Analytical Expression for Tidal Damping in Alluvial Estuaries

An expression for tidal damping or amplification is derived through an analytical solution of the St. Venant's equations in a Lagrangian reference frame. Whether damping or amplification occurs depends on the balance between a friction term and an amplification term. The friction term is composed of the friction number g/C2, the Froude number F, a friction factor f, and the wave-type number, sin(ε). The amplification term consists of the estuary shape number h/b, which is large in deep and strongly tapering estuaries, and which is small in shallow estuaries of near constant cross section. The degree of damping or amplification further depends on the tidal range-to-depth ratio H/h. The expression derived appears to correspond very well with numerical solutions of the St. Venant equations for estuaries where H/h< 1. Most natural estuaries belong to that category.