Role of non-linearities induced by deterministic forcing in the low-frequency dynamics of transitional shock wave/boundary layer interaction

Abstract

Direct numerical simulations are carried out to investigate the underlying mechanism of the low-frequency unsteadiness of a transitional shock reflection with separation at M=1.5. To clarify the nonlinear mechanisms, the incoming laminar boundary layer is forced with two different arrangements of oblique unstable modes. Each wave arrangement is given by a combination of two unstable waves such that their difference in frequency falls in a low-frequency range corresponding to a Strouhal number (based on the length of interaction) of 0.04. This deterministic forcing allows the introduction of nonlinearities, and high-order statistical tools are used to identify the properties of quadratic couplings. It is found that the low-frequency unsteadiness and the transition to turbulence are decoupled problems. On the one hand, the unstable modes of the boundary layer interact nonlinearly such that energy cascades to higher frequencies, initiating the turbulent cascade process, and to lower frequencies. On the other hand, the low-frequency quadratic coupling of the oblique modes is found to be responsible for low-frequency unsteadiness affecting the separation point. The direction of the quadratic interactions is extracted and it is shown that, in the presence of low-frequency unsteadiness, these interactions enter the separated zone just before reattachment and travel both downstream and upstream, extending beyond the separation point, hence feeding the low-frequency bubble response. In addition to the two main arrangements of oblique modes, two other combinations are analysed, including multiple oblique waves and streaks. Interestingly, their inclusion did not alter the low-frequency unsteadiness phenomenon. Furthermore, the effect of the forcing difference frequency is examined and it is shown that the breathing phenomenon is sensitive to the range of frequencies present in the system due to a low-pass filter effect.

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Identifiers

ORCID for Pushpender K. Sharma: orcid.org/0000-0003-2078-2559

ORCID for Neil Sandham: orcid.org/0000-0002-5107-0944

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