arXiv subjects

B. K. Shivamoggi

Publications and source records attributed to B. K. Shivamoggi.

At least 19 recordsLinked to original sources

arXiv2024

Polytropic Gas Effects in Parker's Solar Wind Model and Coronal Hole Flows

A detailed and systematic investigation of polytropic gas effects in Parker's solar wind model and coronal-hole flows is given. We present a viable equation governing the acceleration of solar wind of a polytropic gas and give its exact analytical and numerical solutions and deduce its asymptotic analytic properties (i) near the sun, (ii) far away from the sun, (iii) near the Parker sonic critical point (where the wind speed is equal to the speed of sound in the wind). We proceed to give a detailed and systematic investigation of coronal-hole polytropic gas outflows which contribute to bulk of the solar wind. We will model coronal-hole outflow by considering a single radial stream tube and invoke phenomenological considerations to represent its rapidly-diverging flow geometry. We give analytical and numerical solutions for this outflow and deduce its asymptotic analytic properties in the three flow regimes above. We find that, in general, the polytropic effects cause the Parker sonic critical point to move closer to the sun than that for the case with isothermal gas. Furthermore, the flow acceleration is found to exhibit (even for an infinitesimal deviation from isothermality of the gas) a power-law behavior rather than an exponential-law behavior near the sun or a logarithmic-law behavior far away from the sun, thus implying a certain robustness of the power-law behavior. The Parker sonic critical point is shown to continue to be of X-type, hence facilitating a smooth transition from subsonic to supersonic wind flow through the transonic regime. Our analytical and numerical solutions for coronal-hole outflows show that the super-radiality of the stream tube causes the Parker sonic critical point to move further down in the corona, and the gas to become more diabatic (the polytropic exponent $γ$ drops further below 5/3), and the flow acceleration to be enhanced further.

astro-ph.SR↗

arXiv2020

Parker's Stellar Wind Model for Polytropic Gas Flows

Parker's hydrodynamic stellar wind model is extended to polytropic gas flows. A compatible theoretical formulation is given and detailed numerical and systematic asymptotic theoretical considerations are presented. The polytropic conditions are shown to lead to tenuous and faster wind flows and hence enable the stars to lose their angular momentum more quickly.

astro-ph.SR↗

arXiv2019

Exact Solutions for the Fluid Impulse for Incompressible and Compressible Flows

Impulse formulations of the Euler (and Navier-Stokes) equations were considered by Kuz'min [1] and Oseledets [2] and different impulse formulations are produced by various gauge transformations (Russo and Smereka[3]). The extension of the Kuz'min-Oseledets formulation to the compressible, barotropic case was considered by Tur and Yanovsky [4] and Shivamoggi [5]. Here, we construct exact solutions for the fluid impulse density for incompressible and compressible barotropic flows and discuss their physical signifcance.

physics.flu-dyn↗

arXiv2018

Topological Implications of the Total Generalized Electron-Flow Magnetic Helicity Invariant in Electron Magnetohydrodynamics

Topological implications of the total generalized electron-flow magnetic helicity He in electron magnetohydrodynamics(EMHD) are explored. The invariance of He is shown to imply the invariance of the sum of the linkage of the magnetic field lines, the linkage of electron-flow vorticity field lines and the mutual linkage among these two sets of field lines. This result appears to support a change in the magnetic field topology and hence pave the way for magnetic reconnection in EMHD via a change in the concomitant electron-flow vorticity topology.

physics.plasm-ph↗

arXiv2018

Effects of Stellar Rotation in Parker's Hydrodynamic Stellar Wind Model: How Protostars and Strong Rotators Lose their Angular Momentum Fast

The effects of the stellar rotation and the consequent azimuthal stellar wind flow in Parker's [9] hydrodynamic stellar wind model are discussed. Of special interest is the emergence of a whole new hydrodynamic physics via a new critical point in the stellar wind flow, which supersedes the critical point in Parker's [9] hydrodynamic model. The effect of the stellar rotation is shown to cause the new critical point to occur lower in the corona, so the stellar wind experiences a stronger afterburner (as in an aircraft jet engine) action in the corona. For strong rotators, the new critical point is shown to occur at a fixed location for a given star, determined only by the basic stellar parameters like the mass M and the angular velocity, the variations in the stellar wind environment notwithstanding. The stellar rotation leads to stronger density fall-off and enhanced acceleration of the stellar wind at large distances from the star - this effect materializes even close to the star, for strong rotators. The stellar rotation causes the physical throat section of the effective de Laval nozzle associated with the stellar wind flow to become narrower, indicative of an enhanced flow acceleration. Thus, the stellar rotation leads to tenuous and faster stellar wind flows without change in the mass flux, and hence provides an efficient physical mechanism for protostars and strong rotators to lose their angular momentum quickly.

