Internal Solitary Waves in a Layered Weakly Stratified Flow
65
4450
4500
4550
Depth, m
14h 08'
15h 30'
Time, h (4 Dec 2013)
Fig. 4 Interfacial solitary wave affected by the Kelvin – Helmholtz instability
Time, h (4 Dec 2013)
Depth, m
12h 24'
13h 59'
4450
4500
4550
Fig. 5 Broad solitary wave with K–H billows
Conclusion
In this contribution we have considered the problem on stable internal waves at
the interface between the exponentially stratified fluid layers. An ordinary differential equation describing large amplitude solitary waves has been obtained using the
long-wave scaling procedure. Parametric range of the solitary waves is characterized
including extreme regimes such as broad plateau-shape solitary waves. It is demonstrated that these solitary wave regimes can be affected by the Kelvin–Helmholtz
instability generated due to the velocity shear at the interface.
Acknowledgements This work was supported by Russian Foundation for Basic Research (grant
No 15-01-03942). RYuT acknowledges the support by Russian Sciences Foundation (grant No
16–17-10149).
References
1. Benney, D. J., & Ko, D. R. S. (1978). The propagation of long large amplitude internal waves.
Studies in Applied Mathematics, 59, 187–199.
2. Choi, W., & Camassa, R. (1999). Fully nonlinear internal waves in a two-fluid system. Journal
of Fluid Mechanics, 396, 1–36.
65
4450
4500
4550
Depth, m
14h 08'
15h 30'
Time, h (4 Dec 2013)
Fig. 4 Interfacial solitary wave affected by the Kelvin – Helmholtz instability
Time, h (4 Dec 2013)
Depth, m
12h 24'
13h 59'
4450
4500
4550
Fig. 5 Broad solitary wave with K–H billows
Conclusion
In this contribution we have considered the problem on stable internal waves at
the interface between the exponentially stratified fluid layers. An ordinary differential equation describing large amplitude solitary waves has been obtained using the
long-wave scaling procedure. Parametric range of the solitary waves is characterized
including extreme regimes such as broad plateau-shape solitary waves. It is demonstrated that these solitary wave regimes can be affected by the Kelvin–Helmholtz
instability generated due to the velocity shear at the interface.
Acknowledgements This work was supported by Russian Foundation for Basic Research (grant
No 15-01-03942). RYuT acknowledges the support by Russian Sciences Foundation (grant No
16–17-10149).
References
1. Benney, D. J., & Ko, D. R. S. (1978). The propagation of long large amplitude internal waves.
Studies in Applied Mathematics, 59, 187–199.
2. Choi, W., & Camassa, R. (1999). Fully nonlinear internal waves in a two-fluid system. Journal
of Fluid Mechanics, 396, 1–36.