Eringen's model of nonlocal elasticity. We employ a fractional power-law attenuation kernel and spatially temper it, to make the model physically valid and mathematically consistent. The spatial dispersion relation is derived, but it turns out to be difficult to solve, both analytically and numerically. Consequently, we use numerical techniques to extract the real and imaginary parts of the complex wavenumber for a wide range of frequency values. From the dispersion plots, it is found that the phase velocity dispersion of elastic waves in the tempered nonlocal elastic bar is similar to that from the time-fractional Zener model. Further, we also examine the unusual attenuation pattern obtained for the elastic wave propagation in the bar.

cond-mat.mtrl-sci↗

arXiv2015

Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional calculus

An analogy is drawn between the diffusion-wave equations derived from the fractional Kelvin-Voigt model and those obtained from Buckingham's grain-shearing (GS) model [J. Acoust. Soc. Am. 108, 2796-2815 (2000)] of wave propagation in saturated, unconsolidated granular materials. The material impulse response function from the GS model is found to be similar to the power-law memory kernel which is inherent in the framework of fractional calculus. The compressional wave equation and shear wave equation derived from the GS model turn out to be the Kelvin-Voigt fractional-derivative wave equation and the fractional diffusion-wave equation respectively. Also, a physical interpretation of the characteristic fractional-order present in the Kelvin-Voigt fractional derivative wave equation and time-fractional diffusion-wave equation is inferred from the GS model. The shear wave equation from the GS model predicts both diffusion and wave propagation in the fractional framework. The overall goal is intended to show that fractional calculus is not just a mathematical framework which can be used to curve-fit the complex behavior of materials, but rather it can be justified from real physical process of grain-shearing as well.

physics.geo-ph↗