Stability and accuracy of Runge-Kutta-based split-explicit time-stepping algorithms for free-surface ocean models

<p>Because of the Boussinesq assumption employed in the vast majority of oceanic models,<br>the acoustic waves are filtered and the fast dynamics corresponds to the external<br>gravity-wave propagation which is much faster than other (internal) processes.<br>The fast and slow dynamics are traditionally split into separate subproblems<br>where the fast motions are nearly independent of depth. &#160;It is thus natural to<br>model these motions with a two-dimensional (barotropic) system of equations while<br>the slow processes are modeled with a three-dimensional (baroclinic) system.<br>However such splitting is inexact, the barotropic mode is not strictly depth-independent<br>meaning that the separation of slow and fast modes is non-orthogonal, even in the linear case.<br>A consequence is that there are some fast components contained in the slow motions which induce<br>instabilities controlled by time filtering of the fast mode.<br>In this talk we present an analysis of the stability and accuracy of the barotropic&#8211;baroclinic mode splitting<br>in the case where the baroclinic mode is integrated using a Runge-Kutta<br>scheme and the barotropic mode is integrated explicitly (i.e. the so-called split-explicit approach).<br>By referring to the theoretical framework developed by Demange et al. (2019),<br>the analysis is based on an eigenvector decomposition using the true<br>(depth-dependent) barotropic mode. We investigate several strategies to achieve stable<br>integrations whose performance is assessed first on a theoretical ground and then<br>by idealized linear and nonlinear numerical experiments.</p>