Abstract: In this paper, a numerical model for predicting the unsteady nearshore circulation due to wave-current interaction was proposed. In addition to the traditional continuity, momentum and energy equations, the dispersion and refraction relations were included in the governing equations. Moreover, the effects of lateral shears, wind, radiation and bottom stresses were analysed in the governing equations. Therefore, we expect that this model may more completely and exactly reflect the law of wave-current interaction.In part (Ⅱ) we will adopt the.selective lumping two-step explicit finite element method to solve the model, and some examples will be presented.

Key words: Hilbert space, coercivity condition, compact, imbedding mapping, elliptic equation, numerical model, finite element method, unsteady circulation, nearshore circulation