Lubrication theory for viscous currents with S = 1

Here we consider the prototype thin viscous current which propagates over a horizontal solid boundary in a linearly-stratified ambient such that ρc = ρb = ρa(z = 0). This corresponds to the S = 1 case and is also relevant to an intrusion. The non-stratified counterpart is considered in Chapter 11. The system satisfies the Boussinesq assumption.