  A numerical method is proposed for solving the two layer shallow water
equations with variable bathymetry in one dimension based on high-resolution
f-wave-propagation finite volume methods. The method splits the jump in the
fluxes and source terms into waves propagating away from each grid cell
interface. It addresses the required determination of the system's
eigenstructure and a scheme for evaluating the flux and source terms. It also
handles dry states in the system where the bottom layer depth becomes zero,
utilizing existing methods for the single layer solution and handling single
layer dry states that can exist independently. Sample results are shown
illustrating the method and its handling of dry states including an idealized
ocean setting.
