Geodesic
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
Danalie de los Angeles Azofeifa-Chaves1 ; Federico Angel Velázquez Muñoz2 ; Anatoliy Filonov2 ; Miguel Angel Moreles1
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
Mathematical modelling of natural phenomena, Tome 19 (2024), article no. 23.

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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.
DOI : 10.1051/mmnp/2024019

Danalie de los Angeles Azofeifa-Chaves 1 ; Federico Angel Velázquez Muñoz 2 ; Anatoliy Filonov 2 ; Miguel Angel Moreles 1

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 
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Danalie de los Angeles Azofeifa-Chaves; Federico Angel Velázquez Muñoz; Anatoliy Filonov; Miguel Angel Moreles. 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. Mathematical modelling of natural phenomena, Tome 19 (2024), article  no. 23. doi : 10.1051/mmnp/2024019. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2024019/

[1] J.C. Garwood, R.C. Musgrave, A.J. Lucas Life in internal waves Oceanography 2020 38 49

[2] R.N. Ibragimov, A. Tartakovsky Spectral analysis of the efficiency of vertical mixing in the deep ocean due to interaction of tidal currents with a ridge running down a continental slope Math. Model. Natural Phenomena 2014 119 137

[3] M.F. Lavín and S.G. Marinone, An overview of the physical oceanography of the gulf of california. Nonlinear- Processes in Geophysical Fluid Dynamics: a tribute to the scientific ‘work of Pedro Ripa (2003) 173–204.

[4] F.A. Velazquez-Munoz, A. Filonov Tidal energy flows between the midriff islands in the gulf of California Energies 2021 621

[5] A. Filonov, I. Tereshchenko, L.B. Ladah, D.A. Pantoja-Gonzalez, F.A. Velazquez-Muñoz High amplitude internal tidal waves generated over an underwater sill in the gulf of california Continent. Shelf Res 2020 104290

[6] A.F. Blumberg, G.L. Mellor A description of a three-dimensional coastal ocean circulation model Three- dimensional Coastal Ocean Models 1987 1 16

[7] C. Ai, Y. Ma, C. Yuan, G. Dong Non-hydrostatic model for internal wave generations and propagations using immersed boundary method Ocean Eng 2021 108801

[8] J. Kampf, Advanced Ocean Modelling: Using Open-source Software. Springer Science Business Media (2010).

[9] A.S. Almgren, J.B. Bell, W.Y. Crutchfield Approximate projection methods: Part I. Inviscid analysis SIAM J. Sci. Comput 2000 1139 1159

[10] O.B. Fringer, S.W. Armfield, R.L. Street Reducing numerical diffusion in interfacial gravity wave simulations Int. J. Numer. Methods Fluids 2005 301 329

[11] N.L. Fischer, H.P. Pfeiffer Unified discontinuous Galerkin scheme for a large class of elliptic equations Phys. Rev. D 2022 024034

[12] T. Bui-Thanh From Godunov to a unified hybridized discontinuous Galerkin framework for partial differential equations J. Computat. Phys 2015 114 146

[13] R.A. Locarnini, T.P. Boyer, A.V. Mishonov, J.R. Reagan, M.M. Zweng, O.K. Baranova, H.E. Garcia, D. Seidov, K.W. Weathers, C.R. Paver World Ocean Atlas 2018, Vol. 5: Density NOAA Atlas NESDIS 2019 41

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