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Optimal control of the Primitive Equations of the ocean with Lagrangian observations

Published online by Cambridge University Press:  21 April 2009

Maëlle Nodet
Maëlle Nodet*
Affiliation:
Université de Grenoble, INRIA. maelle.nodet@inria.fr
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Abstract

We consider an optimal control problem for the three-dimensional non-linear Primitive Equations of the ocean in a vertically bounded and horizontally periodic domain. We aim to reconstruct the initial state of the ocean from Lagrangian observations. This inverse problem is formulated as an optimal control problem which consists in minimizing a cost function representing the least square error between Lagrangian observations and their model counterpart, plus a regularization term. This paper proves the existence of an optimal control for the regularized problem. To this end, we also prove new energy estimates for the Primitive Equations, thanks to well-chosen functional spaces, which distinguish the vertical dimension from the horizontal ones. We illustrate the result with a numerical experiment.

Keywords

Optimal controlpartial differential equationsPrimitive Equationsnumerical simulation
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 2 , April 2010 , pp. 400 - 419
Copyright
© EDP Sciences, SMAI, 2009

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