The three-dimensional flows in an inward-turning inlet were numerically investigated at different incoming flow conditions. When the incoming flow conditions change, the shock angle and the shock interaction form of the external compression wave change, and the development of the near-wall low-energy fluid and the streamwise vortex is also affected. The impingement of the shock wave leads to a sharp increase in the vorticity of the low kinetic energy fluid. Under the pressure gradient caused by the shock wave, the high-vorticity fluid migrates from the cowl to the ramp and entrains the mainstream fluid to form a streamwise vortex, for which the velocity gradient (∂v/∂y + ∂w/∂z) along the vortex axis can accurately determine the rotation direction and the Hopf bifurcation position. By considering high Reynolds number flows, the pressure gradient along the vortex axis is developed to estimate the simplified dilation term (velocity gradient) due to its ease of measurement. However, the pressure gradient (∂p/∂x) along the vortex axis can lead to bias when evaluating the cross-flow state of the streamwise vortex, with the shock wave structure and high-vorticity fluid leading to under- and overestimation, respectively. This study provides a theoretical basis for an accurate determination of the flow state of a streamwise vortex in an inward-turning inlet and thus lays the foundation for effective vortex control.
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