Forcing a three-dimensional, hydrostatic, primitive-equation model for application in the surf zone: 1. Formulation

[1] An Eulerian analysis for wave forcing of three-dimensional (3D) wave-averaged mean circulation in the surf zone is presented. The objective is to develop a dynamically consistent formulation for applications in a 3D primitive equation model. The analysis is carried out for the case of shallow-water linear waves interacting with wave-averaged depth-independent horizontal currents that vary on larger space scales and timescales. Variations in wave properties are governed by a wave action equation that includes wave-current interactions and dissipation representative of wave breaking. Wave forcing of the mean currents consists of a surface stress and a body force. The surface stress is proportional to the wave energy dissipation. The body force includes one term that is related to gradients of part of the radiation stress tensor and a second term that is related to the vortex force and is proportional to a product of the mean wave momentum and the vertical component of the mean vorticity vector. In addition, there is a nonzero normal velocity at the mean surface that arises from the divergence of the mean Eulerian wave mass flux. This velocity results in an additional momentum flux forcing of the mean flow. Applications of this formulation to the DUCK94 field experiment are presented in part 2.