Analytical Solution of One-Dimensional Bay Forced by Sea Breeze

This paper introduces a closed-form analytical solution of the one-dimensional (1D), depth-averaged linearized momentum and continuity equations that incorporates linear bottom friction and the non-linear wind stress. The solution describes wind-forced motion in a 1D basin with horizontal bottom as governed by water depth, basin length, bottom friction coefficient, wind speed, and fundamental frequency of an oscillatory wind. The solution displays in compact form general behavior and dependencies of the physical processes, including generation of wind-induced harmonies of the forcing motion, damping, and resonance. The solution can serve as a benchmark test for numerical models of the shallow-water equations, as well as provide estimates of wind-induced motion in enclosed water bodies.