zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Magneto hydrodynamic stability of self-gravitational fluid cylinder. (English) Zbl 1205.76304
Summary: The self-gravitating instability of a fluid cylinder pervaded by magnetic field and endowed with surface tension has been discussed. The dispersion relation is derived and some reported works are recovered as limiting cases from it. The capillary force is destabilizing only in the small axisymmetric domain and stabilizing otherwise. The magnetic field has a strong stabilizing effect in all modes of perturbation for all wavelengths. The self-gravitating force is destabilizing in the axisymmetric perturbation. However the magnetic field effect modified a lot the destabilizing character of the model and could overcome the capillary and self-gravitating instability of the model for all short and long wavelengths.
MSC:
76W05Magnetohydrodynamics and electrohydrodynamics
76D17Viscous vortex flows
References:
[1]Donnelly, R.; Glaberson, W.: Experiments on the capillary instability of a liquid jet, Proc. roy. Soc. lond. 290A, 547 (1966)
[2]Yuen, M. C.: Nonlinear capillary instability of a liquid jet, J. fluid mech. 33, 151 (1968) · Zbl 0155.55703 · doi:10.1017/S0022112068002429
[3]Nayfeh, A.: Nonlinear stability of a liquid jet, Phys. fluids 13, 841 (1970) · Zbl 0214.25402 · doi:10.1063/1.1693025
[4]Nayfeh, A.; Hassan, S. D.: The method of multiple scales and nonlinear dispersive waves, J. fluid mech. 48, 463 (1971) · Zbl 0239.76021 · doi:10.1017/S0022112071001708
[5]Kakutani, T.; Inoue, I.; Kan, T.: Nonlinear capillary waves on the surface of liquid column, J. phys. Soc. jpn. 37, 529 (1974)
[6]Rayleigh, J. W.: The theory of sound, (1945) · Zbl 0061.45904
[7]Chandrasekhar, S.: Hydrodynamic and hydromagnetic stability, (1961) · Zbl 0142.44103
[8]Radwan, A. E.: Instability of a hollow jet with effectives of surface tension and fluid inertial, J. phys. Soc. jpn. 58, 1225 (1989)
[9]Abramowitz, M.; Stegun, I.: Handbook of mathematical functions, (1970)
[10]Chandrasekhar, S.; Fermi, E.: Problems of gravitational stability in the presence of a magnetic field, Astrophys. J. 116, 118 (1953)
[11]Radwan, A. E.: Capillary gravitodynamic instability of two fluids interface, Phys. scripta 51, 484 (1995)