A new theoretical approach is presented for the derivation of free surface profiles of two-dimensional steady and unsteady flows by solving the Reynolds-averaged Navier-Stokes equations applied to the turbulent flow regime. This approach enables us to compute the steady and unsteady curvilinear flows having small curvatures, such as free overfall and constant velocity surge. In addition, the applications of the theory to the second-order waves are illustrated through the problems of small height bore and second-order tide.
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Bose et al. (2007) studied this question.
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