The linearization of the quadratic resistance term in the equations of motion for a pure harmonic tide in a canal and the identification of the Chézy parameter C

Abstract

In the hydrodynamic equations, which govern wave propagation in a shallow water basin, the friction term plays a very important rôle [10]. In the applications, however, the coefficient of this term is often unknown. In this paper an identification method is described for the 1-dimensional case.

The procedure requires first the approximation of the shallow water semi-linear time-dependent partial differential system by means of a linear time-dependent one in such a way that the equivalence of the dissipated energies is obtained. The usual separation of variables transforms then the time-dependent linear system into a time-independent one.

On the last system the identification is performed introducing a parametrization of the friction coefficient, a set of observed data and the least square error criterion. The minimization is obtained making use of the gradient method and introducing an adjoint partial differential system in order to compute exactly the derivatives of the error functional.