Ph.D. Dissertation Defense: Jose H. Garcia
Beta-Plane Approximation of Wind Driven Ocean Circulation using a First Order System Least-Squares Formulation
Jose H. Garcia
Applied Mathematics,Ìý
Date and time:Ìý
Thursday, April 3, 2014 - 4:00pm
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Grandview Conference Room at 1320 Grandview Ave
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Earth's oceans represent roughly 70% of the total surface of the planet. Their sheer size and the nature
of salty water as a fluid, makes them the biggest repository of heat for the planet and as such, it makes
them very signicant in driving many of the complex phenomena of Earth's climate. Ocean models give us
a glimpse into the nature of the oceans and are essential tools for understanding the Earth's climate.
A fundamental component of an Earth's Ocean model is its dynamical core, which simulates the movement
of the fluid in a rotational frame of reference. For this research, the model is described by the Incompressible
Navier-Stokes equations in a rotational frame of reference.
We present an alternative First Order Least-Squares Finite Element formulation for the numerical solution
of the stationary linear problem. The formulation is considered in all three spatial dimensions, i.e., without
the hydrostatic hypothesis most often used in other numerical models based on the hydrostatic primitive
equations [1].
In order to validate the computer model, a classical experiment for Beta-Plane approximation of wind
driven ocean circulation is utilized. To this extend, the sliced cylinder model introduced by Pedlosky &
Greenspan (1967) [2] denes the physical domain. The focus of the validation process is the analysis of the
solution for two expected phenomena, the thin Ekman layers induced in the system as well as the east-west
asymmetry of the pressure eld for the interior circulation.
References
[1] Iskandarani, M and Haidvogel, D.B. and Levin, J.C. A three-dimensional spectral element model for the
solution of the hydrostatic primitive equations, Journal of Computational Physics, 2003, 186, 2, 397{425
[2] R. C. Beardsley (1969). A laboratory model of the wind-driven ocean circulation. Journal of Fluid Me-
chanics, 38, pp 255-271