Skip to main content Accessibility help

Reconsideration of spanwise rotating turbulent channel flows via resolvent analysis

  • Satoshi Nakashima (a1), Mitul Luhar (a2) and Koji Fukagata (a1)

We study the effect of spanwise rotation in turbulent channel flow at both low and high Reynolds numbers by employing the resolvent formulation proposed by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382). Under this formulation, the nonlinear terms in the Navier–Stokes equations are regarded as a forcing that acts upon the remaining linear dynamics to generate the turbulent velocity field in response. A gain-based decomposition of the forcing–response transfer function across spectral space yields models for highly amplified flow structures, or modes. Unlike linear stability analysis, this enables targeted analyses of the effects of rotation on high-gain modes that serve as useful low-order models for dynamically important coherent structures in wall-bounded turbulent flows. The present study examines a wide range of rotation rates. A posteriori comparisons at low Reynolds number ( $\mathit{Re}_{\unicode[STIX]{x1D70F}}=180$ ) demonstrate that the resolvent formulation is able to quantitatively predict the effect of varying spanwise rotation rates on specific classes of flow structure (e.g. the near-wall cycle) as well as energy amplification across spectral space. For fixed inner-normalized rotation number, the effects of rotation at varying friction Reynolds numbers appear to be similar across spectral space, when scaled in outer units. We also consider the effects of rotation on modes with varying speed (i.e. modes that are localized in regions of varying mean shear), and provide suggestions for modelling the nonlinear forcing term.

Corresponding author
Email address for correspondence:
Hide All
Brethouwer, G. 2005 The effect of rotation on rapidly sheared homogeneous turbulence and passive scalar transport. Linear theory and direct numerical simulations. J. Fluid Mech. 542, 305342.
Brethouwer, G. 2017 Statistics and structure of spanwise rotating turbulent channel flow at moderate Reynolds number. J. Fluid Mech. 828, 424458.
Gomez, F., Blackburn, H. M., Rudman, M., Sharma, A. S. & McKeon, B. J. 2016a Streamwise-varying steady transpiration control in turbulent pipe flow. J. Fluid Mech. 796, 588616.
Gomez, F., Blackburn, H. M., Rudman, M., Sharma, A. S. & McKeon, B. J. 2016b On the coupling of direct numerical simulation and resolvent analysis. In Progress in Turbulence VI, Springer Proceedings in Physics, vol. 165, pp. 8791. Springer.
Grundestam, O., Wallin, S. & Johansson, A. V. 2008 Direct numerical simulations of rotating turbulent channel flow. J. Fluid Mech. 598, 177199.
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.
Johnston, J. P., Halleen, R. M. & Lezius, D. K. 1972 Effect of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow. J. Fluid Mech. 56, 533557.
Kristoffersen, R. & Andersson, H. I. 1993 Direct simulations of low-Reynolds-number turbulent flow in a rotating channel. J. Fluid Mech. 256, 395415.
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 ≈ 5200. J. Fluid Mech. 774, 245258.
Luhar, M., Sharma, A. S. & McKeon, B. J. 2014 Opposition control within the resolvent analysis framework. J. Fluid Mech. 749, 597626.
Luhar, M., Sharma, A. S. & McKeon, B. J. 2015 A framework for studying the effect of compliant surfaces on wall turbulence. J. Fluid Mech. 768, 415441.
Luhar, M., Sharma, A. S. & McKeon, B. J. 2016 On the design of optimal compliant walls for turbulence control. J. Turbul. 17, 787806.
McKeon, B. J. 2017 The engine behind (wall) turbulence: perspectives on scale interactions. J. Fluid Mech. 817, P1.
McKeon, B. J., Jacobi, I. & Sharma, A. S. 2013 Experimental manipulation of wall turbulence: a systems approach. Phys. Fluids 25, 031301.
McKeon, B. J. & Sharma, A. S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336382.
Moarref, R., Jovanovic, M. R., Sharma, A. S., Tropp, J. A. & McKeon, B. J. 2014 A low-order decomposition of turbulent channel flow via resolvent analysis and convex optimization. Phys. Fluids 26, 051701.
Moarref, R., Sharma, A. S., Tropp, J. A. & McKeon, B. J. 2013 Model-based scaling and prediction of the streamwise energy intensity in high-Reynolds number turbulent channels. J. Fluid Mech. 734, 275316.
Nakashima, S., Fukagata, K. & Luhar, M. 2017 Assessment of suboptimal control for turbulent friction reduction via resolvent analysis. J. Fluid Mech. 828, 496526.
Reynolds, W. C. & Tiederman, W. G. 1967 Stability of turbulent channel flow, with application to Malkus’s theory. J. Fluid Mech. 27, 253272.
Sharma, A. S. & McKeon, B. J. 2013 On coherent structure in wall turbulence. J. Fluid Mech. 728, 196238.
Taira, K., Brunton, S. L., Dawson, S. T. M., Rowley, C. W., Colonius, T., McKeon, B. J., Schmidt, O. T., Gordeyev, S, Theofilis, V. & Ukeiley, L. S. 2017 Modal analysis of fluid flows: an overview. AIAA J. 55, 40134041.
Tritton, D. J. 1992 Stabilization and destabilization of turbulent shear flow in a rotating fluid. J. Fluid Mech. 241, 503523.
Wallin, S., Grundestam, O. & Johansson, A. V. 2013 Laminarization mechanisms and extreme-amplitude states in rapidly rotating plane channel flow. J. Fluid Mech. 730, 177199.
Weideman, J. A. & Reddy, S. C. 2000 A Matlab differentiation matrix suite. ACM Trans. Math. Softw. 26, 465519.
Wu, H. & Kasagi, N. 2004 Effects of arbitrary direction system rotation on turbulent channel flow. Phys. Fluids 16, 979990.
Xia, Z., Shi, Y. & Chen, S. 2016 Direct numerical simulation of turbulent channel flow with spanwise rotation. J. Fluid Mech. 788, 4256.
Yang, Y. T. & Wu, J. Z. 2012 Channel turbulence with spanwise rotation studied using helical wave decomposition. J. Fluid Mech. 692, 137152.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed