@Article{IJNAM-10-571,
author = {A. Kacimi, T. Aliziane and B. Khouider},
title = {The Arakawa Jacobian Method and a Fourth-Order Essentially Nonoscillatory Scheme for the Beta-Plane Barotropic Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2013},
volume = {10},
number = {3},
pages = {571--587},
abstract = {<p style="text-align: justify;">In this paper we use the Arakawa Jacobian method [1] and the fourth-order essentially
non-oscillatory (ENO-4) scheme of Osher and Shu [15] to solve the equatorial beta-plane barotropic
equations. The Arakawa Jacobian scheme is a second order centred finite differences scheme that
conserves energy and enstrophy. The fourth-order essentially non-oscillatory scheme is designed
for Hamilton-Jacobi equations and traditionally used to track sharp fronts. We are interested in
the performance of these two methods on the baratropic equations and determine whether they
are adequate for studying the barotropic instability. The two methods are tested and compared
on two typical exact solutions, a smooth Rossby wave-packet and a discontinuous shear, on the
long-climate scale of 100 days. The numerical results indicate that the Arakawa Jacobian method
conserves energy and enstrophy nearly exactly, as expected, captures the phase speed the Rossby
wave, and achieves an overall second order accuracy, in both cases. The same properties are
preserved by the ENO-4 scheme but the fourth order accuracy is observed only for the smooth
Rossby wave solution while in the case of the discontinuous shear, it yields an overall third order
accuracy, even in the smooth regions, away from the discontinuity.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/583.html}
}