AUTHORS: Oxana Kurkina, Ekaterina Rouvinskaya, Andrey Kurkin, Lidiya Talalushkina, Ayrat Giniyatullin
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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 density stratification 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 waves 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. Thus for the solitary internal waves of positive polarity weakly nonlinear theory overestimates the near-bottom velocities and underestimates the near-surface current. For solitary waves of negative polarity, which are the most typical for hydrological conditions of low and middle latitudes, the situation is the opposite. II mode soliton’s velocity field in almost two-layer fluid reaches its maximal absolute values in a middle layer instead of near-bottom and near-surface maximums for I mode solitons.
KEYWORDS: Internal waves, Gardner equation, near-bottom velocity, near-surface velocity
REFERENCES:
[1] Jackson C.R., An Atlas of Internal Solitary-like Waves and Their Properties, 2nd ed., Global Ocean Associates, 2004, 560 p.
[2] Kurkina O.E., Ruvinskaya E.A., Pelinovsky E.N., Kurkin A.A., Soomere T., Dynamics of solitons in nonintegrable version of the modified Korteweg-de Vries equation, Journal of Experimental and Theoretical Physics Letters, 2012, Vol. 95, No. 2, pp. 91-95.
[3] Talipova T.G., Pelinovsky E.N., Kurkina O.E., Rouvinskaya E.A., Propagation of solitary internal waves in two-layer ocean of variable depth, Izvestiya. Atmospheric and Oceanic Physics, 2015, Vol. 51, No. 1, pp. 89-97.
[4] Rouvinskaya E., Talipova T., Kurkina O., Soomere T., Tyugin D., Transformation of Internal Breathers in the Idealised Shelf Sea Conditions, Continental Shelf Research, 2015, Vol. 110, pp. 60-71.
[5] Vlasenko V., Brandt P., Rubino A., Structure of Large-Amplitude Internal Solitary Waves, Journal of Physical Oceanography, 2000, Vol. 30, pp. 2172-2185.
[6] Rouvinskaya E., Kurkina O., Kurkin A., Investigation of the structure of large amplitude internal solitary waves in a three-layer fluid, Bulletin of Moscow State Regional University. Series “Physics and mathematics”, 2011, No. 2, pp. 61-74.
[7] Pelinovsky E., Polukhina O., Slunyaev A., Talipova T., Chapter 4 in the book “Solitary Waves in Fluids”, Boston: WIT Press. Southampton, 2007.
[8] Yang Y.J., Fang Y.C., Tang T.Y., Ramp S.R., Convex and concave types of second baroclinic mode internal solitary waves, Nonlinear Processes in Geophysics, 2010, Vol. 17, pp. 605-614.
[9] Kurkina O., Kurkin A., Rouvinskaya E., Soomere T., Propagation regimes of interfacial solitary waves in a three-layer fluid, Nonlinear Processes in Geophysics, 2015, Vol. 22, pp. 117-132.
[10] Kurkina O.E., Kurkin A.A., Pelinovsky E.N., Semin S.V., Talipova T.G., Churaev E.N., Structure of Currents in the Soliton of an Internal Wave, Oceanology, 2016, Vol. 56, No. 6, pp. 767-773.
