Modelling turbulence generation in solitary waves on shear shallow water flows | Zendy

Gaël Loïc Richard | Zendy; Sergey Gavrilyuk | Zendy

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Modelling turbulence generation in solitary waves on shear shallow water flows

Author(s) -

Gaël Loïc Richard,

Sergey Gavrilyuk

Publication year - 2015

Publication title -

journal of fluid mechanics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.72

H-Index - 226

eISSN - 1469-7645

pISSN - 0022-1120

DOI - 10.1017/jfm.2015.236

Subject(s) - turbulence , mechanics , physics , waves and shallow water , shearing (physics) , shear (geology) , dispersion (optics) , shear flow , shear velocity , k epsilon turbulence model , classical mechanics , geology , optics , petrology , thermodynamics

International audienceWe derive a dispersive model of shear shallow water flows which takes into account a non-uniform horizontal velocity. This model generalizes the Green-Naghdi model to the case of shear flows. Besides the classical dispersion term in the Green-Naghdi model related to the acceleration of the free surface, it also contains a new dispersion parameter related to the flow structure. This parameter is related to the second moment of the velocity fluctuation with respect to the vertical coordinate. The distinction between shearing and turbulence based on the scale of variation of the velocity fluctuation is proposed. In particular, an equation for the turbulence generation is derived. Solitary waves for this model are obtained in explicit form. Comparison of solitary wave profiles with experimental ones is also performed. The agreement is very good apart from the small region near the top of the wave

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