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We investigate, within the framework of the nonlinear shallow water equations (NSWE), the generation and evolution of large-scale eddies with vertical axis (macrovortices hereinafter) which are responsible for much of the horizontal mixing occurring at the boundaries between the main channel and the flood planes of a compound channel. We show that the mechanism of generation of vorticity is essentially inviscid and is analogous to that occurring at a curved shock. Numerical experiments performed by means of a recently developed shock-capturing model for the solution of the NSWE, and described in Brocchini et al. (2001), clarify some features of macrovortices generation and allow us to quantify the momentum transfer across the channel.

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A numerical method is proposed to study the scattering of seismic shear waves induced by the presence of underground cavities in homogeneous soils. The method is based on the superposition of two solutions: the solution of the free-wave propagation problem in a uniform half-space, easily determined analytically, and the solution of the wave scattering problem due to the cave presence, evaluated numerically by means of an ad hoc code implemented by using the ANSYS Parametric Design Language. In the twodimensional setting, this technique is applied to the case of a single cave, placed at a certain depth from the ground level. The frequency spectrum of the seismic shear oscillation on the ground surface is determined for different dimensions and depths of the cave and compared with the spectrum registered without caves. The influence of the cave dimensions and depth on the spectrum amplification is analyzed and discussed.