TY - JOUR
T1 - Energy transfer in turbulent flows behind two side-by-side square cylinders
AU - Zhou, Yi
AU - Nagata, Koji
AU - Sakai, Yasuhiko
AU - Watanabe, Tomoaki
AU - Ito, Yasumasa
AU - Hayase, Toshiyuki
N1 - Funding Information:
This work was in part supported by the National Natural Science Foundation of China (nos. 91952105 and 11802133), the Natural Science Foundation of Jiangsu Province (no. BK20180454) and the Fundamental Research Funds for the Central Universities (no. 30918011325). Part of this study was also supported byMEXT KAKENHI (nos. 18H01367 and 18H01369). Part of the numerical simulations were carried out on the supercomputer at Tohoku University (nos. J18I078 and J19I100: Institute of Fluid Science, Tohoku University; and no. CP02APR18: Advanced Fluid Information Research Center, Institute of Fluid Science, Tohoku University).
Funding Information:
This work was in part supported by the National Natural Science Foundation of China (nos. 91952105 and 11802133), the Natural Science Foundation of Jiangsu Province (no. BK20180454) and the Fundamental Research Funds for the Central Universities (no. 30918011325). Part of this study was also supported by MEXT KAKENHI (nos. 18H01367 and 18H01369). Part of the numerical simulations were carried out on the supercomputer at Tohoku University (nos. J18I078 and J19I100: Institute of Fluid Science, Tohoku University; and no. CP02APR18: Advanced Fluid Information Research Center, Institute of Fluid Science, Tohoku University). The authors acknowledge the helpful discussions with Dr J. C. Vassilicos (Lille Fluid Mechanics Laboratory–Kampé de Fériet, Lille, France). We are also grateful to the anonymous referees for their valuable comments.
Publisher Copyright:
© The Author(s), 2020.
PY - 2020
Y1 - 2020
N2 - Our previous study (J. Fluid Mech., vol. 874, 2019, pp. 677-698) confirmed that two different types of energy spectra (i.e. non-Kolmogorov and quasi-Kolmogorov spectra) can be found in turbulent flows behind two side-by-side square cylinders. In the upstream region (i.e. with being the cylinder thickness), albeit the turbulent flow is highly inhomogeneous and intermittent and Kolmogorov's hypothesis does not hold, the energy spectrum exhibits a well-defined power-law range for over one decade. Meanwhile, the power-law exponent of the corresponding second-order structure function is 1, which is significantly larger than the expected value, i.e. At the downstream location, i.e., in contrast, the quasi-Kolmogorov energy spectrum (and also the 2/3 scaling of the second-order structure) can be identified. Through decomposing the streamwise velocity fluctuations into the spanwise average of instantaneous velocity and the turbulent residual, we demonstrate that the non-Kolmogorov spectrum at is caused by the turbulent residual part. To shed light on the physics of the scale-by-scale energy transfer, we resort to the Kármán-Howarth-Monin-Hill equation. At, the expected balance between the nonlinear term and the dissipation term cannot be detected. Instead, the contributions from the non-local pressure, advection, nonlinear transport and turbulent transport terms are dominant. Moreover, because the corresponding flow field is highly intermittent, the magnitudes of the non-local pressure, advection, nonlinear transport and turbulent transport terms are significantly larger than that of the dissipation term. At a far downstream location, i.e., where the dual-wake flow is fully turbulent and becomes much more homogeneous and isotropic, within a short intermediate range the two dominant terms in the two-point turbulent kinetic energy budget are the nonlinear transport term and the dissipation term, which to some extent echoes Kolmogorov's scenario, albeit the contribution from the large-scale advection term cannot be ignored. By comparing the behaviour of the one-point and two-point energy transfer, it can be seen that the two different energy transfer processes are actually closely related, that is, the similar relative importance of the viscous dissipation and the same role of the non-negligible terms in terms of being a source or sink term.
AB - Our previous study (J. Fluid Mech., vol. 874, 2019, pp. 677-698) confirmed that two different types of energy spectra (i.e. non-Kolmogorov and quasi-Kolmogorov spectra) can be found in turbulent flows behind two side-by-side square cylinders. In the upstream region (i.e. with being the cylinder thickness), albeit the turbulent flow is highly inhomogeneous and intermittent and Kolmogorov's hypothesis does not hold, the energy spectrum exhibits a well-defined power-law range for over one decade. Meanwhile, the power-law exponent of the corresponding second-order structure function is 1, which is significantly larger than the expected value, i.e. At the downstream location, i.e., in contrast, the quasi-Kolmogorov energy spectrum (and also the 2/3 scaling of the second-order structure) can be identified. Through decomposing the streamwise velocity fluctuations into the spanwise average of instantaneous velocity and the turbulent residual, we demonstrate that the non-Kolmogorov spectrum at is caused by the turbulent residual part. To shed light on the physics of the scale-by-scale energy transfer, we resort to the Kármán-Howarth-Monin-Hill equation. At, the expected balance between the nonlinear term and the dissipation term cannot be detected. Instead, the contributions from the non-local pressure, advection, nonlinear transport and turbulent transport terms are dominant. Moreover, because the corresponding flow field is highly intermittent, the magnitudes of the non-local pressure, advection, nonlinear transport and turbulent transport terms are significantly larger than that of the dissipation term. At a far downstream location, i.e., where the dual-wake flow is fully turbulent and becomes much more homogeneous and isotropic, within a short intermediate range the two dominant terms in the two-point turbulent kinetic energy budget are the nonlinear transport term and the dissipation term, which to some extent echoes Kolmogorov's scenario, albeit the contribution from the large-scale advection term cannot be ignored. By comparing the behaviour of the one-point and two-point energy transfer, it can be seen that the two different energy transfer processes are actually closely related, that is, the similar relative importance of the viscous dissipation and the same role of the non-negligible terms in terms of being a source or sink term.
KW - turbulence simulation
KW - turbulence theory
KW - wakes
UR - http://www.scopus.com/inward/record.url?scp=85091974620&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85091974620&partnerID=8YFLogxK
U2 - 10.1017/jfm.2020.611
DO - 10.1017/jfm.2020.611
M3 - Article
AN - SCOPUS:85091974620
VL - 903
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
M1 - 2020611
ER -