3D Analytical Solution to Tidal Equations in a Narrow Bay with Combined Lateral and Longitudinal Varying Topography

Progressive modifications in submarine topography and shorelines drastically affect tidal dynamics in bays. This study examines the influence of topographic slope, bay length, and driving forces on tidal currents following land reclamation. Tidal equations are analytically solved using infinite series, deriving expressions for tidal levels and currents in narrow bays with varying topography. Tidal levels, influenced by topographic variations, are characterized by amplitude and phase lag of their complex amplitude. These levels demonstrate high sensitivity to longitudinal slope variations but remain relatively stable under lateral slope changes. Under constant topographic slopes, even minor changes in bay length can drastically modify amplitude and phase lag, highlighting the sensitivity of tidal dynamics to geometric alterations. Tidal velocity notably increases with steeper longitudinal slopes and modestly rises with elevated lateral slopes. However, changes in longitudinal and lateral slopes do not considerably alter flow patterns. While external forces predominantly regulate tidal velocity with negligible effects on flow patterns, endogenous resistance influences velocity but minimally impacts flow structure. These findings enhance the understanding of tidal responses to geometric and topographic changes, providing valuable guidance for land reclamation projects and coastal management strategies.