Serre and Boussinesq Models for Favre Waves in Trapezoidal Cross-Sectional Channels

We present two mathematical models for weakly dispersive non-linear waves in prismatic channels of trapezoidal cross-sections. The first model, derived from a variational principle, is an extension of the well known Serre equations. The second one is a variation of Winckler and Liu’model (Winckler and Liu in J Fluid Mech 770:156–188, 2015 [1]), which belongs to the family of Boussinesq-type equations. Both are valid for arbitrary cross-sectional channels, but the very common case of constant, trapezoidal sections is investigated here in view of understanding and modelling Favre waves in such channels. The first model allows theoretical derivations in agreement with previous publications (including scale model measurements). The second model is well suited to numerical implementation and allows studying the dynamics of Favre waves. It is verified through an analytical solution and validated from published measured data.