Wavelet-based resolvent analysis of intermittently turbulent Stokes boundary layer*

In this work, we study turbulent flow over periodic oscillating walls in the intermittently turbulent regime using wavelet-based resolvent analysis. Wavelet-based resolvent analysis uses wavelet transforms, rather than Fourier transforms in time, to form the resolvent operator. This preserves both frequency and time information and allows identification of time-localized nonlinear forcing modes that are optimally amplified by the linearized Navier-Stokes operator about a turbulent mean profile. This method is applied to the intermittently turbulent Stokes boundary layer systematically to study the time-localized forcing, response, and amplification mechanisms. We first analyze the time-localized singular values at different wavelengths. Fast decay in the singular values at length scales corresponding to high intensity in the two-dimensional energy spectra is observed, indicative of low-rank behavior at energetic length scales. This alignment confirms the validity of the wavelet-based resolvent framework applied to length scales of interest, and identifying the time-localized forcing and response modes at these length scales illuminates the temporal laminar-to-turbulent transition mechanisms in the intermittently turbulent regime.