Though Boussinesq-type wave equations are widely used in the nearshore wave field, it is still a challenge for these kinds of equations to describe the velocity profiles along water column after wave breaking occur. For example undertow, plays a key role in generating sandbars, is quite difficult to be simulated by a Boussinesq-type model (usually used in a phase-resolving beach evolution model). The ad-hoc method developed by Lynett (wave breaking velocity effects in depth integrated models. Coastal Engineering, 2006, 53(4):325–333.) seems greatly improve the performance of Boussinesq-type equations for undertow calculation. However this method is a post-processing modification skill, the accurate prediction of undertow profiles greatly depends on the accuracy of predicted wave elevation and depth averaged velocities before modification. Hence Boussinesq-type equations with fully nonlinear characteristics instead of those with only weak nonlinearity should be used to simulate breaking waves, as proved by many researches that the former could give better results than the later in wave breaking zone. In the present paper, a new set of fully nonlinear Boussinesq equations and the above mentioned ad-hoc method are combined to form a wave breaking model, aiming to simulate the undertow profiles. The model is first validated by simulating regular waves breaking on a plane beach, then the undertow profiles are calculated, numerical results are compared against three available data sets and the performance of wave breaking model before and after modification is detailed discussed.
However, these kinds of wave modules belong to depth-integrated models with a typical assumption that the vertical profile of velocity can be represented by a polynomial, wherein the order of the polynomial is proportional to the accuracy of the resulting model. Implicit with this velocity profile, and often a direct inviscid assumption, is a lack of ability to simulate turbulence.
