Statistical structure of self-sustaining attached eddies in turbulent channel flow
Abstract The linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend's attached eddies. Based on this observation, in the present study, we perform a numerica...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Yongyun Hwang [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Journal of fluid mechanics - Cambridge [u.a.] : Cambridge Univ. Press, 1956, 767(2015), Seite 254-289 |
|---|---|
| Übergeordnetes Werk: |
volume:767 ; year:2015 ; pages:254-289 |
| Links: |
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| DOI / URN: |
10.1017/jfm.2015.24 |
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OLC1966572980 |
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| 245 | 1 | 0 | |a Statistical structure of self-sustaining attached eddies in turbulent channel flow |
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| 520 | |a Abstract The linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend's attached eddies. Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies in the original theory, providing direct evidence on the existence of Townsend's attached eddies. It is shown that a single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length [formula omitted: see PDF] between [formula omitted: see PDF] and [formula omitted: see PDF] , where [formula omitted: see PDF] is half the height of the channel, the former is found to be self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] , while the latter is self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] where [formula omitted: see PDF] is the wall-normal direction. The scaling suggests that the smallest attached eddy would be a near-wall coherent motion in the form of a streak and quasi-streamwise vortices aligned to that, whereas the largest one would be an outer motion with a very-large-scale motion (VLSM) and large-scale motions (LSMs) aligned to that. The attached eddies in between, the size of which is proportional to their distance from the wall, contribute to the logarithmic region and fill the space caused by the length scale separation. The scaling is also found to yield behaviour consistent with the emergence of [formula omitted: see PDF] spectra in a number of previous studies. Finally, a further discussion is provided, in particular on Townsend's inactive motion and several recent theoretical findings. | ||
| 650 | 4 | |a Fluid mechanics | |
| 650 | 4 | |a turbulent boundary layers | |
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| 650 | 4 | |a Flow velocity | |
| 650 | 4 | |a Reynolds number | |
| 650 | 4 | |a turbulence simulation | |
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10.1017/jfm.2015.24 doi PQ20160617 (DE-627)OLC1966572980 (DE-599)GBVOLC1966572980 (PRQ)c2776-cdfa9a72abd19028f21b04dc1c6eb83a252bd3f8b021fedd0fd31963c4fff7c50 (KEY)0059670120150000767000000254statisticalstructureofselfsustainingattachededdies DE-627 ger DE-627 rakwb eng 530 DNB Yongyun Hwang verfasserin aut Statistical structure of self-sustaining attached eddies in turbulent channel flow 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Abstract The linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend's attached eddies. Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies in the original theory, providing direct evidence on the existence of Townsend's attached eddies. It is shown that a single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length [formula omitted: see PDF] between [formula omitted: see PDF] and [formula omitted: see PDF] , where [formula omitted: see PDF] is half the height of the channel, the former is found to be self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] , while the latter is self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] where [formula omitted: see PDF] is the wall-normal direction. The scaling suggests that the smallest attached eddy would be a near-wall coherent motion in the form of a streak and quasi-streamwise vortices aligned to that, whereas the largest one would be an outer motion with a very-large-scale motion (VLSM) and large-scale motions (LSMs) aligned to that. The attached eddies in between, the size of which is proportional to their distance from the wall, contribute to the logarithmic region and fill the space caused by the length scale separation. The scaling is also found to yield behaviour consistent with the emergence of [formula omitted: see PDF] spectra in a number of previous studies. Finally, a further discussion is provided, in particular on Townsend's inactive motion and several recent theoretical findings. Fluid mechanics turbulent boundary layers Turbulent flow turbulence theory Flow velocity Reynolds number turbulence simulation Enthalten in Journal of fluid mechanics Cambridge [u.a.] : Cambridge Univ. Press, 1956 767(2015), Seite 254-289 (DE-627)12954647X (DE-600)218334-1 (DE-576)014996871 0022-1120 nnns volume:767 year:2015 pages:254-289 http://dx.doi.org/10.1017/jfm.2015.24 Volltext http://search.proquest.com/docview/1656297775 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_47 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2027 GBV_ILN_2192 GBV_ILN_4046 GBV_ILN_4313 GBV_ILN_4700 AR 767 2015 254-289 |
