Tidal Energy Dissipation in Well-mixed Estuaries

Abstract

Long water waves are strongly distorted and lose substantial energy as they propagate through shallow estuarine waters. The energy dissipation is mainly due to increased bottom frictional effects. Using the linearized Telegrapher's equations, an analytical expression is obtained for tidal energy dissipation in terms of estuarine geometric features and tidal harmonic parameters. For estimating the harmonic parameters, the full St. Venant system of equations is numerically solved and a large amount of data is generated for hypothetical one-dimensional, well-mixed estuaries, subject to semi-diurnal tidal action. Relations are then developed expressing the tidal energy dissipation as a function of prevailing macroscopic estuarine features. The effectiveness and applicability limitations of linearization are discussed. Simulation results are verified with actual data, The average tidal energy dissipation was found to be proportional to the third power of the tidal Reynolds number, This result is in agreement with experimental data and theories pertaining to rate of energy dissipation, diffusion in homogeneous turbulent flow and dispersion in shear flow.