## 4 Conclusions  
To generate the turbulent boundary layer flow in a numerical domain, a synthetic inflow generator was applied. It was based on spatial and temporal correlation functions, which had the form of an exponential function. To validate the turbulent boundary layer profiles that were obtained by using the synthetic inflow generator, the results obtained were precisely compared with existing data. From the results, it can be concluded that  
Figure 15: Energy spectrum distribution at the inlet (**a**,**c**) and for \(y/d=50\) (**b**,**d**). In addition, (**a**,**b**) are the results from Case 01 and (**c**,**d**) from Case 09.  
the turbulent boundary layer was successfully generated. In the mean velocity profile \(u^{+}\), the boundary layer agreed well with the overall range of the domain, and the axial and shear stresses were in good agreement with the DNS data.  
To observe the effect of the inflow length scales imposed at the inlet section on the development of a turbulent boundary layer, the length scales were varied with a focus on studying their effect. The results showed that a larger length scale in the inlet section had a faster rate of recovery in terms of the wall shear stress, which implies that larger length scales in the inlet section would be essential to the rapid development of the boundary layer, and thereby the realization of a fully developed turbulent boundary layer.  
In addition to the variation of the inlet length scale, the inlet plane was separated into two different zones with the aim of imposing two or three different length scales on each zone. The proximity of the wall was chosen to be approximately \(y/h=0.1\) and \(0.2\) so that the two ranges were first \(0<y^{+}<15\) (in the middle of the buffer layer zone) and \(15<y^{+}<150\) and, secondly, \(0<y^{+}<30\) (in the buffer layer zone) and \(30<y^{+}<150\). Based on the results obtained, it can be seen that the length scale variation in the region \(y^{+}<15\) did not significantly impact the recovery of the wall shear stress. However, the size of the length scale in the region of approximately \(15<y^{+}<30\) contributed significantly to the generation of turbulent energy near the wall surface.  
Conceptualization, Y.-T.L. and H.-C.L.; methodology, Y.-T.L. and H.-C.L.; software, Y.-T.L. and L.K.G.; validation, Y.-T.L. and H.-C.L.; formal analysis, Y.-T.L. and H.-C.L.; investigation, Y.-T.L.; data curation, Y.-T.L.; writing--original draft preparation, Y.-T.L.; writing--review and editing, Y.-T.L. and L.K.G.; supervision, H.-C.L.; project administration, Y.-T.L. and H.-C.L.; funding acquisition, Y.-T.L. and H.-C.L. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the Korea Meteorological Administration Research and Development Program \"The Standard Weather Observation and its Application\" under Grant (KMA2018-00221). This work was supported by 'Human Resources Program in Energy Technology' of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea (No. 2021400000140). In addition, this work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2019R11A3A01058576).  
The authors declare that there are no conflicts of interest with respect to the authorship and publication of this article.