Boundary layers of an anchored magnetic field in a highly conductive flow

2010 ◽  
Vol 466 (2123) ◽  
pp. 3153-3166 ◽  
Author(s):  
Manuel Núñez ◽  
Alberto Lastra
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Asymptotic Analysis ◽  
Small Parameter ◽  
Order Approximation ◽  
First Order ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
First Order Approximation ◽  
Distance To The Boundary

The effects of the flow of an electrically conducting fluid upon a magnetic field anchored at the boundary of a domain are studied. By taking the resistivity as a small parameter, the first-order approximation of an asymptotic analysis yields a boundary layer for the magnetic potential. This layer is analysed both in general and in three particular cases, showing that while in general its effects decrease exponentially with the distance to the boundary, several additional effects are highly relevant.

Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field

2021 ◽  
Vol 76 (3) ◽  
pp. 265-283
Author(s):  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Axial Magnetic Field ◽  
Order Approximation ◽  
Ideal Gas ◽  
Field Region ◽  
First Order ◽  
First Order Approximation ◽  
Flow Variables

Abstract The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.

scholarly journals On the justification of Gaussian heuristic method in the theory of random vibration

1979 ◽  
Vol 1 (3-4) ◽  
pp. 1-11
Author(s):  
Nguyen Cao Menh
Keyword(s):  
Small Parameter ◽  
Random Vibration ◽  
Order Approximation ◽  
Heuristic Method ◽  
Second Order ◽  
Input Process ◽  
Mean Values ◽  
First Order ◽  
Gaussian Input ◽  
First Order Approximation

Recently in the problems of random vibration, the heuristic method, in which output process is supposed to be Gaussian when Gaussian input process is given, is applied [1, 2]. This method is called the “Gaussian heuristic method”. This paper deals with the justification of “Gaussian heuristic method”, form that two following important conclusions are proved: - “Gaussian heuristic method” gives density function of probability with the first order approximation with respect to the small parameter ε. - Applying this method we get mean values and second order correlation functions in second order approximation with respect to the small parameter ε.

On the spin-up of an electrically conducting fluid Part 1. The unsteady hydromagnetic Ekman-Hartmann boundary-layer problem

1969 ◽  
Vol 39 (3) ◽  
pp. 561-586 ◽  
Author(s):  
Edward R. Benton ◽  
David E. Loper
Keyword(s):  
Boundary Layer ◽  
Axial Magnetic Field ◽  
Alfven Wave ◽  
Flat Plates ◽  
Initial Value ◽  
Boundary Layer Problem ◽  
First Order ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Layer Problem

The prototype spin-up problem between infinite flat plates treated by Greenspan & Howard (1963) is extended to include the presence of an imposed axial magnetic field. The fluid is homogeneous, viscous, and electrically conducting. The resulting boundary initial-value problem is solved to first order in Rossby number by Laplace transform techniques. In spite of the linearization the complete hydromagnetic interaction is preserved: currents affect the flow and the flow simultaneously distorts the field. In part 1, we analyze the impulsively started time dependent approach to a final steady Ekman–Hartmann boundary layer on a single insulating flat plate. The transient is found to consist of two diffusively growing boundary layers, inertial oscillations, and a weak Alfvén wave front. In part 2, these one plate results are utilized in discussing spin-up between two infinite flat insulating plates. Two distinct and important hydromagnetic spin-up mechanisms are elucidated. In all cases, the spin-up time is found to be shorter than in the corresponding non-magnetic problem.

Effect of a strong axial magnetic field on swirling flow in a cylindrical cavity with a top rotating lid

2019 ◽  
Vol 30 (11) ◽  
pp. 1950092
Author(s):  
Subas Chandra Dash ◽  
Navtej Singh
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Cylindrical Cavity ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Axial Magnetic Field ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Steady Magnetic Field ◽  
Flow Domain

Behavior of swirling flow in a cylindrical container with top rotating lid has been investigated under the influence of a strong axial magnetic field. The flow is assumed to be axisymmetric for the parameters considered in the study. The flow domain consists of a cylindrical cavity with a top rotating lid packed with viscous incompressible electrically conducting fluid, e.g. liquid metal. A steady magnetic field acts perpendicular to the bottom wall of the cavity. When the top rotating lid rotates an Ekman boundary layer develops in vicinity to the top rotating lid. However, the presence of a Hartmann boundary layer not only restrains the vortex breakdown but also shifts its position to some extent. All the walls of the cavity are assumed to be electrically insulated.

scholarly journals Boundary-layer analysis of a pile-up of walls of edge dislocations at a lock

2016 ◽  
Vol 26 (14) ◽  
pp. 2735-2768 ◽  
Author(s):  
Adriana Garroni ◽  
Patrick van Meurs ◽  
Mark A. Peletier ◽  
Lucia Scardia
Keyword(s):  
Boundary Layer ◽  
Order Approximation ◽  
Order Term ◽  
First Order ◽  
Layer Analysis ◽  
Pile Up ◽  
Constant Shear Stress ◽  
Energy Formula ◽  
First Order Approximation ◽  
Edge Dislocations

In this paper, we analyse the behaviour of a pile-up of vertically periodic walls of edge dislocations at an obstacle, represented by a locked dislocation wall. Starting from a continuum nonlocal energy [Formula: see text] modelling the interactions — at a typical length-scale of [Formula: see text] — of the walls subjected to a constant shear stress, we derive a first-order approximation of the energy [Formula: see text] in powers of [Formula: see text] by [Formula: see text]-convergence, in the limit [Formula: see text]. While the zeroth-order term in the expansion, the [Formula: see text]-limit of [Formula: see text], captures the “bulk” profile of the density of dislocation walls in the pile-up domain, the first-order term in the expansion is a “boundary-layer” energy that captures the profile of the density in the proximity of the lock. This study is a first step towards a rigorous understanding of the behaviour of dislocations at obstacles, defects, and grain boundaries.

Improved first-order approximation of eigenvalues and eigenvectors

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 1721-1727
Author(s):  
Prasanth B. Nair ◽  
Andrew J. Keane ◽  
Robin S. Langley
Keyword(s):  
Order Approximation ◽  
Eigenvalues And Eigenvectors ◽  
First Order ◽  
First Order Approximation

FIRST-ORDER APPROXIMATION OF THE NUMBER-PROJECTED SO(2N) TAMM-DANCOFF EQUATION AND ITS REDUCTION BY THE SCHUR FUNCTION

1999 ◽  
Vol 08 (05) ◽  
pp. 461-483
Author(s):  
SEIYA NISHIYAMA
Keyword(s):  
Wave Function ◽  
Order Approximation ◽  
Approximate Equation ◽  
Variation Principle ◽  
Schur Function ◽  
Soliton Theory ◽  
First Order ◽  
Fermion Systems ◽  
Group Manifold ◽  
First Order Approximation

First-order approximation of the number-projected (NP) SO(2N) Tamm-Dancoff (TD) equation is developed to describe ground and excited states of superconducting fermion systems. We start from an NP Hartree-Bogoliubov (HB) wave function. The NP SO(2N) TD expansion is generated by quasi-particle pair excitations from the degenerate geminals in the number-projected HB wave function. The Schrödinger equation is cast into the NP SO(2N) TD equation by the variation principle. We approximate it up to first order. This approximate equation is reduced to a simpler form by the Schur function of group characters which has a close connection with the soliton theory on the group manifold.

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