Scaling of vertical coherence and logarithmic energy profile for wall-attached eddies during sand and dust storms

High-frequency observation data, including all three components of instantaneous fluctuating velocity, temperature, as well as particulate matter 10 ( PM₁₀ ), collected from the unstable atmospheric surface layer at $z/L = -0.11$ and $-$ 0.12, L being the Obukhov length, during sand and dust storms (SDS), were used to explore the scaling of vertical coherence and the logarithmic energy profile for wall-attached eddies. The present results demonstrate good agreement with the self-similar range of the wall-attached features for velocity and temperature components, as well as for PM₁₀ at lower heights ( $z<15$ m) during SDS. Following the idea depicted by Davenport ( Q. J. R. Meteorol. , vol. 372, 1961, pp. 194–211), an empirically derived transfer kernel comprises implicit filtering via a scale-dependent gain and phase, parametrically defined as |HL²(f)|=exp (c₁-c₂δ /λ ₓ) , where c₁ and c₂ are parameters, δ is the boundary layer thickness and λ ₓ is the streamwise wavelength. Linear coherence spectrum analysis is applied as a filter to separate the coherent and incoherent portions. After this separation procedure, the turbulence intensity decay for wall-attached eddies is described in a log–linear manner, which also identifies how the scaling parameter differs between the measured components. These findings present abundant features of wall-attached eddies during SDS which further are used to improve/enrich existing near-wall models.