Tides in Coastal Seas. Influence of Topography and Bottom Friction

Tides are important in various ways, e.g., by affecting navigation and coastal safety and by acting as a driver for sediment transport and seabed dynamics. To explain spatial patterns of tidal phase and range, observed in coastal seas around the world, we present an idealised process-based model. It solves the depth-averaged linearised shallow water equations, including the Coriolis effect and bottom friction, on schematised geometries with rectilinear coastlines and stepwise topographic variations. Based on an extended Klein-Gordon equation (accounting for bottom friction), Kelvin and Poincaré modes are identified as the fundamental wave solutions in a channel of uniform width and depth. We analyse their spatial structures and dynamic properties, addressing the roles of bottom friction and transverse topographic steps. The solution for a semi-enclosed basin, including topographic steps, is then obtained as a superposition of these wave modes, by applying a collocation technique. As an example, we present solutions that grossly explain the amphidromic system of the Gulf of California. Finally, we discuss the modelling approach and address the links with morphodynamics and climate change.