Modulational stability of wave packets at fluid interface of layer and half-space

• Autorzy: Avramenko Olga , Naradovyi Volodymyr

Identyfikatory

DOI

10.17512/jamcm.2025.2.01

• Języki publikacji: EN

Abstrakty

EN

The modulational stability of internal wave packets propagated along the surface of a hydrodynamic system consisting of a lower half-space and an upper layer covered with a rigid lid is investigated. The study is conducted within the framework of a nonlinear low-dimensional model incorporating surface tension on an interface using the method of multi-scale expansions implemented via symbolic computation. The evolution equation of the envelope of the wave packet takes the form of the Schrodinger equation. Conditions ¨ for the modulational stability of the solution of the evolution equation are identified for various physical and geometrical characteristics of the system. Significant influence on the modulational stability of the system’s geometrical characteristics and surface tension is observed for relatively small liquid layer thicknesses. For large layer thicknesses, the stability diagram degenerates to that of a system composed of two half-spaces.

Słowa kluczowe

EN

modulational stability; internal waves; multi-scale expansions; surface tension; Benjamin-Feir index; evolution equation

PL

stabilność modulacyjna; fale wewnętrzne; ekspansje wieloskalowe; napięcie powierzchniowe; indeks Benjamina-Feira; równanie ewolucji

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2025
• Tom: Vol. 24, nr 2
• Strony: 5--17
• Opis fizyczny: Bibliogr. 23 poz., rys.

Twórcy

autor

Avramenko Olga

• Department of Mathematics, National University of Kyiv Mohyla Academy Kyiv, Ukraine

autor

Naradovyi Volodymyr

• Department of Informatics, Programming, Artificial Intelligence, and Technological Education Volodymyr Vynnychenko Central Ukraine State University Kropyvnytskyi, Ukraine

Bibliografia

• [1] Benjamin, T.B., & Feir, J.E. (1967). The disintegration of wave trains on deep water Part 1. Theory. J. Fluid Mech., 27(3), 417-430 , DOI: 10.1017/S002211206700045X.
• [2] Zakharov, V.E. (1968). Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. App. Mech. Techn. Phys., 9, 190-194, DOI: 10.1007/BF00913182.
• [3] Sedletsky, Y. (2021). A fifth-order nonlinear Schrodinger equation for waves on the surface of ¨ finite-depth fluid. Ukr. J. Phys., 66(1), 41-54, DOI: 10.15407/UJPE66.1.41.
• [4] Ablowitz, M.J., Luo, H.-D., & Musslimani, Z.H. (2023). Six wave interaction equations in finite-depth gravity waves with surface tension. J. Fluid Mech., 961, A3, DOI: 10.1017/jfm .2023.128.
• [5] Ionescu, A.D., & Pusateri, F. (2018). Global regularity for 2D water waves with surface tension. Mem. Amer. Math. Soc., 256, 123 pp., DOI: 10.48550/arXiv.1408.4428.
• [6] Dull, W.P. (2021). Validity of the nonlinear Schr ¨ odinger approximation for the two-dimensional ¨ water wave problem with and without surface tension in the arc length formulation. Arch. Rational Mech. Anal., 239, 831-914, DOI: 10.1007/s00205-020-01586-4.
• [7] Hasimoto, H., & Ono, H. (1972). Nonlinear modulation of gravity waves. J. Phys. Soc. Japan, 33(3), 805-811, DOI: 10.1143/JPSJ.33.805.
• [8] Nayfeh, A. (1976). Nonlinear propagation of wave-packets on fluid interface. Trans. ASME, Ser. E: J. Appl. Mech., 43(4), 584-588, DOI: 10.1115/1.3423936.
• [9] Grimshaw, R.H.J., & Pullin, D.I. (1985). Stability of finite-amplitude interfacial waves. Part 1. Modulational instability for small-amplitude waves. J. Fluid Mech., 160, 297-315, DOI: 10.10 17/S0022112085003494.
• [10] Selezov, I., Avramenko, O., Kharif, C., & Trulsen, K. (2003). High-order evolution equation for nonlinear wave-packet propagation with surface tension accounting. Comptes Rendus. Mecanique ´ , 331(3), 197-201, DOI: 10.1016/S1631-0721(03)00043-3.
• [11] Abrashkin, A.A., & Pelinovsky, E.N. (2018). Dynamics of a wave packet on the surface of an inhomogeneously vortical fluid (Lagrangian description). Izv. Atmos. Ocean. Phys., 54, 101-105, DOI: 10.1134/S0001433818010036.
• [12] Li, S., Chen, J., Cao, A., & Song, J. (2019). A nonlinear Schrodinger equation for gravity waves ¨ slowly modulated by linear shear flow. Chinese Phys. B, 28, 124701, DOI: 10.1088/1674-1056/ ab53cf.
• [13] Li, S., Xie, X., Chen, D., & Song, J. (2022). Modulation effect of linear shear flow on interfacial waves in a two-layer fluid with finite layer depths. Phys. Fluids, 34, 092105, DOI: 10.1063/ 5.0098077.
• [14] Pal, T., & Dhar, A.K. (2022). Stability analysis of finite amplitude interfacial waves in a two- -layer fluid in the presence of depth uniform current. Ocean Dynam., 72, 241-257, DOI: 10.1007/s10236-022-01503-1.
• [15] Pal, T., & Dhar, A.K. (2024). Weakly nonlinear modulation of interfacial gravity-capillary waves. Ocean Dynam., 74, 133-147, DOI: 10.1007/s10236-023-01594-4.
• [16] Segur, H., Henderson, D., Carter, J., Hammack, J., Li, C., Pheiff, D., & Socha, K. (2005). Stabilizing the Benjamin-Feir instability. J. Fluid Mech., 539, 229-271, DOI: 10.1017/S002211 200500563X.
• [17] Wu, G., Liu, Y., & Yue, D.K.P. (2006). A note on stabilizing the Benjamin-Feir instability. J. Fluid Mech., 556, 45-54, DOI: 10.1017/S0022112005008293.
• [18] Onorato, M., Osborne, A.R., Serio, M., Cavaleri, L., Brandini, C., & Stansberg, C.T. (2006). Extreme waves, modulational instability and second order theory: wave flume experiments on irregular waves. Europ. J. Mech. - B/Fluids, 25(5), 586-601, DOI: 10.1016/j.euromechflu.2006 .01.002.
• [19] Zakharov, V.E., & Ostrovsky, L.A. (2009). Modulation instability: The beginning. Physica D: Nonlinear Phenom., 238(5), 540-548, DOI: 10.1016/j.physd.2008.12.002.
• [20] El, G.A., & Hoefer, M.A. (2016). Dispersive shock waves and modulation theory. Physica D: Nonlinear Phenom., 333, 11-65, DOI: 10.1016/j.physd.2016.04.006.
• [21] Armaroli, A., Eeltink, D., Brunetti, M., & Kasparian, J. (2018). Nonlinear stage of Benjamin- -Feir instability in forced/damped deep-water waves. Phys. Fluids, 30(1), 017102, DOI: 10.1063/ 1.5006139.
• [22] Berti, M., Maspero, A., & Ventura, P. (2022). Full description of Benjamin-Feir instability of Stokes waves in deep water. Invent. Math., 230, 651-711, DOI: 10.1007/s00222-022-01130-z.
• [23] Berti, M., Maspero, A., & Ventura, P. (2023). Benjamin-Feir instability of Stokes waves in finite depth. Arch. Rat. Mech. Anal., 247, 91, DOI: 10.1007/s00205-023-01916-2.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki i promocja sportu (2025).