Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-23T07:27:44.369Z Has data issue: false hasContentIssue false
  • English
  • Français

Aligned-fields magnetogasdynamic wakes

Published online by Cambridge University Press:  28 March 2006

D. N. Fan
D. N. Fan
Affiliation:
Graduate School of Aerospace Engineering, Cornell University, Ithaca, New York
Get access Rights & Permissions [Opens in a new window]

Abstract

The effect of compressibility is included here in a study of wakes created in two-dimensional, steady, aligned-fields, magnetogasdynamic flow past obstacles. The gas is assumed to be viscous, resistive, and thermally conducting. With the Oseen type of approximation as well as the magnetogasdynamic boundary-layer approximation, a great simplification in the formulation of wakes results. The boundary-layer equations, although linearized, still retain the coupling between the velocity, the magnetic, and the temperature fields. The solution of the magnetogasdynamic wake, in general, is a superposition of three individual-wake components, each satisfying a diffusion type of equation. Only one of them is capable of extending upstream. Hence the wake picture is generally characterized by a conventional downstream wake with also the possibility of the existence of an upstream one.

To be sure, the general features of the magnetogasdynamic wakes in aligned-fields flows are similar to those of an incompressible fluid; however, the flow now, instead of just being subalfvénic, must be subcritical for the upstream wake to occur. That is, the flow condition corresponding to the occurrence of the upstream wake is such that the sum of the square of the Mach number M∞ and the square of the Alfvén number A∞ is less than unity. Evidently it is the mechanism of magneto-sonic-wave propagation that modifies the transition of wakes from the Alfvénic point A∞ = 1 (for an incompressible fluid) to the subcritical are $A^2_\infty + M^2_\infty = 1$ in the Taniuti-Resler diagram.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 20 , Issue 3 , November 1964 , pp. 433 - 445
Copyright
© 1964 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahlstrom, H. G. 1963 Experiments on the upstream wake in magneto-fluid dynamics. J. Fluid Mech., 15, 205–22.Google Scholar
Chester, W. 1961 The effect of a magnetic field on the flow of a conducting fluid past a body of revolution. J. Fluid Mech., 10, 459–65.Google Scholar
Clauser, F. H. 1963 Concept of field modes and the behavior of the magnetohydrodynamic field. Phys. Fluids, 6, 231–53.Google Scholar
Fan, D. N. 1963 Magnetogasdynamic flows with viscosity, resistance, and heat conduction. M. Aero E Thesis, Graduate School of Aerospace Engineering, Cornell University, Ithaca.
Glauert, M. B. 1963 Magnetohydrodynamic wakes. J. Fluid Mech., 15, 1–12.Google Scholar
Gourdine, M. C. 1960 On the role of viscosity and conductivity in magnetohydrodynamics. JPL Tech. Rep. No. 32-3 Calif. Inst. Technol.Google Scholar
Hasimoto, H. 1959 Viscous flow of a perfectly conducting fluid with a frozen magnetic field. Phys. Fluids, 2, 338.Google Scholar
Hasimoto, H. 1960 Magnetohydrodynamic wakes in a viscous conducting fluid. Rev. Mod. Phys., 32, 860–6.Google Scholar
Lary, E. C. 1962 A theory of thin airfoils and slender bodies in fluids of finite electrical conductivity with aligned fields. J. Fluid Mech., 12, 209–26.Google Scholar
Ludford, G. S. S., Singh, M. P. 1963 On the motion of a sphere through a conducting fluid in the presence of a magnetic field. Proc. Camb. Phil. Soc. 59, 625–35.Google Scholar
Pai, S. I. 1962 Magnetogasdynamics and Plasma Dynamics. Vienna: Springer-verlag.
Resler, E. L. & McCune, J. E. 1960 Some exact solutions in linearized magnetoaerodynamics for arbitrary magnetic Reynolds numbers. Rev. Mod. Phys. 32, 848–54.Google Scholar
Sakurai, T. 1963 On the mechanics of a magnetohydrodynamical twin wake. J. Fluid Mech., 15, 610–22.Google Scholar
Sears, W. R. 1960 Some remarks about flow past bodies. Rev. Mod. Phys., 32, 701–5.Google Scholar
Sears, W. R. 1961 On a boundary-layer phenomenon in magneto-fluid dynamics. Astronautica Acta, 7, 223–36.Google Scholar
Stewartson, K. 1963 Magneto-fluid dynamics of bodies in aligned fields. Proc. Roy. Soc. A, 275, 70–86.Google Scholar
Tamada, K. 1962 Flow of a slightly conducting fluid past a circular cylinder with strong, aligned magnetic field. Phys. Fluids, 5, 817–23.Google Scholar