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We derive a hyperbolic system of equations approximating the two-layerdispersive shallow water model for shear flows recently proposed by Gavrilyuk,Liapidevskii \& Chesnokov (J. Fluid Mech., vol. 808, 2016, pp. 441--468). Theuse of this system for modelling the evolution of surface waves makes itpossible to avoid the major numerical challenges in solving dispersive shallowwater equations, which are connected with the resolution of an elliptic problemat each time instant and realization of non-reflecting conditions at theboundary of the calculation domain. It also allows one to reduce thecomputation time. The velocities of the characteristics of the obtained modelare determined and the linear analysis is performed. Stationary solutions ofthe model are constructed and studied. Numerical solutions of the hyperbolicsystem are compared with solutions of the original dispersive model. It isshown that they almost coincide for large time intervals. The system obtainedis applied to study non-stationary undular bores produced after interaction ofa uniform flow with an immobile wall, non-hydrostatic shear flows over a localobstacle and the evolution of breaking solitary wave on a sloping beach.

Hyperbolic Model for Free Surface Shallow Water Flows with Effects of Dispersion, Vorticity and Topography