ABSTRACT
Recently Ram, Geva, and Sadot [J. Fluid Mech. 768, 219-235 (2015)] showed, experimentally, the formation of a secondary Mach stem generated from the reflection of the primary Mach stem in the aerodynamic regime. Such a phenomenon has never been observed, either experimentally or numerically, in the framework of weak acoustic shocks. In this work, the formation of a secondary Mach stem is observed from the reflection of acoustic shock waves on a convex-concave boundary giving rise to a complex five-shock pattern. This study is fully numerical and is based on the numerical solution of a nonlinear acoustic system of equations using a recently developed discontinuous Galerkin solver.
ABSTRACT
The reflection of plane waves on a perfectly reflecting surface is a well-known phenomenon in physics. This particular case of the famous Snell-Descartes laws, also called mirror reflection, is valid only for linear waves. For nonlinear shock waves, it is known that this law breaks for sufficiently grazing angles. This paper provides some experimental evidence of this phenomenon for amplitude more than 100 times as small as in previous measurements in air. This is achieved by means of ultrasonic periodic shock waves in water. For grazing angles (typically from 0 degrees to 7 degrees) three different patterns exhibiting strong differences with the mirror law can be observed. The first one is the nonlinear regular reflection for which the incident shock and the reflected one merge on the rigid surface but the incident and reflected angles are different. The second pattern looks similar to the Mach reflection in aerodynamics. In this case, three shocks are present: the incident and reflected shocks merge just above the rigid surface into a third one connected to the rigid surface. In the third pattern, only the incident shock is visible. These experimental results are successfully compared with a theory through accurate numerical simulations.
