zbMATH — the first resource for mathematics

On perturbations of a tangential discontinuity surface between two non-uniform flows of an ideal incompressible fluid. (English. Russian original) Zbl 1458.76043
J. Appl. Mech. Tech. Phys. 60, No. 2, 211-223 (2019); translation from Prikl. Mekh. Tekh. Fiz. 60, No. 2, 32-46 (2019).
Summary: The development of perturbations of a tangential discontinuity surface separating two stationary flows of an ideal incompressible fluid slowly varying in space is studied taking into account surface tension. Perturbations are described using complex Hamiltonian equations. The dependences of the amplitude of perturbations on the coordinate and time are obtained.
76E17 Interfacial stability and instability in hydrodynamic stability
76B45 Capillarity (surface tension) for incompressible inviscid fluids
Full Text: DOI
[1] V. P. Maslov, Perturbation Theory and Asymptotic Methods (Moscow State University, Moscow, 1965) [in Russian].
[2] Rukhadze, A. A.; Silin, V. P., Geometric Optics Method in Electrodynamics of an Inhomogeneous Plasma, Usp. Fiz. Nauk, 82, 499-535, (1964) · Zbl 0116.45802
[3] A. B. Mikhailovskii, Theory of Plasma Instabilities (Atomizdat, Moscow, 1970) [in Russian].
[4] Iordanskii, S. V., Stability of Inhomogeneous States and Continual Integrals, Zh. Eksp. Teor. Fiz., 94, 180-189, (1988)
[5] Kulikovskii, A. G.; Lozovskii, A. V.; Pashchenko, N. T., On the Development of Perturbations on a Uniformly Homogeneous Background, Prikl. Mat. Mekh., 71, 761-774, (2007)
[6] Kulikovskii, A. G., Evolution of Perturbations on a Steady Weakly Inhomogeneous Background. Complex Hamiltonian Equations, Prikl. Mat. Mekh., 81, 3-17, (2017)
[7] Kulikovskii, A. G.; Shikina, I. S., On the Development of Perturbations at the Interface between Two Liquids, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 5, 46-49, (1977)
[8] Kelvin, L., The Influence of Wind on Waves in Water Supposed Frictionless, Philos. Mag., 42, 368-374, (1871)
[9] R. Betchov and W. Criminale, Stability of Parallel Flows (Academic Press, New York, 1967). · Zbl 0248.76018
[10] M. V. Fedoryuk, Asymptotic Methods for Linear Ordinary Differential Equations (Nauka Moscow, 1983) [in Russian]. · Zbl 0538.34001
[11] Berk, H. L.; Cay Nevins, W.; Roberts, K. V., New Stokes’ Lines in WKB Theory, J. Math. Phys., 23, 988-1002, (1982) · Zbl 0488.34050
[12] M. A. Lavrentev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable (Nauka, Moscow, 1965) [in Russian].
[13] M. V. Fedoryuk, Saddle-Point Method (Nauka, Moscow, 1977) [in Russian]. · Zbl 0463.41020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.