Email this article Solitary Waves in Two-Layer Fluid with Piecewise Exponential Stratification
- Authors: Makarenko N.I.1, Maltseva J.L.1, Cherevko A.A.1
-
Affiliations:
- Lavrentyev Institute of Hydrodynamics SB RAS
- Issue: Vol 87, No 2 (2023)
- Pages: 186-199
- Section: Articles
- URL: https://journals.rcsi.science/0032-8235/article/view/138851
- DOI: https://doi.org/10.31857/S0032823523020091
- EDN: https://elibrary.ru/TZPUKQ
- ID: 138851
Cite item
Open Access
Access granted
Subscription Access
Abstract
The problem on internal stationary waves in a two-layer fluid with density, depending exponentially on the depth inside the layers and having a jump at the interface, is considered. A non-linear equation of the second-order long-wave approximation is derived, and their asymptotic submodels, describing solitary waves of finite amplitude, are discussed. Dispersive properties and wave propagation regimes depending on dimensionless parameters of the background piecewise constant flow are studied.
Keywords
About the authors
N. I. Makarenko
Lavrentyev Institute of Hydrodynamics SB RAS
Author for correspondence.
Email: makarenko@hydro.nsc.ru
Russia, Novosibirsk
J. L. Maltseva
Lavrentyev Institute of Hydrodynamics SB RAS
Author for correspondence.
Email: maltseva@hydro.nsc.ru
Russia, Novosibirsk
A. A. Cherevko
Lavrentyev Institute of Hydrodynamics SB RAS
Author for correspondence.
Email: cherevko@hydro.nsc.ru
Russia, Novosibirsk
References
- Krauss W. Interne Wellen. Berlin: Gebruder Borntraeger, 1966.
- Yih C.S. Stratified Flows. N.Y.: Acad. Press, 1980.
- LeBlond P.H., Mysak L.A. Waves in the Ocean. N.Y.: Elsevier, 1978.
- Ovsyannikov L.V., Makarenko N.I., Nalimov V.I., et al. Nonlinear Problems of the Theory of Surface and Internal Waves. Novosibirsk: Nauka, 1985. (in Russian)
- Ilichev A.T. Solitary Waves in Fluid Dynamics. Moscow: Fizmatlit, 2003. (in Russian)
- Helfrich K.R., Melville W.K. Long nonlinear internal waves // Annu. Rev. Fluid Mech., 2006, vol. 38, pp. 395–425.
- Dubreil-Jacotin M.L. Sur les theoremes d’existence relatifs aux ondes permanentes perodiques а deux dimensions dans les liquides heterogenes // J. Math. Pure Appl., 1937, vol. 16., no. 9, pp. 43–67.
- Long R.R. Some aspects of the flow of stratified fluid. I. A theoretical investigation // Tellus, 1953, vol. 5, pp. 42–57.
- Voronovich A.G. Strong solitary internal waves in a 2.5-layer model // J. Fluid Mech., 2003, vol. 474, pp. 85–94.
- Goullet A., Choi W. Large amplitude internal solitary waves in a two-layer system of piecewise linear stratification // Phys. Fluids, 2008, vol. 20, pp. 096601. https://doi.org/10.1063/1.2978205
- Makarenko N.I., Maltseva J.L. Asymptotic models of internal stationary waves // J. Appl. Mech. Tech. Phys., 2008, vol. 49, no. 4, pp. 646–654.
- Makarenko N.I., Maltseva J.L. Solitary waves in a weakly stratified two-layer fluid // J. Appl. Mech. Techn. Phys., 2009, vol. 50, no. 2, pp. 229–234.
- Sutherland B.R. Internal Gravity Waves. Cambridge: Univ. Press, 2010.
- Makarenko N.I., Maltseva J.L. Phase velocity spectrum of internal waves in a weakly-stratified two-layer fluid // Fluid Dyn., 2009, vol. 44, no. 2, pp. 278–294.
- Miyata M. An internal solitary wave of large amplitude // La Mer, 1985, vol. 23, no. 2, pp. 43–48.
- Choi W., Camassa R. Fully nonlinear internal waves in a two-fluid system // J. Fluid Mech., 1999, vol. 396, pp. 1–36.
- Makarenko N., Maltseva J., Morozov E., Tarakanov R., Ivanova K. Internal waves in marginally stable abyssal stratified flow // Nonlin. Proces. Geophys., 2018, vol. 25, pp. 659–669.
- Makarenko N.I., Maltseva J.L., Morozov E.G., Tarakanov R.Yu., Ivanova K.A. Steady internal waves in deep stratified flows // J. Appl. Mech. Tech. Phys., 2019, vol. 60, no. 2, pp. 248–256.
- Carr M., Fructus D., Grue J., Jensen A., Davies P.A. Convectively induced shear instability in large amplitude internal solitary waves // Phys. Fluids, 2008, vol. 20, pp. 126601.
- Van Haren H., Gostiaux L., Morozov E., Tarakanov R. Extremely long Kelvin–Helmholtz billow trains in the Romanche fracture zone // Geophys. Res. Lett., 2014, vol. 44, pp. 8445–8451.
Supplementary files
