Boundary layer transition is a hot research topic in fluid mechanics and aerospace engineering. In low-speed flows, twodimensional\nTollmien-Schlichting (T-S) waves always dominate the flow instability, which has been modeled by Coder and\nMaughmer from 2013. However, in supersonic flows, three-dimensional oblique Tollmien-Schlichting waves become\ndominant in flow instability. Inspired by Coder and Maughmerâ??s NTS amplification factor transport equation for twodimensional\nTollmien-Schlichting waves in low-speed flows and Kroo and Sturdzaâ??s linear stability theory (LST) analysis\nresults for oblique Tollmien-Schlichting waves in supersonic flows, a new amplification factor transport equation for oblique\nTollmien-Schlichting waves has been developed based on LST. The compressible Falkner-Skan similarity equations are\nintroduced to build the relationships between nonlocal variables and local variables so that all the variables used in the\npresent model can be calculated using local variables. Applications of this new transport equation to the flows over\nsupersonic flat plate, 3% thick biconvex airfoil, and one modified supersonic laminar airfoil show promising results compared\nwith the standard LST analysis results.
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