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

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

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.Comment: 10 page

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

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

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

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

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

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

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