Shock Interactions with Heavy Gaseous Elliptic Cylinders: Two Leeward-side Shock Competition Modes and a Heuristic Model for Interfacial Circulation Deposition at Early times Typeset Using Revt E X 2

1 Shock interactions with heavy gaseous elliptic cylinders: Two leeward-side shock competition modes and a heuristic model for interfacial circulation deposition at early times Abstract We identify two diierent modes, Types I and II, of interaction for planar shocks accelerating heavy prolate gaseous ellipses. These modes arise from diierent interactions of the incident shock (IS) and transmitted shock (TS) on the leeward side of the ellipse. A time ratio t T =t I (M; ; ; 0 ; b), which characterizes the mode of interaction, is derived heuristically. Here, the principal parameters governing the interaction are the Mach number of the shock (M), the ratio of the density of the ellipse to the ambient gas density, (> 1), 0 ; b (the ratios of speciic heats of the two gases), (the aspect ratio). Salient events in shock{ellipse interactions are identiied and correlated with their signatures in circulation budgets and on{axis space-time pressure diagrams. The two modes yield diierent mechanisms of the baroclinic vorticity generation. We present a heuristic model for the net baroclinic circulation generated on the interface at the end of the early-time phase by both the IS and TS and validate the model via numerical simulations of the Euler equations. In the range 1:2 M 3:5, 1:54 5:04 and = 1:5 and 3:0, our model predicts the baroclinic circulation on the interface within a band of 10% in comparison to converged numerical simulations.