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10.1017/jfm.2015.24 doi PQ20160617 (DE-627)OLC1966572980 (DE-599)GBVOLC1966572980 (PRQ)c2776-cdfa9a72abd19028f21b04dc1c6eb83a252bd3f8b021fedd0fd31963c4fff7c50 (KEY)0059670120150000767000000254statisticalstructureofselfsustainingattachededdies DE-627 ger DE-627 rakwb eng 530 DNB Yongyun Hwang verfasserin aut Statistical structure of self-sustaining attached eddies in turbulent channel flow 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Abstract The linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend's attached eddies. Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies in the original theory, providing direct evidence on the existence of Townsend's attached eddies. It is shown that a single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length [formula omitted: see PDF] between [formula omitted: see PDF] and [formula omitted: see PDF] , where [formula omitted: see PDF] is half the height of the channel, the former is found to be self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] , while the latter is self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] where [formula omitted: see PDF] is the wall-normal direction. The scaling suggests that the smallest attached eddy would be a near-wall coherent motion in the form of a streak and quasi-streamwise vortices aligned to that, whereas the largest one would be an outer motion with a very-large-scale motion (VLSM) and large-scale motions (LSMs) aligned to that. The attached eddies in between, the size of which is proportional to their distance from the wall, contribute to the logarithmic region and fill the space caused by the length scale separation. The scaling is also found to yield behaviour consistent with the emergence of [formula omitted: see PDF] spectra in a number of previous studies. Finally, a further discussion is provided, in particular on Townsend's inactive motion and several recent theoretical findings. Fluid mechanics turbulent boundary layers Turbulent flow turbulence theory Flow velocity Reynolds number turbulence simulation Enthalten in Journal of fluid mechanics Cambridge [u.a.] : Cambridge Univ. Press, 1956 767(2015), Seite 254-289 (DE-627)12954647X (DE-600)218334-1 (DE-576)014996871 0022-1120 nnns volume:767 year:2015 pages:254-289 http://dx.doi.org/10.1017/jfm.2015.24 Volltext http://search.proquest.com/docview/1656297775 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_47 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2027 GBV_ILN_2192 GBV_ILN_4046 GBV_ILN_4313 GBV_ILN_4700 AR 767 2015 254-289 |
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10.1017/jfm.2015.24 doi PQ20160617 (DE-627)OLC1966572980 (DE-599)GBVOLC1966572980 (PRQ)c2776-cdfa9a72abd19028f21b04dc1c6eb83a252bd3f8b021fedd0fd31963c4fff7c50 (KEY)0059670120150000767000000254statisticalstructureofselfsustainingattachededdies DE-627 ger DE-627 rakwb eng 530 DNB Yongyun Hwang verfasserin aut Statistical structure of self-sustaining attached eddies in turbulent channel flow 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Abstract The linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend's attached eddies. Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies in the original theory, providing direct evidence on the existence of Townsend's attached eddies. It is shown that a single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length [formula omitted: see PDF] between [formula omitted: see PDF] and [formula omitted: see PDF] , where [formula omitted: see PDF] is half the height of the channel, the former is found to be self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] , while the latter is self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] where [formula omitted: see PDF] is the wall-normal direction. The scaling suggests that the smallest attached eddy would be a near-wall coherent motion in the form of a streak and quasi-streamwise vortices aligned to that, whereas the largest one would be an outer motion with a very-large-scale motion (VLSM) and large-scale motions (LSMs) aligned to that. The attached eddies in between, the size of which is proportional to their distance from the wall, contribute to the logarithmic region and fill the space caused by the length scale separation. The scaling is also found to yield behaviour consistent with the emergence of [formula omitted: see PDF] spectra in a number of previous studies. Finally, a further discussion is provided, in particular on Townsend's inactive motion and several recent theoretical findings. Fluid mechanics turbulent boundary layers Turbulent flow turbulence theory Flow velocity Reynolds number turbulence simulation Enthalten in Journal of fluid mechanics Cambridge [u.a.] : Cambridge Univ. Press, 1956 767(2015), Seite 254-289 (DE-627)12954647X (DE-600)218334-1 (DE-576)014996871 0022-1120 nnns volume:767 year:2015 pages:254-289 http://dx.doi.org/10.1017/jfm.2015.24 Volltext http://search.proquest.com/docview/1656297775 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_47 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2027 GBV_ILN_2192 GBV_ILN_4046 GBV_ILN_4313 GBV_ILN_4700 AR 767 2015 254-289 |
