Abstract
This brief communication quantifies the time-events that contribute to the dynamics of wall-bounded flows with rough walls. Lumley’s Proper Orthogonal Decomposition (POD) methodology has been used to extract the energetic modes of the flow. We have used the concept of entropy, a representation of lack of organization in the flow, to represent the extent of spread of turbulent kinetic energy to higher modes. The rough-wall dynamics is dominated by fast activity (short time period) propagating modes and slow activity (long time period) roll modes. A single dominant timescale has been captured for all the propagating modes in flows over smooth walls; multiple dominant timescales representing various vortex shedding events are captured for rough walls. Variable-interval time averaging technique has been used to obtain the bursting frequency. The bursting frequency of rough-wall turbulence is higher compared to smooth-wall turbulence, suggesting that roughness enhances turbulence production activity. Another insightful observation for rough walls revealed by our study is that the vortex shedding frequency of roughness elements is much higher compared to the bursting frequency of rough-wall turbulence. POD provides a straightforward method to extract the natural frequency of shed vortices due to roughness, an important dynamical activity in rough-wall turbulent boundary layers.
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References
Bandyopadhyay P.: Rough-wall turbulent boundary layers in the transition regime. J. Fluid Mech. 180, 231–266 (1987)
Bandyopadhyay R., Watson R.D.: Structure of rough-wall turbulent boundary layers. Phys. Fluids 31, 1877–1880 (1988)
Berkooz G., Holmes P., Lumley J.L.: The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25, 539–575 (1993)
Bhaganagar K., Kim J., Coleman G.: Effect of roughness on wall-bounded turbulence. Flow Turbul. Combust. 72, 463–492 (2004)
Blackwelder R.F., Haritonidis J.H.: Scaling of the bursting frequency in turbulent boundary layers. J. Fluid Mech. 132, 87–103 (1983)
Juttijudata V., Lumley J.L., Rempfer D.: Proper orthogonal decomposition in Squire’s coordinate system for dynamical models of channel turbulence. J. Fluid Mech. 534, 195–225 (2005)
Lumley, J.L.: Coherent Structures in Turbulence, Transition and Turbulence, pp. 215–245. Academic Press, New York (1981)
Manhart M., Wangle H.: A spatiotemporal decomposition of a fully inhomogeneous turbulent flow field. Theor. Comput. Fluid Dyn. 5, 223–242 (1993)
Morrison J.F., Tsai H.M., Bradshaw P.: Conditional sampling schemes for turbulent flows based on variable-interval time averaging (VITA) algorithm. Exp. Fluids 7, 173–189 (1989)
Prabhu R.D., Collis S.S., Chang Y.: The influence of control on proper orthogonal decomposition of wall-bounded turbulent flows. Phys. Fluids 13(2), 520–537 (2000)
Sen M., Bhaganagar K., Juttijudata V.: Application of proper orthogonal decomposition (POD) to investigate a turbulent boundary layer in a channel with rough walls. J. Turbul. 8(1), 1–21 (2007)
Sirovich L., Ball K.S., Handler R.A.: Propagating structures in wall-bounded turbulent flows. Theor. Comput. Fluid Dyn. 2, 307–317 (1991)
Webber G.A., Handler R.A., Sirovich L.: The Karhunen-Love decomposition of minimal channel flow. Phys. Fluids 9, 1054 (1997)
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Bhaganagar, K., Juttijudata, V. Turbulent time-events in channel with rough walls. Theor. Comput. Fluid Dyn. 26, 583–589 (2012). https://doi.org/10.1007/s00162-011-0242-x
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DOI: https://doi.org/10.1007/s00162-011-0242-x