Spatial length scales of large-scale structures in atmospheric surface layers

Synchronous multipoint measurements were performed in the atmospheric surface layer at the Qingtu Lake Observation Array site to obtain high-Reynolds-number $[{\mathrm{Re}}_{\tau }\sim O\left({10}^6\right)]$ data. Based on the selected high-quality data in the near-neutral surface layer, the spatial length scales of the large-scale dominant structures in the outer region of the turbulent boundary layer are investigated. The characteristic length scales are extracted from the two-point streamwise velocity correlations. Results show that the spatial length scales are invariant over a three order of magnitude change in Reynolds number $[{\mathrm{Re}}_{\tau }\sim O\left({10}^3\right)-O\left({10}^6\right)]$. However, they increase significantly with the wall-normal distance, showing reasonable collapses on outer-scaled axes. The variation of the spanwise width scale in the logarithmic region follows a linear increase, with the rate of increase much larger than that in the wake region. Moreover, the variation of the wall-normal length scale is also revealed, which displays a qualitative behavior similar to that of the spanwise width scale. The universal laws revealed in the present work contribute to a better understanding of the dominant structures in the outer region of the turbulent boundary layer at high Reynolds numbers.

Figure 1

(a) Photograph of the spanwise measurement array installed at the QLOA site. (b) Schematic of the sonic anemometers arranged in the spanwise array.

Figure 2

Two-point correlations of the streamwise velocity fluctuations: (a) streamwise, $z_{\mathrm{ref}}\approx 0.05\delta$; (b) spanwise, $z_{\mathrm{ref}}\approx 0.033\delta$; and (c) wall normal, $z_{\mathrm{ref}}\approx 0.098\delta$ and $0.14\delta$. The current ASL results are shown by red and blue solid lines, the existing laboratory TBL results (from Hutchins and Marusic [6], Wu and Christensen [40], and Ganapathisubramani et al. [44]) are represented by open symbols, and the existing ASL data (from Hutchins et al. [11]) are denoted by a blue dashed line.

Figure 3

Characteristic streamwise length scales $L_x$ (outer scaled) based on $R_{uu}$ in the streamwise direction for varying ${\mathrm{Re}}_{\tau }$. Black closed circles denote the current ASL results and open symbols are the existing TBL and ASL data (from Hutchins and Marusic [6], Hutchins et al. [11], Lee and Sung [17], and Tutkun et al. [39]).

Figure 4

Characteristic spanwise width scale $L_y$ (outer scaled) based on the spanwise variation of $R_{uu}$ for varying ${\mathrm{Re}}_{\tau }$. The existing TBL and ASL results (from Hutchins and Marusic [6], Hutchins et al. [11], Tomkins and Adrian [30], and Tutkun et al. [39]) are also included in the figure for comparison.

Figure 5

Characteristic wall-normal length scale $L_z$ (outer scaled) based on $R_{uu}$ in the wall-normal direction for varying ${\mathrm{Re}}_{\tau }$. Black closed circles denote the current ASL results and open circles are the existing laboratory TBL data from Tutkun et al. [39].

Figure 6

Variation of the streamwise length scale $L_x$ with wall-normal distance: (a) linear abscissa and (b) logarithmic abscissa. Black closed squares are the current ASL results; blue open symbols are the existing TBL and ASL data (from Hutchins and Marusic [6], Hutchins et al. [11], Lee and Sung [17], Volino et al. [38], Tutkun et al. [39], and Ganapathisubramani et al. [44]), and the dashed line is the fitting curve for symbols at $z_{\mathrm{ref}}>0.006\delta$.

Figure 7

Variation of the spanwise width scale $L_y$ with wall-normal distance: (a) linear abscissa and (b) logarithmic abscissa. Symbols are the same as shown in Fig. 6 except for another four available TBL experimental results (from Tomkins and Adrian [30], Hutchins et al. [37], Wu and Christensen [40], and Krogstad and Antonia [42]). Solid lines are curve fitted to symbols for $z_{\mathrm{ref}}<0.15\delta ,0.15\delta <z_{\mathrm{ref}}<0.3\delta$, and $z_{\mathrm{ref}}>0.3\delta$, respectively, and the dashed line is the fitting curve for symbols at $z_{\mathrm{ref}}>0.006\delta$.

Figure 8

Variation of the wall-normal length scale $L_z$ with wall-normal distance: (a) linear abscissa and (b) logarithmic abscissa. Symbols and lines are the same as shown in Fig. 7.

Figure 9

Ratio of the spanwise and wall-normal length scales. The dashed line represents the average value.