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10.1017/jfm.2015.24 doi PQ20160617 (DE-627)OLC1966572980 (DE-599)GBVOLC1966572980 (PRQ)c2776-cdfa9a72abd19028f21b04dc1c6eb83a252bd3f8b021fedd0fd31963c4fff7c50 (KEY)0059670120150000767000000254statisticalstructureofselfsustainingattachededdies DE-627 ger DE-627 rakwb eng 530 DNB Yongyun Hwang verfasserin aut Statistical structure of self-sustaining attached eddies in turbulent channel flow 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Abstract The linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend's attached eddies. Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies in the original theory, providing direct evidence on the existence of Townsend's attached eddies. It is shown that a single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length [formula omitted: see PDF] between [formula omitted: see PDF] and [formula omitted: see PDF] , where [formula omitted: see PDF] is half the height of the channel, the former is found to be self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] , while the latter is self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] where [formula omitted: see PDF] is the wall-normal direction. The scaling suggests that the smallest attached eddy would be a near-wall coherent motion in the form of a streak and quasi-streamwise vortices aligned to that, whereas the largest one would be an outer motion with a very-large-scale motion (VLSM) and large-scale motions (LSMs) aligned to that. The attached eddies in between, the size of which is proportional to their distance from the wall, contribute to the logarithmic region and fill the space caused by the length scale separation. The scaling is also found to yield behaviour consistent with the emergence of [formula omitted: see PDF] spectra in a number of previous studies. Finally, a further discussion is provided, in particular on Townsend's inactive motion and several recent theoretical findings. Fluid mechanics turbulent boundary layers Turbulent flow turbulence theory Flow velocity Reynolds number turbulence simulation Enthalten in Journal of fluid mechanics Cambridge [u.a.] : Cambridge Univ. Press, 1956 767(2015), Seite 254-289 (DE-627)12954647X (DE-600)218334-1 (DE-576)014996871 0022-1120 nnns volume:767 year:2015 pages:254-289 http://dx.doi.org/10.1017/jfm.2015.24 Volltext http://search.proquest.com/docview/1656297775 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_47 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2027 GBV_ILN_2192 GBV_ILN_4046 GBV_ILN_4313 GBV_ILN_4700 AR 767 2015 254-289 |
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10.1017/jfm.2015.24 doi PQ20160617 (DE-627)OLC1966572980 (DE-599)GBVOLC1966572980 (PRQ)c2776-cdfa9a72abd19028f21b04dc1c6eb83a252bd3f8b021fedd0fd31963c4fff7c50 (KEY)0059670120150000767000000254statisticalstructureofselfsustainingattachededdies DE-627 ger DE-627 rakwb eng 530 DNB Yongyun Hwang verfasserin aut Statistical structure of self-sustaining attached eddies in turbulent channel flow 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Abstract The linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend's attached eddies. Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies in the original theory, providing direct evidence on the existence of Townsend's attached eddies. It is shown that a single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length [formula omitted: see PDF] between [formula omitted: see PDF] and [formula omitted: see PDF] , where [formula omitted: see PDF] is half the height of the channel, the former is found to be self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] , while the latter is self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] where [formula omitted: see PDF] is the wall-normal direction. The scaling suggests that the smallest attached eddy would be a near-wall coherent motion in the form of a streak and quasi-streamwise vortices aligned to that, whereas the largest one would be an outer motion with a very-large-scale motion (VLSM) and large-scale motions (LSMs) aligned to that. The attached eddies in between, the size of which is proportional to their distance from the wall, contribute to the logarithmic region and fill the space caused by the length scale separation. The scaling is also found to yield behaviour consistent with the emergence of [formula omitted: see PDF] spectra in a number of previous studies. Finally, a further discussion is provided, in particular on Townsend's inactive motion and several recent theoretical findings. Fluid mechanics turbulent boundary layers Turbulent flow turbulence theory Flow velocity Reynolds number turbulence simulation Enthalten in Journal of fluid mechanics Cambridge [u.a.] : Cambridge Univ. Press, 1956 767(2015), Seite 254-289 (DE-627)12954647X (DE-600)218334-1 (DE-576)014996871 0022-1120 nnns volume:767 year:2015 pages:254-289 http://dx.doi.org/10.1017/jfm.2015.24 Volltext http://search.proquest.com/docview/1656297775 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_47 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2027 GBV_ILN_2192 GBV_ILN_4046 GBV_ILN_4313 GBV_ILN_4700 AR 767 2015 254-289 |
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Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies in the original theory, providing direct evidence on the existence of Townsend's attached eddies. It is shown that a single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length [formula omitted: see PDF] between [formula omitted: see PDF] and [formula omitted: see PDF] , where [formula omitted: see PDF] is half the height of the channel, the former is found to be self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] , while the latter is self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] where [formula omitted: see PDF] is the wall-normal direction. The scaling suggests that the smallest attached eddy would be a near-wall coherent motion in the form of a streak and quasi-streamwise vortices aligned to that, whereas the largest one would be an outer motion with a very-large-scale motion (VLSM) and large-scale motions (LSMs) aligned to that. The attached eddies in between, the size of which is proportional to their distance from the wall, contribute to the logarithmic region and fill the space caused by the length scale separation. The scaling is also found to yield behaviour consistent with the emergence of [formula omitted: see PDF] spectra in a number of previous studies. 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530 DNB Statistical structure of self-sustaining attached eddies in turbulent channel flow Fluid mechanics turbulent boundary layers Turbulent flow turbulence theory Flow velocity Reynolds number turbulence simulation |
