TY - JOUR

T1 - Scale interactions in turbulent rotating planar Couette flow

T2 - Insight through the Reynolds stress transport

AU - Kawata, Takuya

AU - Henrik Alfredsson, P.

N1 - Funding Information:
T.K. was a visiting researcher at KTH supported by a Grant-In-Aid for Research Fellow No. 17J04115
Publisher Copyright:
© The Author(s) 2019 This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

PY - 2019

Y1 - 2019

N2 - In turbulent planar Couette flow under anticyclonic spanwise system rotation, large-scale roll-cell structures arise due to a Coriolis-force-induced instability. The structures are superimposed on smaller-scale turbulence, and with increasing angular velocity () such roll cells dominate the flow field and small-scale turbulence is instead suppressed in a certain rotation number range <![CDATA[$0 (, where is the channel half-width, the wall velocity). At low rotation numbers around both large-scale roll cells and smaller-scale turbulence coexist. In the present study, we investigate interaction between these structures through a scale-by-scale analysis of the Reynolds stress transport. We show that at low rotation numbers the turbulence productions by the mean flow gradient and the Coriolis force occur at different scales and thereby the turbulent energy distribution over a wide range of scales is maintained. On the other hand at higher rotation numbers, a zero-Absolute-vorticity state is established and production of small scales from the mean shear disappears although large-scale turbulence production is maintained through the Coriolis force. At high enough Reynolds numbers, where scale separation between the near-wall structures and the roll cells is relatively distinct, transition between these different regimes is found to occur rather abruptly around, resulting in a non-monotonic behaviour of the wall shear stress as a function of. It is also shown that at such an intermediate rotation number the roll cells interact with smaller scales by moving near-wall structures towards the core region of the channel, by which the Reynolds stress is transported from relatively small scales near the wall towards larger scales in the channel centre. Such Reynolds stress transport by scale interaction becomes increasingly significant as the Reynolds number increases, and results in a reversed mean velocity gradient at the channel centre at high enough Reynolds numbers.

AB - In turbulent planar Couette flow under anticyclonic spanwise system rotation, large-scale roll-cell structures arise due to a Coriolis-force-induced instability. The structures are superimposed on smaller-scale turbulence, and with increasing angular velocity () such roll cells dominate the flow field and small-scale turbulence is instead suppressed in a certain rotation number range <![CDATA[$0 (, where is the channel half-width, the wall velocity). At low rotation numbers around both large-scale roll cells and smaller-scale turbulence coexist. In the present study, we investigate interaction between these structures through a scale-by-scale analysis of the Reynolds stress transport. We show that at low rotation numbers the turbulence productions by the mean flow gradient and the Coriolis force occur at different scales and thereby the turbulent energy distribution over a wide range of scales is maintained. On the other hand at higher rotation numbers, a zero-Absolute-vorticity state is established and production of small scales from the mean shear disappears although large-scale turbulence production is maintained through the Coriolis force. At high enough Reynolds numbers, where scale separation between the near-wall structures and the roll cells is relatively distinct, transition between these different regimes is found to occur rather abruptly around, resulting in a non-monotonic behaviour of the wall shear stress as a function of. It is also shown that at such an intermediate rotation number the roll cells interact with smaller scales by moving near-wall structures towards the core region of the channel, by which the Reynolds stress is transported from relatively small scales near the wall towards larger scales in the channel centre. Such Reynolds stress transport by scale interaction becomes increasingly significant as the Reynolds number increases, and results in a reversed mean velocity gradient at the channel centre at high enough Reynolds numbers.

KW - rotating turbulence

KW - turbulent boundary layers

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U2 - 10.1017/jfm.2019.668

DO - 10.1017/jfm.2019.668

M3 - Article

AN - SCOPUS:85072781786

SN - 0022-1120

SP - 255

EP - 295

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -