Rotational surf zone modeling for O(μ4) Boussinesq-Green-Naghdi systems

A surf zone model is developed and tested based on the O(μ4) Boussinesq-Green-Naghdi system of Zhang et al. (2013). Because the model is fundamentally rotational, it uses fewer ad hoc assumptions than are found in many Boussinesq breaking wave systems. Eddy viscosity is used to describe both breaking dissipation and bottom friction, with breaking viscosities derived from the turbulent kinetic energy equation coupled with an O(μ4) rotational wave model. In contrast, bottom friction is included by imposing the frictional coefficient-derived boundary stress as an equivalent eddy viscosity. Numerical tests for one horizontal dimension show good agreement with regular and irregular wave breaking tests, and for solitary wave runup. Surface elevation decay, setup, runup, interior orbital velocities, and depth-varying undertow velocities can all be modeled reasonably. Comparison with an O(μ2) system shows similar performance for water surface elevations in the surf zone, demonstrating that the dissipation model is the major controlling factor. However, the O(μ4) model shows significantly improved representations of the velocity profile in the surf zone, as expected.