Newton's third law of motion says, basically, that if you push on me then I push back automatically, even if I do not want to. Fulfilling this condition can be a problem when a discontinuous Galerkin numerical method is applied to a layered model of ocean circulation. The dependent variables can be discontinuous across cell edges, and in particular the one-sided limits of the pressure forcing at an edge need not be equal. One way to define values of the solution at a cell edge is to employ a Riemann problem, in which the dynamics of the PDE are used to interpolate between two states. However, in a model with many layers a Riemann problem could be highly complicated. A much more manageable alternative developed here is to use ideas related to barotropic-baroclinic time splitting to reduce the Riemann problem to a simpler system of lower spatial dimension. This approach is tested in a model problem involving geostrophic adjustment, which is an important process in geophysical fluid flows.