Quasilongitudinal propagation of narrow beams of nonlinear magnetohydrodynamic waves

An equation, analogous to the Khokhlov-Zabolotskaya equation, is derived for narrow beams of quasitransverse waves propagating at small angles to a magnetic field. The effect of diffraction on wave propagation is investigated in the linear approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 21–28, July–August, 1986.     

Certain three-dimensional flows with Mach interaction of shock waves

In [1, 2] it is shown that there is a range of values of the Mach number and geometric parameters for which flow past conical bodies is realized with plane attached shocks and regular intersection of the shocks in space. In the present article we determine the class of solutions corresponding to flow past conical star-shaped bodies with a configuration of the shocks in space of the Mach type.     

Instability of helical magnetohydrodynamic flows

The problem of the linear stability of a single particular class of helical steady-state flows of an ideal incompressible infinitely-conducting fluid in a magnetic field is studied. A necessary and sufficient condition of stability of this class of flows with respect to perturbations of the same symmetry type is obtained by the direct Lyapunov method [1, 2]. A priori two-sided exponential estimates of the perturbation growth are derived, the corresponding exponents being calculated using the steady flow parameters and the initial data for the perturbations. A class of the most rapidly growing perturbations is identified and an exact formula for determining their growth rate is obtained. An example of steady-state flows and initial perturbations whose linear stage of development with time can be described by means of the estimates obtained is constructed. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 150–156, January–February, 1999. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-01771).     

Generation and propagation of pressure waves in supersonic deep-cavity flows

The mechanism behind cavity-induced pressure oscillations in supersonic flows past a deep rectangular cavity is not well understood despite several investigations having been carried out. In particular, the process by which the pressure wave is generated and the path of the pressure wave propagating inside the cavity remains unclear. In the present study, the pressure waves around a deep rectangular cavity over which nitrogen gas flows at a Mach number of 1.7 are visualized using the schlieren method. The length of the cavity is 14.0?mm. The depths of the cavity are selected as 20.0?and 11.7?mm, corresponding to length-to-depth ratios of 0.70 and 1.2, respectively. The pressure waves propagating inside as well as outside the cavity have been successfully visualized using a high-speed camera, and the propagation pattern of these waves is found to be different from that previously predicted by numerical simulation and from those expected in previous oscillation models. In addition, the pressure oscillation near the trailing edge of the cavity is also measured using semiconductor-type pressure transducers simultaneously with the capture of the schlieren images. As a result, the relationship between the shear-layer motion, pressure-wave generation, and pressure oscillation at the trailing edge of the cavity is clarified experimentally.     

Uniformization of the density in reacting magnetohydrodynamic flows

Ionization and recombination provide a transfer between species in a partially ionized plasma. These phenomena modify the continuity equation for each species by linking them together in a common system. The consequences are specially clear when the velocities of ions and neutrals coincide and the flow is weakly compressible: the densities along each trajectory tend to a definite limit depending only on the initial total density and not on the ion/neutral rate. For the general case a weaker global estimate on the final rate between species may be proved.     

On the existence of intermediate magnetohydrodynamic shock waves

We consider the questions related to the structure of shock waves for a system of magnetohydrodynamic equations. Using Conley's connection matrix, we recover and extend earlier results due to C. Conley and J. Smoller. In particular, we give a simpler proof of the existence of fast and slow shocks with structure. We also demonstrate that for some viscosity parameters intermediate shocks occur. Furthermore, under an assumption of transversality, we show that there exist multi-parameter families of these intermediate shocks.This research was done while both authors were visiting the Lefschetz Center for Dynamical Systems at Brown University.Supported in part by the NSF under Grant DMS-8507056.Supported in part by AFOSR 87-0347.     

On the origin of super-rotating layers in magnetohydrodynamic flows

An asymptotic analysis has been performed for the magnetohydrodynamic flow between perfectly conducting concentric cylindrical shells. The flow in the model geometry exhibits all the features which had been discovered in the past for the case of differentially rotating spherical shells considered in the context of geophysical analyses. For strong magnetic fields, the flow domain splits into distinct subregions and exhibits two different types of cores which are separated from each other by a tangent shear layer. The fluid in the inner core flows similar to a solid-body rotation and the outer core is entirely stagnant. With increasing magnetic fields the shear layer becomes thinner and, since the flow rate carried by the layer asymptotes to a finite value, the velocity in the layer increases as the layer thickness decreases. Moreover, the flux carried by the layer rotates in opposite direction compared with the rotation of the body. It is shown that the rotating jet is driven by the electric potential difference between the edges of the inner and the outer core.     

An extensive numerical benchmark of the various magnetohydrodynamic flows

There is a continuous need for an updated series of numerical benchmarks dealing with various aspects of the magnetohydrodynamics (MHD) phenomena (i.e. interactions of the flow of an electrically conducting fluid and an externally imposed magnetic field). The focus of the present study is numerical magnetohydrodynamics (MHD) where we have performed an extensive series of simulations for generic configurations, including: (i) a laminar conjugate MHD flow in a duct with varied electrical conductivity of the walls, (ii) a back-step flow, (iii) a multiphase cavity flow, (iv) a rising bubble in liquid metal and (v) a turbulent conjugate MHD flow in a duct with varied electrical conductivity of surrounding walls. All considered benchmark situations are for the one-way coupled MHD approach, where the induced magnetic field is negligible. The governing equations describing the one-way coupled MHD phenomena are numerically implemented in the open-source code OpenFOAM. The novel elements of the numerical algorithm include fully-conservative forms of the discretized Lorentz force in the momentum equation and divergence-free current density, the conjugate MHD (coupling of the wall/fluid domains), the multi-phase MHD, and, finally, the MHD turbulence. The multi-phase phenomena are simulated with the Volume of Fluid (VOF) approach, whereas the MHD turbulence is simulated with the dynamic Large-Eddy Simulation (LES) method. For all considered benchmark cases, a very good agreement is obtained with available analytical solutions and other numerical results in the literature. The presented extensive numerical benchmarks are expected to be potentially useful for developers of the numerical codes used to simulate various types of the complex MHD phenomena.     

