Supersonic flows past an obstacle in Yukawa liquids

Shock formation, when a supersonic flow passes a stationary obstacle, is ubiquitous in nature. Considering particles mediating via a Yukawa-type interaction as a prototype for a strongly coupled complex plasma, characterized by coupling strength (Gamma, ratio of the average potential to kinetic energy per particle) and screening parameter (kappa, ratio of the mean inter-particle distance to the shielding length), we address the fundamental problem of supersonic fluid flow U-0, past a stationary obstacle immersed in this strongly coupled system. We here report the results on the bow shocks formed in Yukawa liquids when the liquid flows at speeds larger than the speed of sound in the system. Depending on the values of Mach number MCL = U-0 CL, where CL is the longitudinal speed of sound in the system, the bow shocks are found to be either traveling or localized. We find that for the transonic flows (0.8 less than or similar to M-CL less than or similar to 1.2), the bow shocks travel in the upstream direction opposite to the incoming fluid. The phase velocity of the traveling bow shocks is found to be a non-monotonous function of kappa, varying as alpha 1/k(1.11) at a fixed value of Gamma, and is found to be independent of Gamma at a fixed value of kappa. It is observed that for the flow values with M-CL >1.5, the shock waves do not travel in the upstream direction but instead form a stationary arc like structure around the obstacle. For the fluid flows with 1 less than or similar to M-CL less than or similar to 2.6, secondary bow shocks are seen to emerge behind the stationary obstacle which travel in the downstream direction, and the phase velocity of these secondary bow shocks is found to be equal to that of the primary bow shocks. Published by AIP Publishing.