In the numerical modeling of ocean circulation, it is a widespread practice to employ a barotropic-baroclinic time splitting, for which the fast external motions are modeled by a vertically-integrated (barotropic) system that is similar to the shallow water equations and is solved with a relatively short time step. The remaining motions are modeled by solving the full dynamical equations with a relatively long time step. The present talk is concerned with layered (isopycnic) models, for which the vertical coordinate is a quantity related to density. It is assumed here that discontinuous Galerkin (DG) methods are used for the spatial discretization. During the construction of numerical algorithms for this case, some issues to be addressed include the following. (1) There may be regions where one or more layers reduce to negligible thickness. In this case there are problems with extracting velocity from the momentum and mass variables. In addition, numerical algorithms should maintain nonnegative layer thickness. (2) There should be suitable communication between the two subsystems, which employ greatly different timesteps. (3) It is possible for substantial grid-scale noise to arise in the mass, momentum, and velocity fields, such as within and near thin layers. In the present work, problem (3) is addressed by applying a vertex limiter to the mass, momentum, and velocity fields. This limiting should be applied to both subsystems. Ensuring suitable communication between those subsystems raises the prospect of considerable complexity, but this is alleviated by using the idea that the vertical sums of layer variables should equal the corresponding barotropic variables. Another difficulty is that the velocity is not a conserved quantity, so extra steps are used to ensure that the velocity is adjusted in a way that conserves momentum. The results of some numerical computations will be used to illustrate the ideas discussed above.