Abstract We propose the multivariate locally stationary wavelet (mvLSW) process to analyze surface turbulent fluxes in nonstationary atmospheric conditions. Using theoretical spectral characteristics, we generated synthetic data representing stationary and nonstationary turbulence time series. This data enables us to explore the impact of mesoscale atmospheric flows on the stationary microscale turbulence field and detect the spectral gap in the time-varying cospectra. Applying this approach to experimental data collected in Fairbanks, Alaska and Bogota, Colombia, we demonstrated the ability to detect cospectral gaps and compute bandwidth-limited turbulent fluxes arising from stationary components of the atmospheric flow. These findings underscore the importance of considering scale-dependent atmospheric forcing when comparing model and experimental data.