Nonlinear Acoustics and Shock Waves in Sediments and Fluid-Filled Porous Media

摘要

Progress has been made in establishing the appropriate master system of equationssuitable for modeling shock waves and nonlinear wave phenomena in fluid-permeable porous solids. The major accomplishments are: (1) Numerical experiments establishing the existence of shock waves in a 1D system with both Darcy and Navier-Stokes viscosities. (2) The general form of the equations of motion have been deduced from Hamilton's principle of Least Action combined with Onsager's method of irreversible thermodynamics. (3) We analyzed the specific case of a layered fluid/solid medium in depth, and obtained explicit formulas for the nonlinear strain energy and the permeability operator. (4) We have extended the methods of acoustoelasticity to poroelastic media. (5) We have examined the stability of acoustic disturbances in a simple model of a porous medium with a mean flow through the pores.