The linear stability theory is used to investigate the emergence, in supersonic free shear flows such as mixing layers and fully expanded plane jets, of supersonically travelling instability waves, which do not vanish in the ambient space. It is shown that, at supersonic convective Mach numbers, the slow and fast supersonic modes in the mixing layer as well as the sinuous supersonic mode in the plane jet should lead to Mach wave radiation. Direct numerical simulations are further used to study nonlinear stages of instability development in high-speed mixing layers and jets. They have shown that the formation of oblique shock waves attached to large-scale structures is observed in free shear flows forced by modes with supersonic phase speeds. The relevance of this phenomenon to the noise generation by high-speed jets is discussed.
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