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We use a spectral approach to analyze the pressure and wind data from the InSight mission and investigate the diurnal and seasonal trends. Our analyses show that the daytime pressure and wind spectra have slopes of approximately −1.7 and −1.3 and, therefore, do not follow the Kolmogorov scaling (as was also previously reported for a reduced data set in Banfield et al.). We find that the nighttime pressure spectral slope is close to −1 (as reported in Temel et al.), and that the wind speed spectral slope is close to −0.5, flatter than the theoretical slope expected for the shear-dominated regime. We observe strong nocturnal (likely shear-generated) turbulent behavior starting around L _s = 150° (InSight sol 440) that shifts to progressively earlier local times before reaching the “5th season” (InSight sols 530–710) identified by Chatain et al.. The diurnal spectral slope analyses indicate an asymmetry in the diurnal behavior of the Martian boundary layer, with a slow growth and fast collapse mechanism. Finally, the low-frequency (5–30 mHz) pressure data exhibit large spectral slope oscillations. These occur particularly during the periods with a highly stable atmosphere and, therefore, may be linked to gravity wave activity.