physics.plasm-ph↗

arXiv2017

Resonant Mode Conversion of the Second Sound to the First Sound in Liquid Helium II

The experimentally observed disappearance below T = 0.5K of the second sound in liquid He II as a separate wave mode and its subsequent propagation at the speed of the first sound (Peshkov [3]) may be interpreted as a resonant mode conversion of the second sound to the first sound. Near the resonant mode coupling point T = T*, where the frequencies of the two waves become equal, the anomalous effect of entropy changes on the first sound and density changes on the second sound, though generally small, become significant. This leads to the resonant mode coupling of the first sound and the second sound and forces them to lose their identities and hence pave the way for the resonant mode conversion of the second sound to the first sound. We give a theoretical framework for this proposition and an estimate for the fraction of the second sound that is mode-converted to the first sound.

cond-mat.other↗

arXiv2017

Direct Interaction Approximation for Non-Markovianized Stochastic Models in the Turbulence Problem

The purpose of this paper is to explore mathematical aspects associated with the application of the direct interaction approximation (DIA) (Kraichnan [1],[2]) to the non-Markovianized stochastic models in the turbulence problem. This process is shown to lead to a functional equation, and construction of solutions of this equation is addressed within the framework of a continued fraction representation. The relation of the DIA solution to the perturbative solution is discussed. The DIA procedure is applied to the problem of wave propagation in a random medium, which is described by a stochastic differential equation, with the characteristics of the medium represented by stochastic coefficients. The results are compared with those given by the perturbative procedure.

math-ph↗

arXiv2017

Effect of Slipping Motion on the Hasimoto Soliton on a Vortex Filament in Self-Induced Motion: An Exact Solution

A vortex filament immersed in a non-ideal fluid, thanks to viscous diffusion, experiences a slipping motion with respect to the fluid. In recognition of this, in this paper, the effect of this slipping motion on the Hasimoto soliton propagating on a vortex filament is investigated, and an exact solution is given to describe this process. A strong slipping motion is shown to prevent the existence of the Hasimoto soliton. The critical slipping speed (above which the Hasimoto soliton fails to exist) is shown to be equal to the torsion.

physics.flu-dyn↗

arXiv2016

The Okubo-Weiss Criteria in Two-Dimensional Hydrodynamic and Magnetohydrodynamic Flows

The Okubo [2]-Weiss [3] criterion is recast by using the 2D hydrodynamic Beltrami condition (Shivamoggi et al.[13]) that approximates the slow flow-variation ansatz imposed in its derivation. This turns out to provide an interesting interpretation of the Okubo-Weiss criterion very logically in terms of the topological properties of the underlying vorticity manifold. These developments are then extended to 2D quasi-geostrophic flows (via the potential divorticity framework), magnetohydrodynamic flows and electron magnetohydrodynamic flows (via the generalized magnetic flux framework) and the Okubo-Weiss criteria for these cases are considered.

physics.flu-dyn↗

arXiv2016

Kelvin's Canonical Circulation Theorem in Hall Magnetohydrodynamics

The purpose of this paper is to show that, thanks to the restoration of the legitimate connection between the current density and the plasma flow velocity in Hall magnetohydrodynamics (MHD), Kelvin's Circulation Theorem becomes valid in Hall MHD. The ion-flow velocity in the usual circulation integral is now replaced by the canonical ion-flow velocity.

physics.plasm-ph↗

arXiv2016

Plasma Relaxation and Topological Aspects in Electronmagnetohydrodynamics

Parker's formulation of isotopological plasma relaxation process toward minimum magnetics energy states in magnetohydrodynamics (MHD) is extended to electron MHD (EMHD). The lower bound on magnetic energy in EMHD is determined by both the magnetic field and the electron vorticity field topologies, and is shown to be reduced further in EMHD by an amount proportional to the sum of total electron-flow kinetic energy and total electron-flow enstrophy. The EMHD Beltrami condition becomes equivalent to the potential vorticity conservation equation in two-dimensional (2D) hydrodynamics, and the torsion coefficient and turns out to be proportional to potential vorticity. The winding pattern of the magnetic field lines appears to evolve therefore in the same way as "potential vorticity" lines in 2D hydrodynamics.

