Transport of Particles at the Propagation of Breathers of Internal Gravity Waves
Abstract
The distinctive features of particle transport during the propagation of long nonlinear localized wave packets (breathers) in quasi three-layer fluid are investigated in the framework of weakly nonlinear theory. To describe the displacement at the maximum of vertical baroclinic mode the Gardner equation is used. To determine the fields of displacements, vertical and horizontal velocities, which are used for finding of Lagrangian particle trajectories, three variants of the wave fields’ vertical structure are used: linear mode, weakly nonlinear approximation (with taking into account the first nonlinear amendment to linear mode) and weakly nonlinear weakly dispersive approximation (with taking into account both the first nonlinear amendment and the first dispersive amendment to linear mode). Since the velocity fields induced by nonlinear wave packets change immediately, the processes of particle transport are investigated for different initial configurations of breathers. The comparison of the form of particle trajectories for different horizons and different breathers’ configurations is made. It is shown that the use of the weakly nonlinear model is sufficient to determine the trajectories of fluid particles. Taking into account the first dispersive amendment to the modal function almost does not affect the quality and quantity of particles’ displacements. A significant difference between solutions of the problem of fluid particles’ trajectories for two types of nonlinear wave motions in a stratified fluid — solitons and breathers — is revealed.
About the Authors
E. A. Ruvinskaya
Nizhny Novgorod State Technical University n.a. R. E. Alekseev
Russian Federation
Russian Federation
O. E. Kurkina
Nizhny Novgorod State Technical University n.a. R. E. Alekseev
Russian Federation
Russian Federation
A. A. Kurkin
Nizhny Novgorod State Technical University n.a. R. E. Alekseev
Russian Federation
Russian Federation
A. A. Naumov
Nizhny Novgorod State Technical University n.a. R. E. Alekseev
Russian Federation
Russian Federation
References
1. Krauss V. Internal waves. Leningrad, Gidrometeoizdat, 1968. 272 p. (in Russian).
2. Morozov E. G. Ocean internal waves. Moscow, Nauka, 1985. 151 p. (in Russian).
3. Sabinin K. D., Konyaev K. V. Waves inside of the ocean. SPb., Gidrometeoizdat, 1992. 272 p. (in Russian).
4. Bogucki D., Dikky T., Redekopp L. G. Sediment resuspension and mixing by resonantly generated solitary waves. J. Phys. Oceanogr. 1997, 7, 1181—1196.
5. Mak Kinnan J. A., Gregg M. C. Mixing on the late-summer new England shelf-solibores, shear and stratification. Preprint, AGU, 1999, V. 4. 19 p.
6. Muller P., Briscoe M. Diapycnal mixing and internal waves. Oceanography. 2000, 13/2, 98—103.
7. Reeder D. B., Ma B. B., Yang Y. J. Very large subaqueous sand dunes on the upper continental slope in the South China Sea generated by episodic, shoaling deep-water internal solitary waves. Marine Geol. 2011, 279/12, 12—18.
8. Chakrabarti S. (Ed.) Handbook of offshore engineering. London, Elsevier, 2005.
9. Osborne A. R., Burch T. L., Scarlet R. I. The influence of internal waves on deep-water drilling. J. Petroleum Technol. 1978, 30/10, 1497—1504.
10. Osborne A. R. Nonlinear ocean waves and the Inverse Scattering Transform. Elsevier, San Diego, 2010.
11. Song Z. J., Teng B., Gou Y. et al. Comparisons of internal solitary wave and surface wave actions on marine structures and their responses. Appl. Ocean Res. 2011, 33, 120—129.
12. Bogucki D. J., Redekopp L. G. A Mechanism for sediment resuspension by internal solitary waves. Geophys. Res. Lett. 1999, 26, 1317—1320.
13. Stastna M., Lamb K. G. Sediment resuspension mechanisms associated with internal wave in coastal waters. J. Geophys. Res. 2008, 113, C10016.
14. Lamb K. G. Particle transport by nonbreaking, solitary internal waves. J. Geophys. Res. 1997, 102/C8, 18641—18660.
15. Kurkina O. E., Kurkin A. A., Giniyatullin A. R. About transport of particles at propagation of solitary internal gravity waves. Proceedings of Academy of Engineering Sciences. 2011, 92—102. (in Russian).
16. Clarke S., Grimshaw R., Miller P. et al. On the generation of solitons and breathers in the Modified Korteweg—de Vries Equation. Chaos. 2000, 10, 2, 383—392.
17. 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.
18. Slyunyaev A. V. Dynamics of localized waves with large amplitude in a weakly dispersive medium with a quadratic and positive cubic nonlinearity. JETP. 2001, 92, 3, 529—534.
19. Grimshaw R., Pelinovsky E., Talipova T. et al. Short-living large-amplitude pulses in the nonlinear long-wave models described by the modified Korteweg—de Vries equation. Studies in Applied Mathematics. 2005, 114, 2, 189.
20. Lamb K., Polukhina O., Talipova T. et al. Breather generation in the fully nonlinear models of a stratified fluid. Physical Rev. E. 2007, 75, 4, 046306.
21. Lee J.-H., Lozovatsky I., Jang S.-T. et al. Episodes of nonlinear internal waves in the Northern East China Sea. Geophysical Research Letters. 2006, 33, L18601.
22. Toschi F., Bodenschatz E. Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 2009, 41, 1, 375—404.
23. Pelinovsky E., Polukhina O., Slunyaev A., Talipova T. Internal solitary waves. In Grimshaw, R. (ed.), Solitary Waves in Fluids. WIT Press, Southampton, Boston, 2007. P. 85—110.
24. Fofonoff N., Millard R. Jr. Algorithms for computation of fundamental properties of seawater. UNESCO Technical Papers in Marine Science. 1983, 44, 15—25.
25. Teague W. J., Carron M. J., Hogan P. J. A Comparison between the Generalized Digital Environmental Model and Levitus Climatologies. J. Geophys. Res. 1990, 95(C5), 7167—7183.
26. Boyer T. P., Antonov J. I., Garcia H. E. et al. World Ocean Database 2005. Ed. by S. Levitus, NOAA Atlas NESDIS 60. U.S. Government Printing Office, Washington, D.C. 2006. 190 p.
27. Pelinovsky D., Grimshaw R. Structural transformation of eigenvalues for a perturbed algebraic soliton potential. Phys. Lett. A. 1997, 229, 165—172.
Review
For citations:
Ruvinskaya E.A., Kurkina O.E., Kurkin A.A., Naumov A.A. Transport of Particles at the Propagation of Breathers of Internal Gravity Waves. Fundamental and Applied Hydrophysics. 2015;8(3):53-61. (In Russ.)
Views:
69
Email this article 