Shock dynamics in non-uniform media

The theory of shock dynamics in two dimensions is reformulated to treat shock propagation in a non-uniform medium. The analysis yields a system of hyperbolic equations with source terms representing the generation of disturbances on the shock wave as it propagates into the fluid non-uniformities. The theory is applied to problems involving the refraction of a plane shock wave at a free plane gaseous interface. The ‘slow–fast’ interface is investigated in detail, while the ‘fast–slow’ interface is treated only briefly. Intrinsic to the theory is a relationship analogous to Snell's law of refraction at an interface. The theory predicts both regular and irregular (Mach) refraction, and a criterion is developed for the transition from one to the other. Quantitative results for several different shock strengths, angles of incidence and sound-speed ratios are presented. An analogy between shock refraction and the motion of a force field in unsteady one-dimensional gasdynamics is pointed out. Also discussed is the limiting case for a shock front to be continuous at the interface. Comparison of results is made with existing experimental data, with transition calculations based on three-shock theory, and with the simple case of normal interaction

Two-Point LDV Measurements in a Plane Mixing Layer

Investigations into the nature of the large structures in a two-dimensional shear layer were carried out using laser Doppler velocimetry in the GALCIT free-surface water tunnel. By simultaneous measurements of velocity at two points outside the turbulent region, above and below the shear layer, it was possible to measure the strength (total circulation) and location of the vorticity center of the large structures. It was found that structures not in the process of pairing convect downstream with the center of their cores close to the ray y/x along which the mean velocity is given by U_m = l/2(U_1 + U_1 ). The determined value of the mean circulation is consistent with the independent measurements of the mean spacing between the structures. Results indicate that if the large structure vorticity distribution is elliptical, the inclination angle of its axis of symmetry with respect to the now direction is small