TY - JOUR

T1 - Mean flow scaling in a spanwise rotating channel

AU - Yang, X. I.A.

AU - Xia, Z. H.

AU - Lee, J.

AU - Lv, Y.

AU - Yuan, J.

N1 - Funding Information:
X.Y. acknowledges the funding support to the CTR summer program, which made it possible for scientists from five different institutions to collaborate. Z.-H.X. thanks S. Chen for many valuable comments and the National Natural Science Foundation of China (Grants No. 11772297 and No. 11822208) for financial support. X.Y. would like to thanks P. Moin and U. Piomelli for insightful comments and M.-W. Ge for editing the text. J.Y. thanks U. Piomelli and W. Wu for sharing the high Reynolds number DNS data.
Publisher Copyright:
© 2020 American Physical Society.

PY - 2020/7

Y1 - 2020/7

N2 - Since the early work of Johnston [Johnston, Halleent, and Lezius, J. Fluid Mech. 56, 533 (1972)JFLSA70022-112010.1017/S0022112072002502], the mean flow scaling in a spanwise rotating channel has received much attention. While it is known that the mean velocity near the pressure, turbulent side follows a linear scaling U=2ωy+C at high rotation speeds, the functional dependence of C on the Reynolds number and the rotation number has been an open question. Here, U is the mean velocity, ω is the constant rotating speed in the spanwise direction, and C is a constant. In this work, we show that C+=log(lω+)/K, where the superscript + denotes normalization using wall units at the pressure side; lω=uτ,p/2ω is a rotation-induced length scale; K is a constant and K≈κ, where κ is the von Kármán constant; and uτ,p is the wall friction velocity at the pressure side.

AB - Since the early work of Johnston [Johnston, Halleent, and Lezius, J. Fluid Mech. 56, 533 (1972)JFLSA70022-112010.1017/S0022112072002502], the mean flow scaling in a spanwise rotating channel has received much attention. While it is known that the mean velocity near the pressure, turbulent side follows a linear scaling U=2ωy+C at high rotation speeds, the functional dependence of C on the Reynolds number and the rotation number has been an open question. Here, U is the mean velocity, ω is the constant rotating speed in the spanwise direction, and C is a constant. In this work, we show that C+=log(lω+)/K, where the superscript + denotes normalization using wall units at the pressure side; lω=uτ,p/2ω is a rotation-induced length scale; K is a constant and K≈κ, where κ is the von Kármán constant; and uτ,p is the wall friction velocity at the pressure side.

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U2 - 10.1103/PhysRevFluids.5.074603

DO - 10.1103/PhysRevFluids.5.074603

M3 - Article

AN - SCOPUS:85092230540

SN - 2469-990X

VL - 5

JO - Physical Review Fluids

JF - Physical Review Fluids

IS - 7

M1 - 074603

ER -