TY - JOUR

T1 - Third-order structure function in the logarithmic layer of boundary-layer turbulence

AU - Xie, Jin Han

AU - De Silva, Charitha

AU - Baidya, Rio

AU - Yang, Xiang I.A.

AU - Hu, Ruifeng

N1 - Funding Information:
J.-H.X. gratefully acknowledges financial support from the National Natural Science foundation of China Grant No. 92052102. X.Y. is supported by the U.S. Office of Naval Research under Contract No. N000142012315, with Dr. Peter Chang as Technical Monitor. R.H. acknowledges the financial supports from NSFC Grant No. 11972175. C.D.S. thanks the ARC for financial support.
Publisher Copyright:
© 2021 American Physical Society.

PY - 2021/7

Y1 - 2021/7

N2 - Townsend's attached eddy hypothesis (AEH) gives an accurate phenomenological description of the flow kinematics in the logarithmic layer, but it suffers from two major weaknesses. First, AEH does not predict the constants in its velocity scalings, and second, none of the predicted velocity scalings can be obtained from the Navier-Stokes (NS) equations under AEH's assumptions. These two weaknesses separate AEH from more credible theories like Kolmogorov's theory of homogeneous isotropic turbulence, which, despite its phenomenological nature, has one velocity scaling, i.e., Δu3=-(4/5)ϵr, that can be derived from the NS equation. Here, Δu3 is the longitudinal third-order structure function, ϵ is the time-averaged dissipation rate, and r is the displacement between the two measured points. This work aims to address these two weaknesses by investigating the behavior of the third-order structure function in the logarithmic layer of boundary-layer turbulence. We invoke AEH and obtain Δu3=D3ln(r/z)+B3, where Δu is the streamwise velocity difference between two points that are displaced by a distance r in the streamwise direction, z is the wall-normal location of the two points, D3 is a universal constant, and B3 is a constant. We then evaluate the terms in the Kármán-Howarth-Monin (KHM) equation according to AEH and see if NS equations give rise to a nontrivial result that is consistent with AEH. Last, by resorting to asymptotic matching, we determine D3=2.0 (at sufficiently high Reynolds numbers).

AB - Townsend's attached eddy hypothesis (AEH) gives an accurate phenomenological description of the flow kinematics in the logarithmic layer, but it suffers from two major weaknesses. First, AEH does not predict the constants in its velocity scalings, and second, none of the predicted velocity scalings can be obtained from the Navier-Stokes (NS) equations under AEH's assumptions. These two weaknesses separate AEH from more credible theories like Kolmogorov's theory of homogeneous isotropic turbulence, which, despite its phenomenological nature, has one velocity scaling, i.e., Δu3=-(4/5)ϵr, that can be derived from the NS equation. Here, Δu3 is the longitudinal third-order structure function, ϵ is the time-averaged dissipation rate, and r is the displacement between the two measured points. This work aims to address these two weaknesses by investigating the behavior of the third-order structure function in the logarithmic layer of boundary-layer turbulence. We invoke AEH and obtain Δu3=D3ln(r/z)+B3, where Δu is the streamwise velocity difference between two points that are displaced by a distance r in the streamwise direction, z is the wall-normal location of the two points, D3 is a universal constant, and B3 is a constant. We then evaluate the terms in the Kármán-Howarth-Monin (KHM) equation according to AEH and see if NS equations give rise to a nontrivial result that is consistent with AEH. Last, by resorting to asymptotic matching, we determine D3=2.0 (at sufficiently high Reynolds numbers).

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U2 - 10.1103/PhysRevFluids.6.074602

DO - 10.1103/PhysRevFluids.6.074602

M3 - Article

AN - SCOPUS:85110175270

SN - 2469-990X

VL - 6

JO - Physical Review Fluids

JF - Physical Review Fluids

IS - 7

M1 - 074602

ER -