A model of wind‐driven currents and transport of substances in unstratified water bodies is presented. The model employs a coordinate system, consisting of curvilinear functions that are orthogonal in the horizontal plane and a coordinate of “normalized depth.” The method of merging asymptotic expansions was used to obtain analytical expressions for components of current velocity as functions of wind stress and pressure anomaly gradient. The pressure anomaly was calculated using an equation that describes the influence of bottom topography, Coriolis force, inertial forces, wind friction, bottom friction and lateral fri