arXiv subjects

Bhimsen Shivamoggi

Publications and source records attributed to Bhimsen Shivamoggi.

10 recordsLinked to original sources

arXiv2026

On the Role of Chapman's Hydrostatic Solar Wind Mechanism in Parker's Hydrodynamic Solar Wind Model

The role of Chapman's hydrostatic solar wind mechanism (resulting from a hydrostatic force balance condition) in Parker's hydrodynamic solar wind model is investigated by invoking the de Laval nozzle analogy for the production of flow acceleration in the latter model. The action of solar gravity in Parker's hydrodynamic solar wind model is shown to be geometrically equivalent to a enormalization of the actual wind channel area and the renormalization factor is exactly Chapman's hydrostatic radial density profile, which is totally predicated on the hydrostatic force balance condition. This result appears to be traceable to the encapsulation of the solar gravity effects in Parker's hydrodynamic solar wind model by Chapman's hydrostatic solar wind mechanism, even beyond the coronal base. Furthermore, this result is shown to be robust by considering both isothermal gas and polytropic gas models as well as an n-dimensional (n= 1, 2, 3) underlying space for the solar wind.

astro-ph.SR↗

arXiv2025

Direct Interaction Approximation for generalized stochastic models in the turbulence problem

The purpose of this paper is to consider the application of the direct interaction approximation (DIA) developed by Kraichnan to generalized stochastic models in the turbulence problem. Previous developments were based on the Boltzmann-Gibbs prescription for the underlying entropy measure, which exhibits the extensivity property and is suited for ergodic systems. Here, we consider the introduction of an influence bias discriminating rare and frequent events explicitly, as it behooves non-ergodic systems, which is dealt with by a using a Tsallis type autocorrelation model with an underlying non-extensive entropy measure. As an example, we consider a linear damped stochastic oscillator system, and describe the resulting stochastic process. The non-perturbative aspects excluded by Keller's perturbative procedure are found to be minimized in the white-noise limit. In the opposite limit, the physical variances between the random process models don't seem to materialize, and the Uhlenbeck-Ornstein and Tsallis type models are found to yield the same result. In the process, we also deduce some apparently novel mathematical properties of the stochastic models associated with the present investigation -- the gamma distribution and the Tsallis non-extensive entropy.

math-ph↗

arXiv2024

An Exact Invariant for Relativistic Linear Harmonic Oscillator with Time-dependent Frequency

In this paper we give an exact invariant for a relativistic linear harmonic oscillator with time-dependent frequency. This is accomplished, following Eliezer and Gray \cite{EliezerGray}, for the non-relativistic case, by associating a relativistic plane isotropic harmonic oscillator with this problem. This exact invariant reflects the conservation of angular momentum of the associated relativistic plane isotropic oscillator. Departures in the physical interpretations of this exact invariant caused by relativistic effects are pointed out.

physics.class-ph↗

arXiv2022

Generalized Fractal Dimension for a Dissipative Multi-fractal Cascade Model for Fully Developed Turbulence

In this paper (Shivamoggi et al.), we explore a variant for the simple model based on a binomial multiplicative process of Meneveau and Sreenivasan that mimics the multi-fractal nature of the energy dissipation field in the inertial range of fully developed turbulence (FDT), and uses the generalized fractal dimension (GFD) prescription of Hentschel and Proccacia, Halsey et al. However, the presence of an even infinitesimal dissipation in the inertial range is shown to lead to a singularity in the GFD $D_q$ (at $q=1$) of the energy dissipation field and leads to a breakdown of the Meneveau-Sreenivasan binomial multiplicative formulation for a dissipative inertial cascade. The purpose of this paper is to demonstrate that this can be resolved by introducing a new appropriate ansatz for the definition of the GFD $D_q$ to incorporate the effect of a scale-invariant dissipation via a phenomenological dissipative parameter $K$ $( 0 < K < 1)$. This dissipation parameter is also shown to cause a steeper energy spectrum in the inertial range, as to be expected. This ansatz is then generalized to incorporate a more symmetric dissipation via two dissipative parameters $K_1,$ and $K_2$ $( 0 < K_1$ and $K_2 < 1)$

physics.flu-dyn↗

arXiv2021

Stability of Parker's Solar Wind Solution Near the Solar Surface

Stability of Parker's steady solar wind solution near the solar surface is systematically investigated by posing a Sturm-Liouville problem for this solution. Parker's solar wind solution, whether it turns into a breeze or a supersonic wind depending on the pressure in the interstellar medium, is shown to describe the solar wind to start in a stable way as it leaves the solar surface from a state of: rest, co-rotation with the Sun, slow motion. The isothermal gas flow assumption in Parker's solar wind model is then relaxed, and more realistic barotropic fluid and diabatic models are used for the gas flow. The stability of the solar wind flow, as it starts from a state of rest at the solar surface, is shown to continue to hold. Parker's solar wind solution therefore appears to be a stable attractor of this dynamical system.

