Response of a viscous incompressible fluid cylinder to an incident plane compressional elastic wave
- Univ. Central de Venezuela, Caracas (Venezuela)
A longitudinal-plane harmonic wave propagating in an elastic matrix medium impinges upon an infinitely long circular fluid cylinder. The cylinder is made of an incompressible viscous fluid at low Reynolds number. The radius of the cylinder is small compared with the wave-length of the incoming wave. This allows the introduction of a small parameter {epsilon} {equivalent_to} k{sub p}a where k{sub p} is the longitudinal wave number and a is the radius of the cylinder. The fluid is assumed to be of high viscosity, and as a result the Reynolds number, Re, is O({epsilon}{sup 2}). A regular expansion of the solution when {epsilon} {yields} 0 is not enough to describe the amplitude of the solution far from the obstacle. Therefore, a singular perturbation technique is applied and the motion in the far field is obtained. The fluid inertia terms enter into the calculation of the elastic potentials inner expansions at O({epsilon}), through the pressure term present in the radial stress. An expression for the scattering cross section for normally incident plane compressional waves from cylindrical obstacle of any cross section is derived in terms of the far field solution. It depends on three dimensionless parameters, a measure of the fluid viscosity, the ratio of the fluid inclusion density to the elastic medium density, and the ratio of wave speeds in the solid. Consequently, the fluid density affects the scattering cross section dominant term, in contrast with the result obtained where a Stokes approximation for the fluid equations was assumed at all orders. An analysis of the energy scattered by the fluid inclusion when the above parameters vary in their typical physical ranges is performed. A long cylindrical cavity containing the fluid seems to be an important geometry in applications. For example, long, thin cracks saturated by oil in sedimentary rocks may correspond to this model.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 227916
- Journal Information:
- SIAM Journal of Applied Mathematics, Vol. 56, Issue 2; Other Information: PBD: Apr 1996
- Country of Publication:
- United States
- Language:
- English
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