physics.plasm-ph↗

arXiv2015

Beltrami States in 2D Electron Magnetohydrodynamics

In this paper, the Hamiltonian formulations along with the Poisson brackets for two-dimensional (2D) electron magnetohydrodynamics (EMHD) flows are developed. These formulations are used to deduce the Beltrami states for 2D EMHD flows. In the massless electron limit, the EMHD Beltrami states reduce to the force-free states, though there is no force-free Beltrami state in the general EMHD case.

physics.plasm-ph↗

arXiv2012

Plasma Relaxation and Topological Aspects in Hall Magnetohydrodynamics

Parker's formulation of isotopological plasma relaxation process in magnetohydrodynamics (MHD) is extended to Hall MHD. The torsion coefficient alpha in the Hall MHD Beltrami condition turns out now to be proportional to the "potential vorticity." The Hall MHD Beltrami condition becomes equivalent to the "potential vorticity" conservation equation in two-dimensional (2D) hydrodynamics if the Hall MHD Lagrange multiplier beta is taken to be proportional to the "potential vorticity" as well. The winding pattern of the magnetic field lines in Hall MHD then appears to evolve in the same way as "potential vorticity" lines in 2D hydrodynamics.

physics.plasm-ph↗

arXiv2010

Beltrami States for Plasma Dynamics Models

The various plasma models - incompressible magnetohydrodynamic (MHD) model, compressible MHD model, incompressible Hall MHD model, compressible Hall MHD model, electron MHD model, compressible Hall MHD with electron inertia model - notwithstanding the diversity of the underlying physics, are shown to exhibit some common features in the Beltrami states like certain robustness with respect to the plasma compressibility effects (albeit in the barotropy assumption) and the {\it Bernoulli} condition. The Beltrami states for these models are deduced by minimizing the appropriate total energy while keeping the appropriate total helicity constant. A Hamiltonian formulation framework is used to carry out these variational problems.

physics.plasm-ph↗

arXiv2010

Compressible Turbulence: Multi-fractal Scaling in the Transition to the Dissipative Regime

Multi-fractal scaling in the transition to the dissipative regime for fully-developed compressible turbulence is considered. The multi-fractal power law scaling behavior breaks down for very small length scales thanks to viscous effects. However, the effect of compressibility is found to extend the single-scaling multi-fractal regime further into the dissipative range. In the ultimate compressibility limit, thanks to the shock waves which are the appropriate dissipative structures, the single-scaling regime is found to extend indeed all the way into the full viscous regime. This result appears to be consistent with the physical fact that vortices stretch stronger in a compressible fluid hence postponing viscous intervention. The consequent generation of enhanced velocity gradients in a compressible fluid appears to provide an underlying physical basis for the previous results indicating that fully-developed compressible turbulence is effectively more dissipative than its incompressible counterpart.

physics.flu-dyn↗

arXiv2009

Motion of a Vortex Filament in the Local Induction Approximation: Reformulation of the Da Rios-Betchov Equations in the Extrinsic Filament Coordinate Space

In recognition of the highly non-trivial task of computation of the inverse Hasimoto transformation mapping the intrinsic geometric parameter space onto the extrinsic vortex filament coordinate space a reformulation of the Da Rios-Betchov equations in the latter space is given. The nonlinear localized vortex filament structure solution given by the present formulation is in detailed agreement with the Betchov-Hasimoto solution in the small-amplitude limit and is also in qualitative agreement with laboratory experiment observations of helical-twist solitary waves propagating on concentrated vortices in rotating fluids. The present formulation also provides for a discernible effect of the slipping motion of a vortex filament on the vortex evolution.

physics.flu-dyn↗

arXiv2009

Divorticity and Dihelicity In Two-Dimensional Hydrodynamics

A framework is developed based on the concepts of {\it divorticity} ${\textbf B}$($\equiv\nabla\times\bfo$, $\bfo$ being the vorticity) and $\textit{dihelicity} g \lp \equiv\bfv\cdot\textbf{B}\rp$ for discussing the theoretical structure underlying two-dimensional (2D) hydrodynamics. This formulation leads to the global and Lagrange invariants that could impose significant constraints on the evolution of divorticity lines in 2D hydrodynamics.

physics.flu-dyn↗

arXiv2008

Rayleigh-Taylor Instability in a Compressible Fluid

Rayleigh-Taylor instability in a compressible fluid is reconsidered. The density is allowed to vary with pressure under the barotropy assumption. For the case with equal speeds of sound in the two superposed fluids, in order to give a non-trivial compressibility correction to the Rayleigh-Taylor growth rate, the compressibility correction is calculated to $O(g^2/k^2a^4)$. To this order, compressibility effects are found to reduce the growth rate.

physics.flu-dyn↗