Exact solutions are presented for Burgers' equation in a finite layer connected to an underlying semi-infinite medium of different conductivity and diffusivity. A constant-flux boundary condition is assumed at the surface. This has direct application to steady rainfall on layered field soils. At large times, a travelling wave profile develops in the deep layer and the concentration in the upper layer approaches a non-trivial steady state. Water flux and potential energy are continuous across the interface but the concentration gradient may show a marked discontinuity.
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- Information Systems and Management
- Control and Systems Engineering
- Applied Mathematics
- Computational Mathematics
- Modeling and Simulation