“…To date, theoretical investigations [3,4] have assumed that the detached SW is relatively close to the object, meaning that the speed range near Mach number 1 is yet to be B T. Kikuchi takamasa.kikuchi@gmail.com 1 College of Science and Technology, Nihon University, Narashinodai 7-24-1, Funabashi, Chiba 274-8501, Japan 2 Institute of Fluid Science, Tohoku University, Katahira 2-1-1, Aoba, Sendai, Miyagi 980-8577, Japan considered. Some numerical results have also been reported [5][6][7].…”