Orthonormal wavelet expansions are applied to surface-layer measurements of vertical wind speed under various atmospheric stability conditions. The orthonormal wavelet transform allows for the unfolding of these measurements into space and scale simultaneously to reveal the large intermittent behavior in space for the turbulent production wavenumbers. Both Fourier and wavelet power spectra indicated the existence of a -1 power law for the vertical velocity measurements at the production wavenumbers. The -1 power law in the turbulent production range was derived from surface-layer similarity theory. A dimensionless skewness structure function is applied to the wavelet decomposed vertical velocity field to trace the destruction of the shear- or buoyancy-induced anisotropy under various stability conditions. The structure skewness function revealed shear- or buoyancy-induced eddy asymmetry dependence on stability at each scale within the -1 power-law wavenumber range with more isotropy during propagation from smaller to larger wavenumbers. The asymmetry of these events at the turbulent production wavenumbers appeared very localized in space, as well as in scale, and could be described with a simple eddy-overturning model. It is demonstrated that the wavelet transform is suitable for such analysis.