Roller Stresses

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As a wave transitions from non-breaking to fully-breaking, some of the energy is converted into momentum that goes into the aerated region of the water column. This phenomenon is known as the surface roller. The surface roller contribution to the wave stresses (R_{ij}) is given by

R_{ij} = 2E_{sr}w_i w_j


E_{sr} = surface roller energy density [N/m]
w_j = wave unit vector = (cos\  \theta_m, sin\  \theta_m ) [-]

The surface roller is calculated within CMS-Wave. An effect of the surface roller is to shift the peak alongshore current velocity closer to shore. Another side effect of the surface roller is to improve model stability (Sánchez et al. 2011a). The influence of the surface roller on the mean water surface elevation is relatively minor (Sánchez et al. 2011a).


  • Sánchez, A., and W. Wu. 2011a. A non-equilibrium sediment transport model for coastal inlets and navigation channels. Journal of Coastal Research, Special Issue (59):39–48.

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