A note on solution of the dispersion equation for small-amplitude internal waves

• Autorzy: Das D. , Mandal B. N.
• Języki publikacji: EN

Abstrakty

EN

This note is concerned with establishing the nature of the roots of a dispersion equation, which arises in the study of small-amplitude internal waves in two immiscible superposed fluids, wherein the upper fluid has a free surface and the lower fluid has a rigid bottom. All roots of this dispersion equation are found by considering graphs of appropriate functions, and the fact that these are the only possible roots, has been established by Rouche's theorem of complex variable theory.

Słowa kluczowe

EN

dispersion equation; internal waves; Rouche's theorem

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2005
• Tom: Vol. 57, nr 6
• Strony: 493--501
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Das D.

• Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700 108, India

autor

Mandal B. N.

• Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700 108, India

Bibliografia

• 1. R. V. Churchill, J. W. Brown, R. F. Verhey, Complex Variables and Applications, McGraw-Hill, New York 1966.
• 2. H. Lamb,, Hydrodynamics, Cambridge University Press, 1932.
• 3. C. M. Linton, J. R. Cadby, Scattering of oblique waves in a two-layer fluid, J. Fluid Mech., 461, 343–364, 2002.
• 4. C. M. Linton, M. McIVER , The interaction of waves with horizontal cylinders in two layer fluids, J. Fluid Mech., 304, 213–229, 1995.
• 5. P. F. Rhodes-Robinson, On the forced surface waves due to a vertical wave maker in the presence of surface tension, Proc. Camb. Phil. Soc., 70, 323–337, 1971.
• 6. H. H. Sherief, M. S. Faltas, E. I. Saad, Forced gravity waves in two-layered fluids with the upper fluid having a free surface, Can. J. Phys., 81, 675–689, 2003.
• 7. H. H. Sherief, M. S. Faltas, E. I. Saad, Axisymmetric gravity waves in two-layered fluids with the upper fluid having a free surface, Wave Motion , 40, 143–161, 2004.
• 8. J. V. Wehausen, E. V. Laitone, Surface Waves, [in:] Handbuch der Physik, S. Flugge, [Ed.], Springer-Verlag, 1960.