|
Article information
2019 , Volume 24, ¹ 2, p.99-110
Talipova T.G., Didenkulova E.G., Pelinovsky E.N.
Analytical theory and numerical modelling of nonlinear wave packages (breathers) in the ocean stratified by density and currents
The paper addresses the important problem of modelling the transformation of breathers of internal waves in a horizontally heterogeneous medium stratified by density and currents. At present, there are sufficiently detailed hydrological atlases that allow performing calculations of the kinematic characteristics of internal waves for a given density field in an ocean. The data on currents is incomplete, and still there is no necessary accuracy. For solitons of small amplitude, “ignorance” of the flow field leads only to a quantitative difference in the parameters, however for breathers the situation can change qualitatively, and if the sign of cubic nonlinearity changes, the breather simply ceases to exist. Currents lead to differences in the spatial and temporal characteristics of a breather, which is very important when comparing measurement data obtained by different methods (from a buoy or from a moving carrier). In this case, the effects of blocking waves on the opposite currents, which vary horizontally, are possible. All this points require a thorough study of the behavior of breathers on ocean currents. The theory of nonlinear oscillating wave packets in the ocean is developed. The theory is based on the Gardner equation, which is fully integrated by modern methods of the theory of nonlinear waves. Phase relations in breathers are determined. As an example, the calculation of the dynamics of the package of internal waves with the formation of breathers for the conditions close to the conditions of the Baltic Sea in the Gotland Basin is considered.
[full text] [link to elibrary.ru]
Keywords: breathers, Gardner equation, stratified ocean
doi: 10.25743/ICT.2019.24.2.009
Author(s):
Talipova Tatiana Georgievna
Dr.
Position: Leading research officer
Office: Institute of Applied Physics RAS, Nizhny Novgorod State Technical University n.a. R.E. Alekseev
Address: 603950, Russia, Nizhny novgorod, 46 Ulyanova Str.
Phone Office: (831) 4164749
E-mail: tgtalipova@mail.ru
SPIN-code: 4837-6302Didenkulova Ekaterina Gennadievna
PhD.
Position: Research Scientist
Office: Institute of Applied Physics RAS, Nizhny Novgorod State Technical University n.a. R.E. Alekseev
Address: 603950, Russia, Nizhny novgorod, 46 Ulyanova Str.
Phone Office: (831) 4164749
E-mail: eshurgalina@mail.ru
SPIN-code: 3193-2111Pelinovsky Efim Naumovich
Dr. , Professor
Position: General Scientist
Office: Institute of Applied Physics RAS, Nizhny Novgorod State Technical University n.a. R.E. Alekseev
Address: 603950, Russia, Nizhny novgorod, 46 Ulyanova Str.
Phone Office: (831) 4164749
E-mail: pelinovsky@gmail.com
SPIN-code: 8949-9088 References:
[1]. Lee, J.H., Lozovatsky, I., Jang, S-T., Jang, Ch. J., Hong, Ch. S., Fernando, H. J. S. Episodes of nonlinear internal waves in the northern East China Sea. Geophysical Research Letters. 2006; (33): L18601.
[2]. Shroyer, E.L., Moum, J.N., Nash, J.D. Mode 2 waves on the continental shelf: Ephemeral components of the nonlinear internal wavefield. Journal of Geophysical Research. 2010; (115):C07001.
[3]. Osborne, A.R. Nonlinear Ocean Waves and the Inverse Scattering Transform. International Geophysics Series. Academic Press; 2010; (97):944
[4]. Pelinovsky, D., Grimshaw, R. Structural transformation of eigenvalues for a perturbed algebraic soliton potential. Physics Letters A. 1997; (229):165 – 172.
[5]. Ablowitz, M., Segur, H. Solitons and the Inverse Scattering Transform. Philadelphia: SIAM; 1981: 415.
[6]. Grimshaw, R, Pelinovsky, E., Talipova, T., Kurkin, A. Simulation of the transformation of internal solitary waves on oceanic shelves. Journal of Physical Oceanography. 2004; (34):2774-2791.
