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Article Dans Une Revue International Journal of Non-Linear Mechanics Année : 2020

Variational formulation for models of shear shallow water flows and ideal turbulence

Résumé

The shallow water equations without shear effects are similar to the gas dynamics equations with a polytropic equation of state. When the shear effects are taken into account, the equations contain additional evolution equations mathematically analogous to those of the Reynolds stresses in turbulent flows of compressible fluids when the source terms are neglected (ideal turbulence). We show that the non-dissipative model of shear shallow water flows and the model of ideal turbulence admit a similar variational formulation where, in the both cases, the equations for the Reynolds stress tensor evolution are considered as non-holonomic constraints.
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Dates et versions

hal-02148064 , version 1 (05-06-2019)
hal-02148064 , version 2 (20-11-2019)

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Sergey L Gavrilyuk, Henri Gouin. Variational formulation for models of shear shallow water flows and ideal turbulence. International Journal of Non-Linear Mechanics, 2020, 119, pp.103312. ⟨10.1016/j.ijnonlinmec.2019.103312⟩. ⟨hal-02148064v2⟩
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