Hydromagnetic rotating flow of a fourth‐order fluid past a porous plate

The rotating flow in the presence of a magnetic field is a problem belonging to hydromagnetics and deserves to be more widely studied than it has been to date. In the non‐linear regime the literature is scarce. We develop the governing equations for the unsteady hydromagnetic rotating flow of a fourth‐order fluid past a porous plate. The steady flow is governed by a boundary value problem in which the order of differential equations is more than the number of available boundary conditions. It is shown that by augmenting the boundary conditions based on asymptotic structures at infinity it is possible to obtain numerical solutions of the nonlinear hydromagnetic equations. Effects of uniform suction or blowing past the porous plate, exerted magnetic field and rotation on the flow phenomena, especially on the boundary layer structure near the plate, are numerically analysed and discussed. The flow behaviours of the Newtonian fluid and second‐, third‐ and fourth‐order non‐Newtonian fluids are compared for the special flow problem, respectively. Copyright © 2004 John Wiley & Sons, Ltd.     

Generic structure of externally driven tearing modes instabilities

A major limit to steady state and advanced high operation of tokamaks of reactor class is due to the onset of tearing modes that develop magnetic and may cause loss of energy confinement or a major disruption. Here the structure of a classical problem about the effects of external control helical fields is analysed and it is shown to offer a general paradigm of response of low order classical and neoclassical tearing modes to a wide class of external perturbations. New results of principle on the structural stability of the response model are obtained, leading to a clear interpretation of the role of “seed islands" in the onset of neo-classical tearing modes and the role of finite ion larmor radius corrections to Ohm's law. Received 12 November 2001 and Received in final form 4 January 2002     

Auto-solitary solutions in a generalized model of gas discharge contraction

Stable auto-solitary solutions were found on the basis of three-dimensional numerical simulations within the simplest model under global constraint. The model involves a diffusion equation with a nonlinear source term containing both local and non-local nonlinearity. The source term was chosen so as to describe qualitatively the most fundamental peculiarities of discharge physics, namely local nonlinear increase in heating and ionization rate and non-local attenuation of electric field strength with plasma density growth. The properties of the autosolitons created by the model have been investigated employing the different parameters as control parameter. Therefore the results of calculations can be used to construct a process of plasma contraction in gas discharge. Received 26 July 1999 and Received in final form 5 February 2000     

Hydromagnetic stability of plane Couette flow of an upper convected Maxwell fluid

Hydrodynamic stability of plane Couette flow of an upper convectedMaxwell fluid is investigated in presence of a transverse magneticfield assuming that the magnetic Prandtl number is sufficientlysmall. The resulting equation is a modified Orr–Sommerfeldequation. The equations of stability are solved numericallyusing Chebyshev collocation method with QZ algorithm. The criticalvalues of Reynolds number, wave number and wave speed are computedand the results are shown through the neutral curves. By increasingthe amount of elasticity to a certain value, it is shown that,as the Hartmann number increases, the minimum critical Reynoldsnumber decreases and it does not increase again in contrastto the Newtonian case.     

Unsteady hydromagnetic motion of a rotating conducting fluid

The combined effects of stratification and magnetic field on the unsteady motion of a viscous, electrically conducting fluid between two rotating disks are analysed. Solutions are obtained for the linearized equations under Boussinesq approximation and steady state solutions are deduced from them. The results are compared with those obtained by Loper and Benton and Balanet al. Graphs are presented for the steady state velocity, magnetic field and temperature distributions.     

Hydromagnetic oscillatory Couette flow in rotating system with induced magnetic field

This paper presents a study of hydromagnetic Couette flow of an incompress- ible and electrically conducting fluid between two parallel rotating plates, one of which is oscillating in its own plane. A uniform transverse magnetic field is used, and the induced magnetic field is taken into account. The exact solution to the governing equations is obtained in a closed form. The solution to the problem in the case of vanishing and small finite magnetic Prandtl numbers is also derived from the general solution. The asymp- totic behavior of the solution for large values of the frequency parameter is analyzed to gain some physical insights into the flow pattern. Expressions for the shear stress at both the oscillatory and stationary plates due to primary and secondary flows and mass flow rate in the primary and secondary flow directions are also obtained. The results of the fluid velocity and the induced magnetic field are presented. The shear stresses on the plates due to the primary and secondary flows and the corresponding mass flow rates are presented in a tabular form.     

The influence of mode coupling on the non-linear evolution of tearing modes

On the basis of tearing mode theory a simple but physically explicit model of the evolution of toroidally coupled rotating magnetic islands has been developed. The basic mechanism identified by the model in the island evolution is the locking in phase of rotating islands that leads to rapid destabilisation of an initially stable mode. Destabilisation of marginally stable (2, 1) and (3, 1) modes is analysed in several scenarios. It is shown that mode coupling is an effective way of destabilising a m=3 island in a low- plasma. The numerical examples presented show the individual roles of coupling, inertia and a resistive wall. The model was applied for the analysis of MHD observations of an ASDEX discharge. Received 4 May 1999 and Received in final form 23 July 1999     

Unsteady hydromagnetic Couette flow through a porous medium in a rotating system

This paper investigates the unsteady hydromagnetic Couette fluid flow through a porous medium between two infinite horizontal plates induced by the non-torsional oscillations of one of the plates in a rotating system using boundary layer approximation. The fluid is assumed to be Newtonian and incompressible. Laplace transform technique is adopted to obtain a unified solution of the velocity fields. Such a flow model is of great interest, not only for its theoretical significance, but also for its wide applications to geophysics and engineering. Analytical expressions for the steady state velocity and shear stress on the plates are obtained, and the case of single oscillating plate is also discussed. The influence of pertinent parameters on the flow is delineated, and appropriate conclusions are drawn.     

Effects of the anomalous temperature dependence of water density on surface gravity current

This paper reports experimental results on the propagation of a plane water jet at a temperature above the maximum-density temperature (4° C) along the free surface of initially quiescent water at a temperature of about 0°C. For comparison, experiments were performed in which the temperatures of the lower and higher layers were more than 4°C, other conditions being equal. The experiments revealed a number of new hydrodynamic effects, including peculiar flow instability and a fine structure of the density field at large times.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 63–69, January–February, 2005