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Statistical structure of self-sustaining attached eddies in turbulent channel flow |
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statistical structure of self-sustaining attached eddies in turbulent channel flow |
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Statistical structure of self-sustaining attached eddies in turbulent channel flow |
| abstract |
Abstract The linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend's attached eddies. Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies in the original theory, providing direct evidence on the existence of Townsend's attached eddies. It is shown that a single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length [formula omitted: see PDF] between [formula omitted: see PDF] and [formula omitted: see PDF] , where [formula omitted: see PDF] is half the height of the channel, the former is found to be self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] , while the latter is self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] where [formula omitted: see PDF] is the wall-normal direction. The scaling suggests that the smallest attached eddy would be a near-wall coherent motion in the form of a streak and quasi-streamwise vortices aligned to that, whereas the largest one would be an outer motion with a very-large-scale motion (VLSM) and large-scale motions (LSMs) aligned to that. The attached eddies in between, the size of which is proportional to their distance from the wall, contribute to the logarithmic region and fill the space caused by the length scale separation. The scaling is also found to yield behaviour consistent with the emergence of [formula omitted: see PDF] spectra in a number of previous studies. Finally, a further discussion is provided, in particular on Townsend's inactive motion and several recent theoretical findings. |
| abstractGer |
Abstract The linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend's attached eddies. Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies in the original theory, providing direct evidence on the existence of Townsend's attached eddies. It is shown that a single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length [formula omitted: see PDF] between [formula omitted: see PDF] and [formula omitted: see PDF] , where [formula omitted: see PDF] is half the height of the channel, the former is found to be self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] , while the latter is self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] where [formula omitted: see PDF] is the wall-normal direction. The scaling suggests that the smallest attached eddy would be a near-wall coherent motion in the form of a streak and quasi-streamwise vortices aligned to that, whereas the largest one would be an outer motion with a very-large-scale motion (VLSM) and large-scale motions (LSMs) aligned to that. The attached eddies in between, the size of which is proportional to their distance from the wall, contribute to the logarithmic region and fill the space caused by the length scale separation. The scaling is also found to yield behaviour consistent with the emergence of [formula omitted: see PDF] spectra in a number of previous studies. Finally, a further discussion is provided, in particular on Townsend's inactive motion and several recent theoretical findings. |
| abstract_unstemmed |
Abstract The linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend's attached eddies. Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies in the original theory, providing direct evidence on the existence of Townsend's attached eddies. It is shown that a single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length [formula omitted: see PDF] between [formula omitted: see PDF] and [formula omitted: see PDF] , where [formula omitted: see PDF] is half the height of the channel, the former is found to be self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] , while the latter is self-similar along [formula omitted: see PDF] and [formula omitted: see PDF] where [formula omitted: see PDF] is the wall-normal direction. The scaling suggests that the smallest attached eddy would be a near-wall coherent motion in the form of a streak and quasi-streamwise vortices aligned to that, whereas the largest one would be an outer motion with a very-large-scale motion (VLSM) and large-scale motions (LSMs) aligned to that. The attached eddies in between, the size of which is proportional to their distance from the wall, contribute to the logarithmic region and fill the space caused by the length scale separation. The scaling is also found to yield behaviour consistent with the emergence of [formula omitted: see PDF] spectra in a number of previous studies. Finally, a further discussion is provided, in particular on Townsend's inactive motion and several recent theoretical findings. |
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