physics.plasm-ph↗

arXiv2017

Superfluid Turbulence in the Kelvin Wave Cascade Regime

Theoretical considerations are made of superfluid turbulence in the Kelvin wave cascade regime at low temperatures (T < 1K) and length scales of the order or smaller than the intervortical distance. The energy spectrum is shown to be in accord with the Kolmogorov scaling. The vortex line decay equation is shown to have an underlying Hamiltonian framework. Effects of spatial intermittency (exhibited in laboratory experiments) on superfluid turbulence are incorporated via the fractal nature of the vortex lines, for length scales of the order or smaller than the intervortical distance. The spatial intermittency effects are shown to enhance the vortex line density L, for a given value of intervortex spacing L, and to provide for a mechanism commensurate with the enhanced depolarization of vortex lines. The spatial intermittency is found to steepen the energy spectrum in qualitative agreement with laboratory experiments and to enhance vortex line decay.

cond-mat.other↗

arXiv2015

A Generalized Brownian Motion Model for Turbulent Relative Particle Dispersion

In this paper, a generalized Brownian motion model has been applied to describe the relative particle dispersion problem in more realistic turbulent flows. The fluctuating pressure forces acting on a fluid particle are taken to be a colored noise and follow a stationary process and are described by the Uhlenbeck-Ornstein model while it appears plausible to take their correlation time to have a power-law dependence on the flow Reynolds number $R_e$, thus introducing a bridge between the Lagrangian quantities and the Eulerian parameters for this problem. This ansatz is in qualitative agreement with the possibility of a connection speculated earlier by Corrsin [26] between the white-noise representation for the fluctuating pressure forces and the large-$R_e$ assumption in the Kolmogorov [4] theory for the 3D fully developed turbulence (FDT) as well as the argument of Monin and Yaglom [23] and the result of Sawford [13] and Borgas and Sawford [24] that the Lagrangian acceleration is delta-function auto-correlated in the infinite-$R_e$ limit. It also provides an insight into the result that the Richardson-Obukhov scaling holds only in the infinite-$R_e$ limit and disappears otherwise. This ansatz further confirms the Lin-Reid [18] conjecture regarding the connection between the fluctuating pressure-force parameter and the energy dissipation rate in turbulence and leads to an $R_e$-dependent explicit relation between the two speculated by Lin and Reid [18]. More specifically, this ansatz provides a determination of the Richardson-Obukhov constant $g$ as a function of $R_e$, with an asymptotic constant value in the infinite-$R_e$ limit. It is shown to lead to full agreement, in the small-$R_e$ limit as well, with the Batchelor-Townsend [27] scaling for the rate of change of the mean square interparticle separation in 3D FDT, hence validating its soundness further.

physics.flu-dyn↗

arXiv2015

Turbulent Relative Particle Dispersion

In this paper, phenomenological developments are used to explore several aspects of the relative particle dispersion (RPD) in different physical fully-developed turbulence (FDT) situations. The role played by the FDT cascade physics underlying this process is investigated. Many of these aspects are motivated by previous laboratory experiment and numerical simulation results. These are, * spatial intermittency effects exhibiting, * [(a)] reduction of RPD in 3D FDT, corroborating the numerical simulation results (Boffetta and Sokolov [11]); *[(b)] prevalence of power-law scaling of RPD in 2D FDT enstrophy cascade (no matter how weak spatial intermittency effects are), corroborating the difficulty in observing Lin [12] exponentical scaling law in laboratory experiments (Jullien [13]); * quasi-geostrophic FDT aspects exhibiting an enhanced RPD in the baroclinic regime of the energy cascade and a negative eddy-viscosity development to shed some insight into this aspect; * quasi-geostrophic FDT aspects exhibiting particle clumping in the baroclinic regime of the enstrophy cascade; * reduction of RPD, development of the ballistic regime and particle clustering due to compressibility effects in FDT, corroborating the laboratory experiment and numerical simulation results (Cressman et al. [14]). These results are developed from the established scaling relations for the various physical FDT cases and are further validated via alternative dimensional/scaling developments for the various physical FDT cases similar to the one given for 3D FDT by Batchelor and Townsend [15].

physics.flu-dyn↗

arXiv2014

Electron Magnetohydrodynamic Turbulence: Universal Features

The energy cascade of electron magnetohydrodynamic (EMHD) turbulence is considered. Fractal and multi-fractal models for the energy dissipation field are used to determine the spatial intermittency corrections to the scaling behavior in the high-wavenumber (electron hydrodynamic limit) and low-wavenumber (magnetization limit) asymptotic regimes of the inertial range. Extrapolation of the multi-fractal scaling down to the dissipative microscales confirms in these asymptotic regimes a dissipative anomaly previously indicated by the numerical simulations of EMHD turbulence. Several basic features of the EMHD turbulent system are found to be universal which seem to transcend the existence of the characteristic length scale $d_e$ (which is the electron skin depth) in the EMHD problem---(i) equipartition spectrum, (ii) Reynolds-number scaling of the dissipative microscales, (iii) scaling of the probability distribution function (PDF) of the electron-flow velocity (or magnetic field) gradient (even with intermittency corrections), (iv) dissipative anomaly, (v) critical exponent scaling.

physics.plasm-ph↗

arXiv2007

Hall Magnetohydrodynamics with Electron Inertia

Hall magnetohydrodynamic (MHD) with electron inertia is considered. A much wider class of equilibrium solutions and the concomitant self-organization aspects are discussed. The force-free field state B - J is shown to be a consequence of the triple Beltrami condition.

physics.plasm-ph↗