Is geometry above physics in atmospheric boundary layer flow?

We show that the geometry of motions in atmospheric boundary-layer time series exhibits scale-independence regardless of the changing physics. The scale-independence of structures in time series is illustrated for time scales between 3 s and 2 h. Predefined basic structure shapes (sine, step, ramp-cliff and cliff-ramp) are chosen subjectively according to their ubiquitous appearance in the time series. The frequency of occurrence of shapes is shown to change with the time scale, having a pronounced minimum at scales between 2 and 10 min depending on the stability and the shape function. This is in accordance with the minimum of kinetic energy between turbulence and mesoscales. However, the ratios of occurrences between different shapes are approximately scale-independent. Different variables have preferences for different shape structures. The temperature favours sharper shapes, while smoother shapes dominate the wind speed.

The physics of different shapes and scales is examined from various characteristics of individual shapes. Steep edges of shapes are predominantly related to downward transport of heat and momentum, which weakens with increasing scale. On the other hand, sine shapes seem to be related to turbulent eddies and shear instability at small scales, and to internal gravity waves at larger scales with stable stratification.

Therefore, the physics of individual shapes is shown to change with scale, while the geometry remains approximately scale-independent.