Influences of coriolis force and friction on fluid dynamics in specific paraboloid basins

Abstract

Natural water features, such as rivers, lakes, bays, and straits, exhibit diverse shapes and dynamics. Among these, paraboloid basins, resembling the contours of lakes or closed bays, offer a relatively simple yet intriguing case. This study delves into the dynamics of water waves within two distinct paraboloid basin variations: the parabolic canal and the circular paraboloid. In this investigation, we analyze shoreline movement, considering influential factors such as bottom friction and the Coriolis effect through a mathematical model. The foundation of our analysis lies in the two-dimensional shallow water equations, with the Thacker assumption serving as the basis for deriving an analytical solution. To enhance our understanding, we employ a numerical solution, employing the finite volume method on a staggered grid, to simulate wave behavior within these basin variations. For validation, we compare these numerical findings with our analytical solution. Furthermore, this study conducts a sensitivity analysis of the Coriolis parameter and bottom friction parameter under various conditions. Through this exploration, we gain valuable insights into the interplay of these critical factors in shaping the oscillation of water within paraboloid basins, enriching our understanding of coastal and basin dynamics.