Interaction of a Shock with a Longitudinal Vortex

In this paper we study the shock/longitudinal vortex interaction problem in axisymmetric geometry. Linearized analysis for small vortex strength is performed, and compared with results from a high order axisymmetric shocktted Euler solution obtained for this purpose. It is con rmed that for weak vortices, predictions from linear theory agree well with results from nonlinear numerical simulations at the shock location. To handle very strong longitudinal vortices, which may ultimately break the shock, we use an axisymmetric high order essentially non-oscillatory (ENO) shock capturing scheme. Comparisons of shock-captured and shocktted results are performed in their regions of common validity. We also study the vortex breakdown as a function of Mach number ranging from 1:3 to 10, thus extending the range of existing results. For vortex strengths above a critical value, a triple point forms on the shock, leading to a Mach disk. This leads to a strong recirculating region downstream of the shock and a secondary shock forms to provide the necessary deceleration so that the uid velocity can adjust to downstream conditions at the shock. Research supported by NASA contract NAS1-19480 while the authors were in residence at ICASE, NASA Langley Research Center, Hampton, VA 23681-0001. ICASE, Mail Stop 132C, NASA Langley Research Center, Hampton, VA 23681-0001. Program in Computational Science and Engineering, Florida State University, Tallahasee, FL 32306 Division of Applied Mathematics, Brown University, Providence, RI 02912. Research of this author was also supported by ARO grant DAAH04-94-G-0205, NSF grant DMS-9500814, NASA grant NAG1-1145 and AFOSR grant 95-1-0074.