Approximation of the exact traveling wave solutions in wall-bounded flows using resolvent modes

Rashad Moarref, Jae Sung Park, Ati S. Sharma, Ashley P. Willis, Michael D. Graham, Beverley J. McKeon

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Over the past decade, significant attention has been devoted to computing and understanding the exact traveling wave solutions (TWS) of the Navier-Stokes equations (NSE). To better understand the linear and nonlinear mechanisms in the TWS, we consider a low-order approximation of the TWS in terms of a weighted sum of resolvent modes. The resolvent modes represent the most amplified forcing and response modes by the linear mechanisms in the NSE and the weights represent the scaling influence of the nonlinear terms. We show that only a few resolvent modes are sufficient to capture most of the dynamics of the TWS in channel and pipe flows. For the most energetic Fourier modes in the wall-parallel directions, it is shown that the first few most amplified resolvent modes capture approximately 90% of the energy of the velocity field. This illustrates the integral role of linear amplification mechanisms in the NSE in shaping the wall-normal profile of the response. In addition, we show that approximately less than 30% of the nonlinear terms in the NSE is captured by the corresponding resolvent forcing modes. Therefore, a relatively small portion of the Reynolds-stress gradient is required for sustaining the velocity fluctuations.

Original languageEnglish (US)
Title of host publication9th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2015
PublisherTSFP-9
ISBN (Electronic)9780000000002
StatePublished - Jan 1 2015
Event9th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2015 - Melbourne, Australia
Duration: Jun 30 2015Jul 3 2015

Publication series

Name9th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2015
Volume1

Other

Other9th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2015
CountryAustralia
CityMelbourne
Period6/30/157/3/15

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ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes

Cite this

Moarref, R., Park, J. S., Sharma, A. S., Willis, A. P., Graham, M. D., & McKeon, B. J. (2015). Approximation of the exact traveling wave solutions in wall-bounded flows using resolvent modes. In 9th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2015 (9th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2015; Vol. 1). TSFP-9.