Analytical solutions for testing of baroclinic and wind-driven three-dimensional hydrodynamic models

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DOI

https://doi.org/10.4236/jamp.2024.128171

Language of the publication
English
Date
2024-08-20
Type
Article
Author(s)
  • He, Cheng
Publisher
Scientific Research Publishing

Abstract

It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.

Subject

  • Nature and environment,
  • Science and technology

Rights

Pagination

2866-2884

Peer review

Yes

Open access level

Gold

Identifiers

ISSN
2327-4379
2327-4352

Article

Journal title
Journal of Applied Mathematics and Physics
Journal volume
12
Journal issue
8
Accepted date
2024-08-17
Submitted date
2024-07-12

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Collection(s)

Water

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