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Control of oblique breakdown in a supersonic boundary layer at Mach 2.0 using a local cooling strip is investigated by direct numerical simulation. Previous studies have indicated that wall cooling can stabilize first-mode disturbances, but no study has yet investigated the use of local cooling to control oblique breakdown in a supersonic boundary layer. In the present work, local cooling strips with various temperatures and widths are utilized at different locations to control oblique breakdown. Insight is obtained into the stabilizing effect of a cooling wall on the evolution of various disturbances in the streamwise direction. A local cooling strip controls oblique breakdown mainly by suppressing the amplification of the fundamental oblique waves in the streamwise direction, and it is found that this suppressive effect is enhanced by increasing the width and decreasing the temperature of the strip. The stabilizing effect of a local cooling strip on higher-harmonic modes is reinforced when the strip is located farther downstream, although this effect is negligible when compared with the stabilizing effect on the fundamental oblique waves. When the cooling strip is placed in the midstream area, where the steady vortex mode is amplified to the order of the fundamental oblique waves, outstanding performance in suppressing transition is found. Furthermore, in addition to the stabilizing effect of the cooling wall on the fundamental oblique waves, the boundary layer is stabilized by rapid growth of higher-spanwise-wavenumber steady modes. Eventually, oblique breakdown is suppressed and substantial improvements in the skin-friction coefficient are also obtained.

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