Reynolds-number dependence of the Townsend-Perry �constant� in wall turbulence

Diwan, SS and Morrison, JF (2019) Reynolds-number dependence of the Townsend-Perry �constant� in wall turbulence. In: 11th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2019, 30 July through 2 August 2019, Grand Harbour HotelSouthampton; United Kingdom.

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Abstract

We address the question of Reynolds-number dependence of the �Townsend-Perry constant�, which is the slope of the logarithmic variation of the streamwise variance in wall turbulence. We make use of the turbulent pipe flow and boundary layer (TBL) data available in the literature. We find that using a wall-normal length scale, proportional to the square root of the friction Reynolds number (akin to the distance of the �mesolayer� from the wall) and an associated velocity scale, it is possible to obtain a Reynolds-number similarity for the streamwise variance in a region intermediate to the inner and outer layers. In this region, the intermediate-scaled variance follows a logarithmic variation for which the coefficients are independent of Reynolds number, and the extent of the log region increases with increase in Reynolds number. The intermediate-scaled log-law constants for the pipe and TBL are fairly close to each other, suggesting a plausible �universal� behaviour for the variance, in terms of the intermediate variables. The consequence of Re-number invariance of the intermediate-scaled log law is that the classical Townsend-Perry �constant� shows a systematic variation with Reynolds number. For the pipe flow the Townsend-Perry �constant� is seen to increase until the highest Reynolds number, whereas for the TBL it reaches a relatively constant value for sufficiently large Reynolds numbers. These are interesting findings, which can have important implications towards understanding the scaling and structure of the high-Reynolds-number wall turbulence; in particular, their implications for the attached-eddy modelling are briefly discussed. © 2019 International Symposium on Turbulence and Shear Flow Phenomena, TSFP. All rights reserved.

Item Type:	Conference Paper
Publication:	11th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2019
Publisher:	International Symposium on Turbulence and Shear Flow Phenomena, TSFP
Additional Information:	cited By 0; Conference of 11th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2019 ; Conference Date: 30 July 2019 Through 2 August 2019; Conference Code:151732
Keywords:	Atmospheric thermodynamics; Boundary layer flow; Boundary layers; Pipe flow; Shear flow; Turbulence; Turbulent flow, Constant values; High Reynolds number; Length scale; Square roots; Systematic variation; Turbulent pipe flow; Velocity scale; Wall turbulence, Reynolds number
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	20 Nov 2020 06:43
Last Modified:	28 Aug 2022 09:17
URI:	https://eprints.iisc.ac.in/id/eprint/65403

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