Spectral Analysis of Combined Kelvin-Helmholtz and Rayleigh-Taylor Instability Using SPOD and POD

The flow field for 2D and 3D flow combining Kelvin-Helmholtz and Rayleigh-Taylor instabilities is simulated and analyzed using SPOD and POD on their frequency content. While SPOD results are already in the frequency domain, the POD frequency analysis is based on the corresponding spectra of POD time coefficients for each mode. The goal is to identify frequency interactions between KHI and RTI, such as RTI triggered inherent frequencies of KHI. Parameters that affect both KHI and RTI are studied, including shear strength, shear thickness, buoyancy strength, and density difference. Through the frequency analysis, it is found that the flow exhibits multiple characteristic regions of instability. Starting from the developing region, RTI causes the initial perturbation for KHI to develop. Then it progresses into the KHI-dominant region, where the characteristically periodic KHI vortex shedding occurs with distinct frequency peaks observed. Between the KHI- and RTI-dominant regions, there is a transitional region where the shed vortices begin to stretch and bubble due to RTI. In this region, the frequency peaks previously found are shifted and dampened. Lastly, the flow enters the RTI-dominant region, where RTI stretches and bubbles the shed vortices into the characteristic RTI plumes and mushroom structures. This last region loses the frequency peaks observed in the previous two regions.