Similarity solutions for spreading of a two-dimensional non-Newtonian gravity current in a porous layer

► We analyze horizontal spreading of power-law gravity currents in a porous layer. ► We derive similarity solutions to nonlinear problem; ODE solved numerically or analytically for special cases. ► Two different analytical approximations are derived for the general case. ► Rate of spreading of the current is a function of flow behavior index and injection rate. ► Current shape mostly sensitive to injection rate and moderately to flow behavior index.