Characterizing the Response of Focused Laser Differential Interferometry to Mixed-Mode Hypersonic Instabilities

Nonintrusive measurements of boundary-layer instabilities are critical for understanding and predicting laminar-to-turbulent transition in hypersonic flows. One important technique, focused laser differential interferometry (FLDI), requires a rigorous understanding of its response characteristics for accurate data interpretation. Here, the capabilities of FLDI for measuring first- and second-mode boundary-layer instabilities are assessed through computational analysis. Direct numerical simulations (DNSs) of Mach-6 flow over a cone provide density fields containing both instability modes. The FLDI measurement process is simulated by numerically integrating optical beam paths through the DNS data to generate synthetic time-series signals. Analysis reveals that the simulated FLDI signal accurately captures the frequency content of the dominant instabilities. However, comparisons with the underlying DNS data demonstrate that the technique’s finite sampling volume acts as a spatial filter, altering the measured amplitudes between modes. The synthetic FLDI data were decomposed to isolate the spectral and spatial characteristics of the individual first- and second-mode waves, where the second mode was found to be amplified relative to the first mode due to a combination of its wavelength and orientation. This study validates the utility of FLDI for multimode instability analysis and provides quantitative insights into the diagnostic’s measurement effects, directly informing the interpretation of experimental campaigns. **