@Article{NMTMA-8-4,
author = {},
title = {A Conservative Formulation and a Numerical Algorithm for the Double-Gyre Nonlinear Shallow-Water Model},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2015},
volume = {8},
number = {4},
pages = {634--650},
abstract = {<p style="text-align: justify;">We present a conservative formulation and a numerical algorithm for the reduced-gravity shallow-water equations on a beta plane, subjected to a constant wind forcing that leads to the formation of double-gyre circulation in a closed ocean basin. The novelty of the paper is that we reformulate the governing equations into a nonlinear hyperbolic conservation law plus source terms. A second-order fractional-step algorithm is used to solve the reformulated equations. In the first step of the fractional-step algorithm, we solve the homogeneous hyperbolic shallow-water equations by the wave-propagation finite volume method. The resulting intermediate solution is then used as the initial condition for the initial-boundary value problem in the second step. As a result, the proposed method is not sensitive to the choice of viscosity and gives high-resolution results for coarse grids, as long as the Rossby deformation radius is resolved. We discuss the boundary conditions in each step, when no-slip boundary conditions are imposed to the problem. We validate the algorithm by a periodic flow on an $f$-plane with exact solutions. The order-of-accuracy for the proposed algorithm is tested numerically. We illustrate a quasi-steady-state solution of the double-gyre model via the height anomaly and the contour of stream function for the formation of double-gyre circulation in a closed basin. Our calculations are highly consistent with the results reported in the literature. Finally, we present an application, in which the double-gyre model is coupled with the advection equation for modeling transport of a pollutant in a closed ocean basin.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2015.m1408},
url = {https://global-sci.com/article/90590/a-conservative-formulation-and-a-numerical-algorithm-for-the-double-gyre-nonlinear-shallow-water-model}
}