Morphological Evolution

Morphological evolution is computed using the sediment continuity equation, in which the time-averaged pickup and deposition rates are used. The sediment continuity equation is written as

(1)\[\frac{d \bar{Z}_b}{dt} = \frac{1}{1-n}(\bar{P} - \bar{D} - \nabla \cdot {\bar{\mathbf q}_b})\]

where \(\bar{Z}_b\) are the time-averaged depth changes with positive values for erosion and negative values for deposition, \(\bar{P}\) and \(\bar{D}\) are the time averaged pickup and deposition rates averaged over \(dt_{\mbox{morph}}\) in the suspended load model. \({\bar{\mathbf q}_b}\) represents the bedload flux vector averaged over the same time interval in the bedload model. In Tehranirad et al. (2016), \(dt_{\mbox{morph}} = 5 \sim 20\) is recommended to be small enough to capture bed changes induced by tsunami waves. In ship-wake applications, \(dt_{\mbox{morph}}\) should be smaller than the long wave cases. A specific range of morphological time step (\(dt_{\mbox{morph}}\)) for ship-wake applications, however, needs a further investigation based on numerical simulations carried out against measured data.