A hydrodynamic model for the hydraulic jump and internal wave generation over a bottom topography, the case of the San Esteban sill in the Gulf of California

¹ Mathematics Department, Centro de Investigación en Matemáticas, Jalisco S/N, Valenciana, Guanajuato GTO 36023, Mexico
² Physics Department, Universidad de Guadalajara, Blvd. Marcelino García Barragán 1421, Guadalajara JAL 44430, Mexico

^* Corresponding author: moreles@cimat.mx

Received: 24 October 2023
Accepted: 8 November 2024

Abstract

We are concerned with the mathematical and numerical modeling of hydrodynamic processes in the Gulf of California. The dynamic is driven by a forcing tide producing an inflow and outflow from the mouth of the Gulf to the northernmost part. When the tidal flow passes through the area of the Islands in the central part of the Gulf, it channels, increasing its speed. On the San Esteban Sill, a hydraulic jump is formed, then internal waves and solitons are released. Based on observational field campaigns, and hydrostatic 3D modeling, it is claimed that this is a cause–effect phenomenon. Hydrostatic models are unable to produce the groups of soliton-like waves. Consequently, we develop a non-hydrostatic version, a 2D vertical-slice model with the inclusion of density effects. Its hydrographic characteristics, such as stratification and bathymetric features, are modeled with appropriate initial and boundary conditions. The numerical solution is by a pressure projection method. The method is tested on benchmark problems and then applied to the Gulf of California. The data of the observational field campaigns are satisfactorily reproduced by the numerical results.