Non-rotational coherent structures in the flow with different degree of turbulence

Introduction The coherent structures are not satisfactorily defined for a very complex atmospheric flow. The features with a rotational motion, namely the vortices and hairpins, are considered as a typical coherent pattern. In the turbulent flow, however, the non-rotational transient phenomenon may play a crucial role.

Experimental set-up The boundary layer dynamics above surfaces of various roughness was measured in the wind-channel by 2D 2C TR-PIV with nominal input velocity 5 m/s. Five types of surfaces were covered by five different types of elements in order to provide a roughness belonging into slightly rough, moderately rough, rough, very rough and extremely rough categories according to guideline VDI (2000). For each surfaces two measurements were executed. The measurement with the sampling frequency of 100 Hz lasting for 20 s provided the statistical output of the ensembles. The short measurement with high sampling rate of 2000 Hz helped to understand the unsteady dynamics of the flow.

Results Statistics of basic turbulent characteristics are checked if they fall into the given class of the roughness. The data recorded with the high sampling frequency are used for comparison of transient dynamics by means of the coherence detection methods. Firstly, the spatial correlation of the longitudinal and vertical velocity component is calculated and a tilt angle of the area with significant correlation coefficient is retrieved. In case of the turbulent flow belonging to the slightly rough category, the chain of stream-wise vortices followed by a tilted compact region of large-scale non-rotational uniform vectors, corresponding to a sweep or an ejection quadrant event, was clearly detected. This finding supports the theory of hairpin packets, separating the individual zones with distinct zonal velocity, as suggested by Adrian et al. (2000).

Secondly, the Quadrant analyses applied to the momentum flux at each snapshot revealed that the spatially compact regions of the uniform sweep and ejection events contained up to 80% of the total momentum flux. These regions of sweep and ejection alternate in wavy-like fashion with a specific pseudo-frequency. The Proper orthogonal decomposition (POD) was performed to reveal the dynamical modes containing significant amount of turbulent kinetic energy (TKE) for each surface category. The most dominant POD mode occurs with the identical frequency as the sweep/ejection wave for all type of turbulence. In conclusion, the prevailing coherent structures carrying the largest amount of TKE of the turbulent flow seems to be the non-rotational large-scale quadrant events.