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Gravitating instability of a compound liquid jet

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Il Nuovo Cimento B (1971-1996)

Summary

The stability of a self-gravitating gas jet ambient with a selfgravitating liquid is discussed analytically and the results are confirmed numerically. A general eigenvalue relation describing the characteristics of the gas-core liquid jet, based on the linear perturbation techniques, is derived by employing the energy principle. It is found that the fluid densities ratioS plays an important role in the (de-)stabilizing of the present model. If 0≤S<1 (S=s 2/s 1, wheres 2 is the liquid density ands 1 is the gas density), the model is unstable for certain values of the longitudinal wave numberx (mainly 0≤x<1.0668) and stable for the rest. However with increasingS values provided that 0<S<1 the unstable domain is fastly decreasing but never vanishing. AsS>1, unexpected results have been obtained according to which the model is unstable gravitationally not only for long wavelengths but also for very short wavelengths. These analytical results are interpreted physically and confirmed numerically and the disturbance wave numbers at which stability as well as instability are tabulated. IfS=0 we recover the reported works in the literature.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, Ain-Shams University, Abbassia, Cairo, Egypt

    Ahmed E. Radwan

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  1. Ahmed E. Radwan
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Radwan, A.E. Gravitating instability of a compound liquid jet. Nuov Cim B 106, 969–981 (1991). https://doi.org/10.1007/BF02728341

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  • DOI: https://doi.org/10.1007/BF02728341

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