Thompson, Charles

Direct numerical solutions of the three-dimensional time-dependent Navier-Stokes equation are presented for the evolution of three-dimensional finite-amplitude disturbances in the Stokes boundary layer. The basic flow is driven harmonically in time and the disturbances represent a departure from the basic state of the fluid. For fixed value of the fluid viscosity, instability is shown to be a function of the amplitude of oscillation of the basic flow, excitation frequency, and the channel wall geometry. Special attention is given to pressure gradient and surface wave driven flows. Conditions for instability and transition are outlined.

In this work, a numerical technique suitable for evaluating the ultrasonic scattering from a three-dimensional poroelastic material is presented. Following Biot’s derivation of the macroscopic governing equations for a fluid saturated poroelastic material, the predicted two propagating wave equations are formulated in terms of displacement and pressure. Assuming that porosity variations on a microscopic scale have a cumulative effect in generating a scattered field, the scattering attenuation coefficient of a Biot medium can be determined. The scattered fields of the wave equations are numerically evaluated as Neumann series solutions of the Kirchhoff-Helmholtz integral equation. A Padé approximant technique is employed to extrapolate beyond the Neumann series’ radius of convergence (weak scattering regime). In the case of bovine trabecular bone, the relationship between the scattering attenuation coefficient and the structural and mechanical properties of the trabecular bone is of particular interest. The results demonstrate the validity of the linear frequency-dependent assumption of attenuation coefficient n the low frequency range. Further comparisons, between measured observations and the numerical results will be discussed.

In this work, the generation of difference frequency waves arising from the interaction of dual-incident beams on a solid sphere is considered. The high-frequency incident beams induce a radiation force onto the fluid-saturated sphere causing the scatterer to vibrate. An analysis on the contribution between the difference frequency sound and radiation force pressure is of particular interest. The scattered pressure due to the two primary waves are obtained as solutions to the Kirchhoff–Helmholtz integral equation for the fluid–solid boundary. Due to the contrasting material properties between the host fluid and solid sphere, high-order approximations are used to evaluate the integral equation.