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Spanwise-rotating turbulent plane Couette flow (RPCF) is one of the fundamental prototypes for wall-bounded turbulent flows in rotating reference frames. In this turbulent problem, there are large-scale roll cells which are widely studied. In this paper, a penta-decomposition method is proposed to separate the instantaneous velocity and the total kinetic energy into five parts, i.e., a mean part, a streamwise part and a cross-flow part of the secondary flow, and a streamwise part and a cross-flow part of the residual field. The transport equations for the last four shares, which contribute the total turbulent kinetic energy, are derived. According to these transport equations, the mechanisms of energy transfer among different fractions of turbulent kinetic energy can be revealed clearly. Our objective is to explore the energy balance and transfer among different fractions of the turbulent kinetic energy in RPCF based on a series of direct numerical simulation databases at a Reynolds number Rew=Uwh/=1300 (here, Uw is half of the wall velocity difference, and h is the channel half-width) and rotation number Ro=2zh/Uw (z is the constant angular velocity in the spanwise direction) in a range of 0Ro0.9. The results show that the energy is transferred between the streamwise part/cross-flow part of secondary flows and the residual field through the correlation between the vorticity of secondary flows and the shear stress of residual field. The rotation term acts as a bridge to transfer the energy between the streamwise part and the cross-flow part of either the secondary flows or the residual field. Moreover, pressure-strain redistribution term also plays an important role in the energy transfer between streamwise part and cross-flow part in residual field. For the streamwise part of residual field, in certain rotate rates, the energy obtained from the streamwise part of secondary flows by the correlation between the vorticity of secondary flows and the shear stress of residual field is larger than that obtained from mean flow through mean shear, implying that the streamwise motions of secondary flows have a significant influence on the streamwise motions of residual field.
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Keywords:
- spanwise-rotating turbulent plane Couette flow /
- penta-decomposition approach /
- energy transfer
[1] Tillmark N, Alfredsson P H 1996 Proceedings of the Sixth European Turbulence Conference Lausanne, Switzerland, July 2-5, 1996 p391
[2] Bech K H, Andersson H I 1996 Proceedings of the Sixth European Turbulence Conference Lausanne, Switzerland, July 2-5, 1996 p91
[3] Bech K H, Andersson H I 1996 J. Fluid Mech. 317 195
[4] Bech K H, Andersson H I 1997 J. Fluid Mech. 347 289
[5] Nagata M 1998 J. Fluid Mech. 358 357
[6] Nagata M, Kawahara G 2004 Proceedings of the Tenth European Turbulence Conference Trondheim Norway, June 29-July 2, 2004 p391
[7] Alfredsson P H, Tillmark N 2004 IUTAM Symposium on LaminarTurbulent Transition and Finite Amplitude Solutions Bristol, UK, August 9-11, 2004 p173
[8] Barri M, Andersson H I 2007 Proceedings of the 11th EUROMECH European Turbulance Conference Porto, Portugal, June 25-28, 2007 p100
[9] Hiwatashi K, Alfredsson P H, Tillmark N, Nagata M 2007 Phys. Fluids 19 048103
[10] Barri M, Andersson H I 2010 Commun. Comput. Phys. 7 683
[11] Tsukahara T, Tillmark N, Alfredsson P H 2010 J. Fluid Mech. 648 5
[12] Tsukahara T 2011 J. Phys.:Conf. Ser. 318 022024
[13] Lee M J, Kim J 1991 8th Symposium on Turbulent Shear Flows Munich, Germany, September 9-11, 1991 p531
[14] Papavassiliou D V, Hanratty T J 1997 Int. J. Heat and Fluid Flow 18 55
[15] Moser R D, Moin P 1987 J. Fluid Mech. 175 479
[16] Kim J, Moin P, Moser R 1987 J. Fluid Mech. 177 133
[17] Bech K H, Andersson H I 1994 First ERCOFTAC Workshop on Direct and Large-Eddy Simulation Guildford, UK, March 28-1994 p13
[18] Gai J, Xia Z H, Cai Q D, Chen S Y 2016 Phys. Rev. Fluid 1 054401
[19] Cai Q D, Gai J, Sun Z L, Xia Z H 2016 Int. J. Nonlinear Sci. Numer. Simul. 17 305
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[1] Tillmark N, Alfredsson P H 1996 Proceedings of the Sixth European Turbulence Conference Lausanne, Switzerland, July 2-5, 1996 p391
[2] Bech K H, Andersson H I 1996 Proceedings of the Sixth European Turbulence Conference Lausanne, Switzerland, July 2-5, 1996 p91
[3] Bech K H, Andersson H I 1996 J. Fluid Mech. 317 195
[4] Bech K H, Andersson H I 1997 J. Fluid Mech. 347 289
[5] Nagata M 1998 J. Fluid Mech. 358 357
[6] Nagata M, Kawahara G 2004 Proceedings of the Tenth European Turbulence Conference Trondheim Norway, June 29-July 2, 2004 p391
[7] Alfredsson P H, Tillmark N 2004 IUTAM Symposium on LaminarTurbulent Transition and Finite Amplitude Solutions Bristol, UK, August 9-11, 2004 p173
[8] Barri M, Andersson H I 2007 Proceedings of the 11th EUROMECH European Turbulance Conference Porto, Portugal, June 25-28, 2007 p100
[9] Hiwatashi K, Alfredsson P H, Tillmark N, Nagata M 2007 Phys. Fluids 19 048103
[10] Barri M, Andersson H I 2010 Commun. Comput. Phys. 7 683
[11] Tsukahara T, Tillmark N, Alfredsson P H 2010 J. Fluid Mech. 648 5
[12] Tsukahara T 2011 J. Phys.:Conf. Ser. 318 022024
[13] Lee M J, Kim J 1991 8th Symposium on Turbulent Shear Flows Munich, Germany, September 9-11, 1991 p531
[14] Papavassiliou D V, Hanratty T J 1997 Int. J. Heat and Fluid Flow 18 55
[15] Moser R D, Moin P 1987 J. Fluid Mech. 175 479
[16] Kim J, Moin P, Moser R 1987 J. Fluid Mech. 177 133
[17] Bech K H, Andersson H I 1994 First ERCOFTAC Workshop on Direct and Large-Eddy Simulation Guildford, UK, March 28-1994 p13
[18] Gai J, Xia Z H, Cai Q D, Chen S Y 2016 Phys. Rev. Fluid 1 054401
[19] Cai Q D, Gai J, Sun Z L, Xia Z H 2016 Int. J. Nonlinear Sci. Numer. Simul. 17 305
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