An unsteady nonlinear equation, more accurate than those derived in previous studies, is obtained for the process of wave formation on the surface of a vertically flowine film. Perturbation theory is used to investigate the solutions of this equation. The wave cnaracteristics ot the steady-state flow regime are calculated.
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P. L. Kapitsa and S. P. Kapitsa, “Wave flow of thin viscous films,” Zh. Eksp. Teor. Fiz.,19, 105 (1949).
V. E. Nakoryakov, V. G. Pokusaev, S. V. Alekseenko, and V. V. Orlov, “Instantaneous velocity profile in a wavy film,” Inzh.-Fiz. Zh.,33, 399 (1973).
S. V. Alekseenko, V. E. Nakoryakov, and B. G. Pokusaev, “Wave formation on a film flowing along a vertical wall,” Zh. Prikl. Mekh. Tekh. Fiz., No. 6, 77 (1979).
P. L. Kapitsa, “Wave flow of thin viscous films,” Zh. Eksp. Teor. Fiz.,18, 3 (1948).
V. Ya. Shkadov, “Wave flow regimes of a thin viscous film under the influence of gravity,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 43 (1967).
O. Yu. Tsvelodub, “Stationary traveling waves on a film flowing along an inclined plane,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 142 (1980).
E. A. Demekhin and V. Ya. Shkadov, “Nonstationary waves in a viscous film,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 151 (1981).
V. I. Karpman, Nonlinear Waves in Dispersive Media [in Russian], Nauka, Moscow (1973).
N. N. Bogolyubov and Y. A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York (1962).
D. McLaughlin and E. Scott, “Multisoliton perturbation theory,” in: Solitons in Action [Russian translations], Mir, Moscow (1981), pp. 210–268.
Yu. P. Krasnyi and V. V. Mikho, “Nonlinear waves on the surface of a free-flowing vertical film,” Inzh.-Fiz. Zh.,48, 375 (1985).
E. A. Demekhin and V. Ya. Shkadov, “Two-dimensional wave regimes in a thin viscous film,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 63 (1985).
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 68–75, July–August, 1986.
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Krasnyi, Y.P., Mikho, V.V. Self-consistent approach to the problem of nonlinear waves on the surface of a vertically flowing film. Fluid Dyn 21, 564–570 (1986). https://doi.org/10.1007/BF01057141
- Perturbation Theory
- Nonlinear Equation
- Flow Regime
- Nonlinear Wave
- Wave Formation