In case (iii), N, N o -00, but NINo=Polp is taken finite. Here the magnetic energy lunit volume is much higher than the kinetic energy lunit volume on both sides of the vortex sheet. It was argued in Sec. IV that it was sufficient to discuss the roots of Eq. (34) for 0 < n ~ 1. This is also clear physically. Since n = uoPol up, there is no loss of generality if we take the product of density and conductivity (uaPo) on one side of the vortex sheet less than that (up) on the other side. Figure 2 shows that the positive imaginary part of C I of a complex root of Eq. (34), and hence the growth rate of instability, increases steadily with n . In the particular case when density is continuous across the vortex sheet (p = Po) a smaller value of n indicates a larger discontinuity in conductivity. Alternatively, if we take the conductivity to be continuous (u= u o ), then a similar argument as above shows that the effect of a discontinuity in density alone has a stabilizing influence on the vortex sheet.
VI. CONCLUSIONA discontinuity in density or conductivity across a vortex sheet in a finitely conducting, inviscid, and incompressible fluid, in the presence of a uniform magnetic field, is found to have a stabilizing effect on the vortex sheet in the following cases:(i) The fluid on one side of the vortex sheet is nonconducting but that on the other side has a large conductivity or a large velocity, or the wavelength of the disturbances is large.(ii) The fluids on both sides of the vortex sheet have large conductivities, large velocities or the wavelengths of the disturbances are large. The ratio of the conductivities is, however, finite.(iii) N and No, the ratios of the magnetic energy to the kinetic energy, per unit volume, are large on both sides of the vortex sheet, but NINo is finite.
ACKNOWLEDGMENTSThe results of numerical computations reported in the paper were obtained using the IBM 1620 computer installed in the Mathematics Department of Panjab University. The authors are much grateful to Dr. D. Vir for making a program for the numerical work.Low-field magnetization measurements have been made at 4.2 OK on thin-film and bulk NbN samples using a vibrating-sample Foner magnetometer. These data can be used to calculate the upper critical field, HC2, without having to resort to resistivity data, which, particularly in the case of NbN, yield very anomalous results. In the present work the experimental value of HC1 is obtained from the magnetization curves and HC2 is then calculated using the GLAG equations. These calculations and the significance of the Pauli spin paramagnetism and spin-orbit scattering in these materials are discussed.