CONDUIT SOLITARY WAVES IN A VISCOELASTIC MEDIUM

The theory for waves on a buoyant fluid conduit in a more viscous oute r fluid is extended to include a visco-elastic outer fluid. The extern al fluid is treated as a linear Kelvin-type visco-elastic medium and a wave evolution equation is derived. This equation is identical to the purely viscous case with the exception of a new term representing the elastic effects. A conservation law is derived and used in an analyti c treatment for a slowly-varying solitary wave (given initially by the exact solution to the purely viscous case) for the case of small, but non-zero, elasticity. The theory shows that the wave amplitude will d ecay and a shelf. required for the conservation of mass, will develop behind the wave. Numerical solutions of the evolution equation support the analytic approximation. Laboratory experiments show qualitative a greement with the analytic and numerical development. Geophysical appl ications suggest that these effects may be most important for melt mig ration in the asthenosphere.