Isostatic depth partition of an interfacial current ($({\rho }_0-{\rho }_1)h_1=-({\rho }_2-{\rho }_0)h_2$)

Hydrostatic pressure continuity across both interfaces fixes the partition of current thickness. The modified current pressure is $\Delta \rho gh$, with $\Delta \rho =({\rho }_0-{\rho }_1)({\rho }_2-{\rho }_0)/({\rho }_2-{\rho }_1)$. The equivalent radial body force is $-\Delta \rho g{h}_r{\mathbf{e}}_r$.