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TAYLOR INSTABILITY OF A DEBRIS INTERFACE UNDER VARIABLE ACCELERATION. Chap. 8 of THEORETICAL STUDY OF HYDROMAGNETIC STABILITY AND TURBULENCE. INVESTIGATIONS AND DETAILED RESULTS. Annual Report, Period: January 1-December 31, 1961

Technical Report ·
OSTI ID:4835810
S> The Taylor instability of the interface separating an expanding plasma from the hydromagnetic region is studied. The plasma is treated as incompressible and the bubble interface which is assumed to be under variable acceleration is treated as a surface of discontinuity. The motion of the surface of discontinuity is prescribed and the flows determined so as to be compatible. The fluids on either side of the interface are viewed as being ideal hydromagnetic fluids and the boundary conditions appropriate to a moving interface are satisfied. The problem of small motions about such time dependent flows is considered by means of linearization and applied to planar, cylindrical and spherical interfaces. In choosing the appropriate simple flows, the stability problem is reduced to examination of a linear second order differential equation whose time dependent coefficients are functions of the equilibrium. For planar interfaces the stability equation is derived for hydrodynamic and hydromagnetic fluids and solved for a variety of time dependent polynomial and sinusoidal interface accelerations. For a sinusoidal acceleration the problem is reduced to a Mathieu equation whose stability regions are well known. The stability of a cylindrical interface is studied for the case of an infinitely long cylinder. A plasma line source along the axis drives the interface radially against an external axial field with a prescribed timedependent acceleration. The stability equation for this case is a second order differential equation in which the timedependent factors are given by ratios of Bessel functions of imaginary argument. The equation was integrated numerically for expanding and contracting cylinders illustrating stable and unstable perturbations. Limiting cases for large and small cylinder radius were also considered. For the spherical bubble expanding into an ionized atmosphere, the interface stability equation was derived and discussed in the WKB limit. Stability was shown to depend on the polar wave number, bubble density, external density, bubble radius, and surface velocity and acceleration. ln the case of expansion against a uniform vacuum field, it was shown that the bubble grows initially like a prolate spheroid at a rate which is proportional to the square of the magnetic field. (auth)
Research Organization:
Radio Corp. of America. Missile and Surface Radar Div., Moorestown, N.J.
NSA Number:
NSA-16-022718
OSTI ID:
4835810
Report Number(s):
AFSWC-TDR-62-12(Vol.II)(Chap.8
Country of Publication:
Country unknown/Code not available
Language:
English