Coherent Structure Inclination Angles and Amplitude Modulation Behavior in the Atmospheric Surface Layer

Two quasi-empirical models are proposed to describe variations in the widely used amplitude modulation coefficient, $R_{\text{AM}}$, of wall-bounded turbulence with respect to altitude and stratification stability. The models represent $R$ in terms of the inclination angle and size of the dominant large- and small-scale coherent structures in both a flat-plate zero pressure gradient laboratory boundary layer and the atmospheric surface layer. The amplitude modulation coefficient has been widely interpreted as reflecting a phase difference between large- and small-scale structures in wall-bounded turbulence. In the first model, we show how this interpretation can be demonstrated rigorously by educing structure inclination angles for the filtered large- and small-scales via cross-correlation analysis, and incorporating a characteristic eddy size consistent with the attached eddy framework. In the second model, we extend this phase model to describe $R_{\text{AM}}$ under changing stability conditions, by relating the characteristic eddy size to the stratification stability, consistent with the Monin–Obukhov similarity framework. These models enable description of the amplitude modulation behavior in wall-bounded turbulence with a limited number of flow parameters, and can contribute to improvements in inner-outer turbulence modeling efforts.