On the mixing length eddies and logarithmic mean velocity profile in wall turbulence

Michael Heisel; Charitha M. De Silva; Nicholas Hutchins; Ivan Marusic; Michele Guala

doi:10.1017/jfm.2020.23

On the mixing length eddies and logarithmic mean velocity profile in wall turbulence

Michael Heisel, Charitha M. De Silva, Nicholas Hutchins, Ivan Marusic, Michele Guala

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

Since the introduction of the logarithmic law of the wall more than 80 years ago, the equation for the mean velocity profile in turbulent boundary layers has been widely applied to model near-surface processes and parameterize surface drag. Yet the hypothetical turbulent eddies proposed in the original logarithmic law derivation and mixing length theory of Prandtl have never been conclusively linked to physical features in the flow. Here, we present evidence that suggests these eddies correspond to regions of coherent streamwise momentum known as uniform momentum zones (UMZs). The arrangement of UMZs results in a step-like shape for the instantaneous velocity profile, and the smooth mean profile results from the average UMZ properties, which are shown to scale with the friction velocity and wall-normal distance in the logarithmic region. These findings are confirmed across a wide range of Reynolds number and surface roughness conditions from the laboratory scale to the atmospheric surface layer.

Original language	English (US)
Article number	1DUMMY
Journal	Journal of Fluid Mechanics
Volume	887
DOIs	https://doi.org/10.1017/jfm.2020.23
State	Published - 2020

Bibliographical note

Funding Information:
The authors acknowledge funding support from the Institute on the Environment (IonE) and the Australian Research Council. M.G. is supported by a National Science Foundation CAREER grant (NSF-CBET-1351303). M.H.’s visit to the University of Melbourne was supported by the University of Minnesota Graduate School. The authors are grateful to J. A. Sillero for allowing public access to the DNS data. The new PIV measurements from St. Anthony Falls Laboratory are publicly available online at the University of Minnesota data repository ( http://hdl.handle.net/11299/211303 ).

Keywords

Atmospheric flows
Boundary layer structure
Turbulent boundary layers

Publisher link

10.1017/jfm.2020.23

Find It

Find It at U of M Libraries

Cite this

@article{d58981e0153b4298a20836105bded65c,

title = "On the mixing length eddies and logarithmic mean velocity profile in wall turbulence",

abstract = "Since the introduction of the logarithmic law of the wall more than 80 years ago, the equation for the mean velocity profile in turbulent boundary layers has been widely applied to model near-surface processes and parameterize surface drag. Yet the hypothetical turbulent eddies proposed in the original logarithmic law derivation and mixing length theory of Prandtl have never been conclusively linked to physical features in the flow. Here, we present evidence that suggests these eddies correspond to regions of coherent streamwise momentum known as uniform momentum zones (UMZs). The arrangement of UMZs results in a step-like shape for the instantaneous velocity profile, and the smooth mean profile results from the average UMZ properties, which are shown to scale with the friction velocity and wall-normal distance in the logarithmic region. These findings are confirmed across a wide range of Reynolds number and surface roughness conditions from the laboratory scale to the atmospheric surface layer.",

keywords = "Atmospheric flows, Boundary layer structure, Turbulent boundary layers",

author = "Michael Heisel and {De Silva}, {Charitha M.} and Nicholas Hutchins and Ivan Marusic and Michele Guala",

note = "Funding Information: The authors acknowledge funding support from the Institute on the Environment (IonE) and the Australian Research Council. M.G. is supported by a National Science Foundation CAREER grant (NSF-CBET-1351303). M.H.{\textquoteright}s visit to the University of Melbourne was supported by the University of Minnesota Graduate School. The authors are grateful to J. A. Sillero for allowing public access to the DNS data. The new PIV measurements from St. Anthony Falls Laboratory are publicly available online at the University of Minnesota data repository ( http://hdl.handle.net/11299/211303 ). ",

year = "2020",

doi = "10.1017/jfm.2020.23",

language = "English (US)",

volume = "887",

journal = "Journal of Fluid Mechanics",

issn = "0022-1120",

publisher = "Cambridge University Press",

}

TY - JOUR

T1 - On the mixing length eddies and logarithmic mean velocity profile in wall turbulence

AU - Heisel, Michael

AU - De Silva, Charitha M.

AU - Hutchins, Nicholas

AU - Marusic, Ivan

AU - Guala, Michele

N1 - Funding Information: The authors acknowledge funding support from the Institute on the Environment (IonE) and the Australian Research Council. M.G. is supported by a National Science Foundation CAREER grant (NSF-CBET-1351303). M.H.’s visit to the University of Melbourne was supported by the University of Minnesota Graduate School. The authors are grateful to J. A. Sillero for allowing public access to the DNS data. The new PIV measurements from St. Anthony Falls Laboratory are publicly available online at the University of Minnesota data repository ( http://hdl.handle.net/11299/211303 ).

PY - 2020

Y1 - 2020

N2 - Since the introduction of the logarithmic law of the wall more than 80 years ago, the equation for the mean velocity profile in turbulent boundary layers has been widely applied to model near-surface processes and parameterize surface drag. Yet the hypothetical turbulent eddies proposed in the original logarithmic law derivation and mixing length theory of Prandtl have never been conclusively linked to physical features in the flow. Here, we present evidence that suggests these eddies correspond to regions of coherent streamwise momentum known as uniform momentum zones (UMZs). The arrangement of UMZs results in a step-like shape for the instantaneous velocity profile, and the smooth mean profile results from the average UMZ properties, which are shown to scale with the friction velocity and wall-normal distance in the logarithmic region. These findings are confirmed across a wide range of Reynolds number and surface roughness conditions from the laboratory scale to the atmospheric surface layer.

AB - Since the introduction of the logarithmic law of the wall more than 80 years ago, the equation for the mean velocity profile in turbulent boundary layers has been widely applied to model near-surface processes and parameterize surface drag. Yet the hypothetical turbulent eddies proposed in the original logarithmic law derivation and mixing length theory of Prandtl have never been conclusively linked to physical features in the flow. Here, we present evidence that suggests these eddies correspond to regions of coherent streamwise momentum known as uniform momentum zones (UMZs). The arrangement of UMZs results in a step-like shape for the instantaneous velocity profile, and the smooth mean profile results from the average UMZ properties, which are shown to scale with the friction velocity and wall-normal distance in the logarithmic region. These findings are confirmed across a wide range of Reynolds number and surface roughness conditions from the laboratory scale to the atmospheric surface layer.

KW - Atmospheric flows

KW - Boundary layer structure

KW - Turbulent boundary layers

UR - http://www.scopus.com/inward/record.url?scp=85078339890&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85078339890&partnerID=8YFLogxK

U2 - 10.1017/jfm.2020.23

DO - 10.1017/jfm.2020.23

M3 - Article

AN - SCOPUS:85078339890

SN - 0022-1120

VL - 887

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

M1 - 1DUMMY

ER -

On the mixing length eddies and logarithmic mean velocity profile in wall turbulence

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Particle image velocimetry measurements of smooth- and rough-wall turbulence from the SAFL Atmospheric Boundary Layer wind tunnel

Cite this

On the mixing length eddies and logarithmic mean velocity profile in wall turbulence

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Datasets

Particle image velocimetry measurements of smooth- and rough-wall turbulence from the SAFL Atmospheric Boundary Layer wind tunnel

Cite this