Abstract
The problem of steady-state flows in a layer of a continuously stratified fluid is considered. The sufficient condition of existence of families of shear flows that are consistent with the meaning of the laws of conservation of mass, momentum, and energy with a uniform flow is given. Approximate solutions of the smooth-bore type, which describe the wave transitions for pairs of conjugate flows of the first spectral mode, are obtained.
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References
L. V. Ovsyannikov, N. I. Makarenko, V. I. Nalimov, et al.,Nonlinear Problems of the Theory of Surface and Internal Waves [in Russian], Nauka, Novosibirsk (1985).
M. Funakoshi, “Long internal waves in a two-layer fluid,”J. Phys. Soc. Jpn.,54, No. 1, 128–144 (1985).
C. J. Amick and R. E. L. Turner, “Small internal waves in two-fluid systems,”Arch. Rational Mech. Anal.,108, No. 2, 111–139 (1989).
N. I. Makarenko, “Smooth bore in a two-layer fluid,”Int. Ser. Numer. Math.,106, 195–204 (1992).
A. Mielke, “Homoclinic and heteroclinic solutions in two-phase flow,”Adv. Ser. Nonlinear Dyn., Vol. 7: Proc. IUTAM/ISIMM Symp. on Structure and Dynamics of Nonlinear Waves in Fluids, World Scientific (1995), pp. 353–362.
J. W. Miles, “On internal solitary waves.,”Tellus,31, No. 5, 456–462 (1979).
A. A. Borisov and O. G. Derzho, “The structure of steady-state solitary waves of finite amplitude,”Izv. Akad. Nauk SSSR, Ser. Tekh., Nauk., No. 2, 60–70 (1990).
N. V. Gavrilov, “Internal solitary waves immovable in a laboratory coordinate system and smooth bores,”Prikl. Mekh. Tekh. Fiz.,35, No. 1, 29–33 (1994).
V. I. Bukreev and A. V. Gusev, “Forced smooth bore in a continuously stratified fluid,”Dokl. Ross. Akad. Nauk,363, No. 3, 327–329 (1998).
Yih Chia-Shun,Stratified Flows, Academic press, New York (1980).
T. B. Benjamin, “Impulse, flow force and variational principles,”IMA J. Appl. Math.,32, 3–68 (1984).
T. B. Benjamin, “A unified theory of conjugate flows,”Philos. Trans. R. Soc. London, Ser. A,269, 587–643 (1971).
J. T. Beale, “Exact solitary water waves with capillary ripples at infinity,”Commun. Pure Appl. Math.,44, 211–257 (1991).
D. J. Benney and D. R. S. Ko, “The propagation of long large amplitude internal waves,”Stud. Appl. Math.,59, 187–199 (1978).
Additional information
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 69–78. March–April, 1999.
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Makarenko, N.I. Conjugate flows and smooth bores in a weakly stratified fluid. J Appl Mech Tech Phys 40, 249–257 (1999). https://doi.org/10.1007/BF02468521
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DOI: https://doi.org/10.1007/BF02468521