[7]. Grimshaw, R., Pelinovsky, E., Talipova, T. and Kurkina, O. Internal solitary waves: propagation, deformation and disintegration. Nonlinear Processes in Geophysics. 2010; (17):633–649.
[8]. Grimshaw, R., Pelinovsky, D., Pelinovsky, E., Talipova, T. Wave group dynamics in weakly nonlinear long - wave models. Physica D. 2001; 159(1-2):35-57.
[9]. Lamb, K., Polukhina, O., Talipova, T., Pelinovsky, E., Xiao, W., Kurkin, A. Breather generation in the fully nonlinear models of a stratified fluid. Physical Review E. 2007; 75(4):046306.
[10]. Terletska, K., Jung, K.T., Talipova, T., Maderich, V., Brovchenko, I., Grimshaw, R. Internal breather-like wave generation by the second mode solitary wave interaction with a step. Physics of Fluids. 2016; (28):116602.
[11]. Zhang, P., Zhenhua, Xu Zh., Li, Q., Yin, B., Hou, Y., Liu, A.K. The evolution of mode-2 internal solitary waves modulated by background shear currents. Nonlinear Processes in Geophysics. 2018; (25):441–455.
[12]. Rouvinskaya, E., Talipova, T., Kurkina, O., Soomere, T., Tyugin, D. Transformation of internal breathers in the idealised shelf sea conditions. Continental Shelf Research. 2015; (110):60-71.
[13]. Pelinovsky, E.N., Slunyaev, A.V., Polukhina, O.E., Talipova, T.G. Internal Solitary Waves. Solitary Waves in Fluids (editor R. Grimshaw). Southampton. Boston: WIT Press; 2007: 85-110.
[14]. Carnes, M. R. Description and evaluation of GDEM-V3.0, Naval Research Laboratory (NRL) Report NRL/MR/7330-09-9165, Naval Research Laboratory. 2009: 27.
[15]. Kurkina, O., Talipova, T., Pelinovsky, E., Soomere, T. Mapping the internal wave field in the Baltic Sea in the context of sediment transport in shallow water. Journal of Coastal Research. 2011; (SI 64):2042-2047.
[16]. Kurkina, O., Rouvinskaya, E., Talipova, T. Soomere, T. Propagation regimes and populations of internal waves in the Mediterranean Sea basin. Estuarine, Coastal and Shelf Science. 2017; (185):44-54.
[17]. Polukhin, N., Talipova, T., Pelinovsky, E., Lavrenov, I. Kinematic characteristics of the high-frequency internal wave field in the Arctic. Oceanology. 2003; 43(3):333-343.
[18]. Kurkina, O., Talipova, T., Soomere, T., Kurkin, A., Rybin, A. The impact of seasonal changes in stratification on the dynamics of internal waves in the Sea of Okhotsk. Estonian Journal of Earth Sciences. 2017; 66(4):238–255.
[19]. Polukhin, N.V., Pelinovskii, E.N., Talipova, T.G., Muyakshin, S.I. On the effect of shear cur-rents on the vertical structure and kinematic parameters of internal waves. Oceanology. 2004; 44(1):22-29.
[20]. Holloway, P., Pelinovsky, E., Talipova, T. A Generalized Korteweg - de Vries Model of Internal Tide Transformation in the Coastal Zone. Journal of Geophysical Research. 1999; 104(C8):18333-18350.
[21]. Talipova, T.G., Pelinovsky, E.N., Kharif, C. Modulation instability of long internal waves with moderate amplitudes in a stratified horizontally inhomogeneous ocean. JETP Letters. 2011; (94):182–186.
[22]. Rouvinskaya, E., Talipova, T., Kurkina, O., Soomere, T., Tyugin, D. Transformation of internal breathers in the idealised shelf sea conditions. Continental Shelf Research. 2015; (110):60-71.
Bibliography link:
Talipova T.G., Didenkulova E.G., Pelinovsky E.N. Analytical theory and numerical modelling of nonlinear wave packages (breathers) in the ocean stratified by density and currents // Computational technologies. 2019. V. 24. ¹ 2. P. 99-110
|
