Coarse resolution, hydrostatic ocean models are known for their relatively poor representation of some climatically important processes. For example, downslope flows play a key role in the sinking branches of the meridional overturning circulation, yet the present generation of global scale level coordinate ocean climate models poorly resolve the associated physics. Coarse resolution level coordinate models tend to spuriously dilute overflowing waters. The associated gravity driven currents are generally very sluggish, often failing to penetrate to realistic depth. In this study an embedded Lagrangian model to represent downslope flows has been developed and implemented in the GFDL Modular Ocean Model. The Lagrangian model has been tested in two idealized configurations, showing significant differences with traditional parameterisations. These differences indicate that the embedded Lagrangian model is a promising method by which we could parameterise overflows in ocean climate models.