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Interaction of internal and surface waves in a two-layer fluid with free surface

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The interaction of internal and surface waves in a two-layer fluid with free surface has been considered. The stability of wave packets propagation on the contact surface and free surface of hydrodynamic system „layer with rigid bottom - layer with free surface” was investigated. The amplitudes of the second harmonics of the elevations of the contact surface and the free surface are investigated.
Rocznik
Strony
3--9
Opis fizyczny
Bibliogr. 33 poz., wykr.
Twórcy
autor
  • Department of Applied Mathematics, Statistics and Economics, State Pedagogical University, Kirovograd, Ukraine, +38-098-902-67-90
Bibliografia
  • [1] Segur H., Hammack J.L. “Soliton models of long internal”.J.Fluid Mech.- 1982.- 118.- P. 285-304.
  • [2] Yuen H.C., Lake B.M. “Nonlinear dynamics of deep-water waves”. Advances in Appl. Mech.- New York, London.- 1982.- 22.-P. 33-45.
  • [3] Ablowitz M., Segur H. “Solitons and the Inverse Scattering Transform”.- Moscow: Mir, 1987.- 485 p. (In Russian)
  • [4] Whitham J. “Linear and nonlinear waves”.- Moscow: Mir, 1977.- 622 p. (In Russian)
  • [5] Bhatnagar P.L. “Nonlinear waves in one-dimensional dispersive systems”.- Oxford: Clarendon Press, 1979.
  • [6] Lamb J. “Introduction to the theory of solitons”.- Moscow: Mir, 1983.- 294 p. (In Russian)
  • [7] Selezov I.T., Korsunsky S.V. “Wave propagation along the interface between the liquid metal and electrolyte”. Proc. International Conference „MHD Processes to Protection of Environment”. Part 1.-i.- 1992.- P. 111-117.
  • [8] Selezov I.T., Huq P. “Interfacial solitary waves in a three-fluid medium with sourth”. 2nd Eur. Fluid Mech. Conf., Warsaw, 20-24 Sept., 1994, Abstr. Pap. –Warsaw,1994.-250 p.
  • [9] Bontozoglou V. “Weakly nonlinear Kelvin-Helmholz waters between fluids of finite depth”. Int. J. Multiphase Flow.- 1991.- 17, N4.- P. 509-518.
  • [10] Dias F., Kharif Ch. “Nonlinear gravity and capillary-gravity waves”. Part 7. Importance of surface tension Effects, Annu. Rev. Fluid Mech.- 1999.- N31.-P. 301—346
  • [11] Camassa R., Choi W. “On the realm of validity of strongly nonlinear asymptotic approximations for internal waves” J. Fluid Mechanics.- 2006.- 549.- P.1-23.
  • [12] Camassa R., Viotti C. “A model for large-amplitude internal waves with finite-thickness pycnocline” Acta Appl. Math.- 2012.- ı 1.- P. 75 – 84.
  • [13] Debsarma S., Das K. P. “Fourth-order nonlinear evolution equations for a capillary-gravity wave packet in the presence of another wave packet in deep water” Phys. Fluids. – 2007. – 19.– P. 097101-1–097101-16.
  • [14] Debsarma, S., Das, K.P. & Kirby, J.T. “Fully nonlinear higherorder model equations for long internal waves in a two-fluid system” J. Fluid Mech.- 2010.- 654.- P. 281 – 303.
  • [15] Kakinuma T., Yamashita K., Nakayama K. “Surface and internal waves due to a moving load on a very large floating structure” J. Appl. Math.- 2012.- 14 p.
  • [16] Choi W., Camassa R. “Weakly nonlinear internal waves in a two-fluid system”. J. Fluid Mech.- 1996.- 313.- P. 83-103.
  • [17] Holyer J.Y. “Large amplitude progressive interfacial waves”. J. Fluid Mech.- 1979.- 118(3).- P. 433-448.
  • [18] Bourtos Y.Z., Abl-el-Malex M.B., Tewfick A.H. “A format expansion procedure for the internal solitary wave problem in a two-fluid system of constant topography”. Acta Mechanica.- 1991.- 88.- P. 172-197.
  • [19] Nayfeh A.H. “Nonlinear propagation of wave-packets on fluid interface”. Trans. ASME., Ser. E.- 1976.- 43, N4.- P. 584-588.
  • [20] Hasimoto H., Ono H. “Nonlinear modulation of gravity waves”. J. of the Phys. Soc. of Japen.- 1972.- 33.- P. 805-811.
  • [21] Duncan J.H. “Spilling breakers”. Annu. Rev. Fluid Mech.- 2001.- 33.- P. 519-547.
  • [22] Baker G.R. Meiron D.I., Orszag S.A. “Generalized vortex methods of free-surface flow problems”. J.Fluid Mech.- 1982.- N123.- P. 477-501.
  • [23] Bourtos Y.Z., Abl-el-Malex M.B., Tewfick A.H. “A format expansion procedure for the internal solitary wave problem in a two-fluid system of constant topography”. Acta Mechanica.- 1991.- 88.- P. 172-197.
  • [24] Chen Y., Liu P.L.-F. “The unified Kadomtsev - Petviashvily equation for interfacial waves”. J.Fluid Mech.- 1995.- N228.- P. 383-408.
  • [25] Stamp A.P. , Jacka M. “Deep-water internal solitary waves”. J. Fluid Mech.- 1995.- 305.- P. 347-371.
  • [26] Trulsen K. “Wave kinematics computed with the nonlinear Schroedinger method for deep water”. Trans. ASME.-1999.- N121.- P. 126-130.
  • [27] Selezov, I.T., Avramenko, O.V. “The evolution equation of the third order for the nonlinear wave-packets at near-critical wave numbers”. Dynamical Systems 17 (2001): 58-67 (in Russian).
  • [28] Selezov, I., Avramenko, O., Kharif, C., Trulsen, K. “Higher asymptotic approximations for nonlinear internal waves in fluid”. Int. Conf. „Nonlinear Partial differential equations” Book of abstracts, Kyiv. 22-28 Aug, (2001): 105-106.
  • [29] Avramenko, O.V., Selezov, I.T. “The stability of the wave packets in stratified hydrodynamic systems with surface tension”. Applied Hydromechanics 4 (2001): 38—46 (in Russian).
  • [30] Selezov, I.T., Avramenko, O.V., Hurtovyy, Y.V. “Some features of the wave propagating in the two-layer fluid”. Applied Hydromechanics 79 (2005): 80-89 (in Russian).
  • [31] Selezov, I.T., Avramenko, O.V., Hurtovyy, Y.V. “The stability of the wave packets in the two-layer hydrodynamic system”. Applied Hydromechanics 90 (2006): 60-65 (in Russian).
  • [32] Selezov, I.T., Avramenko, O.V., Hurtovyy, Y.V., Naradovy, V.V. “The nonlinear interaction of internal and external gravity waves in two-layer fluid with free surface”. Math. methods and physical and mechanical fields 52 (2009): 72-83 (in Russian).
  • [33] Selezov, I.T., Avramenko, O.V., Naradovy, V.V. “Some features of nonlinear wave propagating in two-layer fluid with free surface”. Dynamical Systems 29 (2011): 53-68 (in Russian).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-1eb5af57-1cea-467f-9b59-477b77f73835
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