Skip to main content
Log in

Vertical structure of the velocity field induced by mode-I and mode-II solitary waves in a stratified fluid

The European Physical Journal E Aims and scope Submit manuscript

Abstract.

The structure of the velocity field induced by internal solitary waves of the first and second modes is determined. The contribution from second-order terms in asymptotic expansion into the horizontal velocity is estimated for the models of almost two- and three-layer fluid for solitons of positive and negative polarity. The influence of the nonlinear correction manifests itself firstly in the shape of the lines of zero horizontal velocity: they are curved and the shape depends on the soliton amplitude and polarity, while for the leading-order wave field they are horizontal. Also the wave field accounting for the nonlinear correction for mode I has smaller maximal absolute values of negative velocities (near-surface for the soliton of elevation, and near-bottom for the soliton of depression) and larger maximums of positive velocities. For solitary waves of negative polarity, which are the most typical for hydrological conditions in the ocean for low and middle latitudes, the situation is the opposite. The velocity field of the mode-II soliton in a smoothed two-layer fluid reaches its maximal absolute values in a middle layer instead of near-bottom and near-surface maximums for mode-I solitons.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C.R. Jackson, An Atlas of Internal Solitary-like Waves and Their Properties, 2nd edition (Global Ocean Associates, 2004)

  2. O.E. Kurkina et al., JETP Lett. 95, 91 (2012)

    Article  ADS  Google Scholar 

  3. T.G. Talipova et al., Izv. Atmos. Ocean. Phys. 51, 89 (2015)

    Article  Google Scholar 

  4. E. Rouvinskaya, Cont. Shelf Res. 110, 60 (2015)

    Article  ADS  Google Scholar 

  5. V. Vlasenko, P. Brandt, A. Rubino, J. Phys. Oceanogr. 30, 2172 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  6. E. Rouvinskaya, O. Kurkina, A. Kurkin, Bulletin of Moscow State Regional University, Series “Physics and Mathematics” Vol. 2 (2011) p. 61

  7. E. Pelinovsky, Solitary Waves in Fluids (WIT Press, Boston, Southampton, 2007) Chapt. 4

  8. O. Kurkina et al., Nonlinear Process. Geophys. 24, 645 (2017)

    Article  ADS  Google Scholar 

  9. Y.J. Yang et al., Nonlinear Process. Geophys. 17, 605 (2010)

    Article  ADS  Google Scholar 

  10. O. Kurkina et al., Nonlinear Process. Geophys. 22, 117 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  11. O.E. Kurkina et al., Oceanology 56, 767 (2016)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Efim Pelinovsky.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kurkina, O., Rouvinskaya, E., Kurkin, A. et al. Vertical structure of the velocity field induced by mode-I and mode-II solitary waves in a stratified fluid. Eur. Phys. J. E 41, 47 (2018). https://doi.org/10.1140/epje/i2018-11654-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2018-11654-3

Keywords

Navigation