Some solutions for steady linearised magnetohydrodynamic flows

Summary It is shown that the solution for the linearised magnetohydrodynamic equations of steady flow may be generated in terms of two independent scalar functions. The two cases of the unperturbed magnetic and velocity vectors parallel and perpendicular are considered. The analysis is applied to the case of steady flow past a wavy wall.     

Certain yawed magnetogasdynamic flows

Certain steady yawed magnetogasdynamic flows, in which the magnetic field is everywhere parallel to the velocity field, are related to certain reduced three-dimensional compressible gas flows having zero magnetic field. Under a restriction, the reduced flows are linked, by certain reciprocal relations, to a four parameter class of plane gas flows. In the instance of constant entropy an approximation method is suggested for obtaining magnetogasdynamic flows from the corresponding plane, irrotational gasdynamic flows and examples are given.

Nomenclature

magnetogasdynamic flow variables H magnetic intensity - q fluid velocity - fluid density - p pressure - s entropy - Q _t, H _t component of q, H in the x–y plane - w , h component of q, H perpendicular to the x–y plane reduced gasdynamic flow factor of proportionality - q* fluid velocity - * fluid density - p* pressure - Q _t ^* =u*î+v*, w* components of q* - l arbitrary constant - A _v Alfvén speed - Q _t, , p fluid velocity, density, pressure of the reciprocal gas dynamic flow - L, n, k, arbitrary constants - , velocity potential, stream function - angle made by Q _t, Q _t ^* , and V with the x-axis - adiabatic gas constant - a ²=(–1)/2 constant - M Mach number - W constant value of w* - E approximate constant value of g(p) - * modified potential function - modified velocity coordinate - +i - complex potential of the irrotational flow - B arbitrary constant - V incompressible flow velocity - V modified fluid velocity - X _p, Y _p points on the profile     

Certain nonisothermal flows of fluid

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 83–92, May–June, 1990.     

Effect of viscosity on the propagation of nonlinear Alfvén waves along a tangential magnetohydrodynamic discontinuity in an incompressible fluid

It is proposed to consider the propagation of surface waves along a tangential magnetohydrodynamic discontinuity in the particular case where the fluid velocities on both sides of the interface are equal to zero. In [1] it was shown that waves called surface Alfvén waves may be propagated along the surface separating a semi-infinite region without a field from a region with a uniform magnetic field. The linear theory of surface Alfvén waves in a compressible medium was considered in [2]. In [3] the damping of surface Alfvén waves as a result of viscosity and heat conduction was investigated. The propagation of low-amplitude nonlinear surface Alfvén waves in an incompressible fluid in the absence of dissipative processes is described by the integrodifferential equation obtained in [4]. By means of a numerical solution of this equation it was shown that a perturbation initially in the form of a sinusoidal wave will break. The breaking time was determined. In this paper the equation derived in [4] is extended to the case of a viscous fluid. It is shown that the equation obtained does not have steady-state solutions. The propagation of periodic disturbances is investigated numerically. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 94–104, November–December, 1986. The author wishes to thank L. S. Fedorov for assisting with the calculations.     

Certain reducible helical hydromagnetic flows

Summary Intrinsic formulations are obtained of the equations governing three-dimensional steady flows of an inviscid magnetic fluid with infinite electrical conductivity both when the streamlines of the magnetic field H and the fluid velocity v everywhere have the same unit tangent, and when H lies in the normal plane to the fluid streamlines at every point, so that v×H=0 and v·H=0 respectively. Using these intrinsic equations certain results concerning hydromagnetic helical flows are derived, and particular classes of such flows are reduced (in the sense of Power and Walker¹)) to associated non-magnetic two-dimensional flows. Finally, reciprocal relations are used to link classes of hydromagnetic helical flows to four-parameter classes of ordinary fluid flows.     

Features of internal and external flows in high-speed vehicles with a magnetohydrodynamic air-intake

The features of the internal and external flows in high-speed vehicles with a magnetohydrodynamic air-intake ensuring additional deceleration of the supersonic flow are considered. Preliminary investigations carried out earlier showed that this MHD flow control makes it possible significantly to increase the gasdynamic component of the vehicle thrust. However, there are significant negative effects, mainly the development of an additional vehicle drag force associated with the magnetic field. Thus, there arises a complex of interrelated problems with opposite effects on the resulting characteristics of the vehicle. In the present study these questions are investigated both on the basis of developed physicomathematical models and numerical methods and by means of the combined optimization of the internal duct profile and the external configuration of the vehicle. It is shown that a strategy for improving the vehicle characteristics can only be chosen by simultaneously analyzing the features of the internal (magnetohydrodynamic) and external (gasdynamic) flows.     

Class of two-dimensional nonstationary flows with shock waves

A numerical investigation was made of a two-dimensional plane-parallel nonsteady motion resulting from the decay of an arbitrary discontinuity on the boundaries of several neighboring angular regions filled by gases in different states.