Gravitohydrodynamic Instability of a Streaming Fluid Cylinder

다국어 초록 (Multilingual Abstract)

The capillary-gravitodynamic instability of a self-gravitating fluid cylinder (radius R_(0)) dispersed in a self-gravitating medium of negligible motion has been developed. General stability criteria are derived, on utilizing the Lagrangian second order differential equation concerning the energy principle as the fluid is stationary. As the fluid is axially streaming we have used the macroscopic perturbation technique of small increments. The stability eigenvalue relations are discussed analytically and the results are confirmed numerically. Both the capillary and the self-gravitating forces are strongly destabilizing in the axisymmetric mode m= 0 as long as the perturbed wavelength, λ is longer than the circumference 2πR_(0)of the fluid cylinder where m is the azimuthal wavenumber. The model is capillarygravitodynamic stable in the domains (λ≤ 2πR_(0), m = 0) of symmetric disturbance and (0 <λ< ∞, m ≠ 0) of asymmetric distrubances. The streaming has strong destabilizing influence not only in the m = 0 mode but also in the modes m ≠ 0. The self-gravitating and capillary forces have destabilizing influences on each other for some states in m = 0 but they have pure stabilizing influences on each other for all states in m ≠ 0 modes. In m = 0 mode the instability of the model is very fast when the capillary and gravitational forces are acting all together and become more and more large as the fluid is axially streaming. The latter, in addition, decreases the stable domains whether the disturbanceis m = 0 or/and m ≠ 0.