Higher Orders Instability of a Hollow Jet Endowed with Surface Tension

• Autorzy: Radwan, A. E. , Ahmed, N. A.
• Języki publikacji: EN

Abstrakty

EN

The higher orders instability of a gas cylinder ambient with an incompressible inviscid liquid endowed with surface tension is analyzed. The perturbation equations up to third order are derived and solved. The surface displacements, the velocity potentials and the dispersion relations are derived for each order of axisymmetric perturbation. It is found that, up to third order, a transition from instability to stability states occurs when the perturbed wavelength equals the circumference of the gas cylinder. The stability discussions for the present model have been done and for the nonhollow jet as well. The hollow jet instability is much larger than that of the nonhollow model. It is found that the maximum temporal amplification prevailing in the hollow jet is much higher than that of the full fluid jet. These results are consistent with some data of the experimental work of Kendall [9], in the first order perturbation.

Słowa kluczowe

PL

pole magnetyczne; siły kapilarne; magnetohydrodynamic stability

EN

magnetic field; capillary force

• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2008
• Tom: Vol. 12, nr 1
• Strony: 69-77
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Radwan, A. E.

autor

Ahmed, N. A.

• Mathematics Department, Faculty of Science, Ain-Shams University, Cairo, Egypt

Bibliografia

• [1] J. Plateau, Statique Experimentale et Theorique des Liquides Soumis aux Seules Forces Moleculaires, Vols. 1 and 2, Gauthier-Villars, Paris, 1873.
• [2] J. Rayleigh, The Theory of Sound, Vols. 1 and 2, Dover, New York, 1945.
• [3] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover, New York, 1981.
• [4] E. F. Gosdde and M. C. Yuen, J. Fluid Mech., 40, 495, 1970.
• [5] R. J. Donnelly and W. Glaberson, Proc. Roy. Soc., London, 290A, 547, 1966.
• [6] A. Meyer and A. Weihs, J. Fluid Mech., 197, 531, 1987.
• [7] M. C. Yuen, J. Fluid Mech., 33, 151, 1968.
• [8] A. H. Nayfeh, Phys. Fluids, 13, 841, 1970.
• [9] J. M. Kendall, Phys. Fluids, 29, 2086, 1986.
• [10] A. E. Radwan and S. S. Elazab, Simon Stevin, 61, 293, (1987).
• [11] A. E. Radwan, J. Phys. Soc. Japan, 58, 1225, 1989.
• [12] A. E. Radwan, J. Magn. Magn. Matrs., 78, 85, 1989.
• [13] P. G. Drazin and W. H. Reid, Hydrodynamic Stability Cambridge Univ. Press, Chap. I, 1981).