Hostname: page-component-669899f699-rg895 Total loading time: 0 Render date: 2025-04-25T19:29:16.847Z Has data issue: false hasContentIssue false
  • English
  • Français

Scaling of vertical coherence and logarithmic energy profile for wall-attached eddies during sand and dust storms

Published online by Cambridge University Press:  25 September 2024

Xuebo Li Open the ORCID record for Xuebo Li [Opens in a new window] ,
Lan Hu Open the ORCID record for Lan Hu [Opens in a new window] ,
Xin Hu  and
Wanting Liu Open the ORCID record for Wanting Liu [Opens in a new window]
Xuebo Li*
Affiliation:
School of Science, Chongqing University of Technology, Chongqing 400054, PR China Center of Spatio-temporal Big Data Research, Chongqing University of Technology, Chongqing 400054, PR China
Lan Hu
Affiliation:
School of Science, Chongqing University of Technology, Chongqing 400054, PR China
Xin Hu
Affiliation:
School of Science, Chongqing University of Technology, Chongqing 400054, PR China
Wanting Liu
Affiliation:
School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

High-frequency observation data, including all three components of instantaneous fluctuating velocity, temperature, as well as particulate matter 10 ($PM_{10}$), collected from the unstable atmospheric surface layer at $z/L = -0.11$ and $-$0.12, $L$ being the Obukhov length, during sand and dust storms (SDS), were used to explore the scaling of vertical coherence and the logarithmic energy profile for wall-attached eddies. The present results demonstrate good agreement with the self-similar range of the wall-attached features for velocity and temperature components, as well as for $PM_{10}$ at lower heights ($z<15$ m) during SDS. Following the idea depicted by Davenport (Q. J. R. Meteorol., vol. 372, 1961, pp. 194–211), an empirically derived transfer kernel comprises implicit filtering via a scale-dependent gain and phase, parametrically defined as $|H_L^2(f)|=\exp (c_1-c_2\delta /\lambda _x)$, where $c_1$ and $c_2$ are parameters, $\delta$ is the boundary layer thickness and $\lambda _x$ is the streamwise wavelength. Linear coherence spectrum analysis is applied as a filter to separate the coherent and incoherent portions. After this separation procedure, the turbulence intensity decay for wall-attached eddies is described in a log–linear manner, which also identifies how the scaling parameter differs between the measured components. These findings present abundant features of wall-attached eddies during SDS which further are used to improve/enrich existing near-wall models.

JFM classification

Boundary Layers: Boundary layer structure Convection: Buoyant boundary layers Geophysical and Geological Flows: Atmospheric flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 996 , 10 October 2024 , A7
Check for updates
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Adrian, R.J. 1979 Conditional eddies in isotropic turbulence. Phys. Fluids 22 (11), 2065–2070.CrossRefGoogle Scholar
Adrian, R.J., Moin, P. & Moser, R.D. 1987 Stochastic estimation of conditional eddies in turbulent channel flow. In Studying Turbulence Using Numerical Simulation Databases. Proceedings of the 1987 Summer Program. Stanford University.Google Scholar
Akhlaq, M., Sheltami, T.R. & Mouftah, H.T. 2012 A review of techniques and technologies for sand and dust storm detection. Rev. Environ. Sci. Bio/Technol. 11, 305–322.CrossRefGoogle Scholar
Albarakat, R. & Lakshmi, V. 2019 Monitoring dust storms in Iraq using satellite data. Sensors 19 (17), 3687.CrossRefGoogle ScholarPubMed
Baars, W.J., Hutchins, N. & Marusic, I. 2016 Spectral stochastic estimation of high-Reynolds-number wall-bounded turbulence for a refined inner-outer interaction model. Phys. Rev. Fluids 1 (5), 054406.CrossRefGoogle Scholar
Baars, W.J., Hutchins, N. & Marusic, I. 2017 Self-similarity of wall-attached turbulence in boundary layers. J. Fluid Mech. 823, R2.CrossRefGoogle Scholar
Baars, W.J. & Marusic, I. 2020 a Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 1. Energy spectra. J. Fluid Mech. 882, A25.CrossRefGoogle Scholar
Baars, W.J. & Marusic, I. 2020 b Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 2. Integrated energy and $a_{1}$. J. Fluid Mech. 882, A26.CrossRefGoogle Scholar
Baars, W.J. & Tinney, C.E. 2014 Proper orthogonal decomposition-based spectral higher-order stochastic estimation. Phys. Fluids 26 (5), 055112.CrossRefGoogle Scholar
Baidya, R., et al. 2019 Simultaneous skin friction and velocity measurements in high Reynolds number pipe and boundary layer flows. J. Fluid Mech. 871, 377–400.CrossRefGoogle Scholar
Baidya, R., Philip, J., Hutchins, N., Monty, J.P. & Marusic, I. 2017 Distance-from-the-wall scaling of turbulent motions in wall-bounded flows. Phys. Fluids 29 (2), 020712.CrossRefGoogle Scholar
Banta, R.M., Pichugina, Y.L. & Brewer, W.A. 2006 Turbulent velocity-variance profiles in the stable boundary layer generated by a nocturnal low-level jet. J. Atmos. Sci. 63 (11), 2700–2719.CrossRefGoogle Scholar
Basley, J., Perret, L. & Mathis, R. 2019 Structure of high Reynolds number boundary layers over cube canopies. J. Fluid Mech. 870, 460–491.CrossRefGoogle Scholar
Bendat, J.S. & Piersol, A.G. 2000 Random data analysis and measurement procedures. Meas. Sci. Technol. 11 (12), 1825–1826.Google Scholar
Berman, S. & Stearns, C.R. 1977 Near-earth turbulence and coherence measurements at Aberdeen Proving Ground, MD. Boundary-Layer Meteorol. 11, 485–506.CrossRefGoogle Scholar
Davenport, A.G. 1961 The spectrum of horizontal gustiness near the ground in high winds. Q. J. R. Meteorol. 87 (372), 194–211.CrossRefGoogle Scholar
Davison, D.S. 1976 Geometric similarity for the temperature field in the unstable atmospheric surface layer. Boundary-Layer Meteorol. 10 (2), 167–180.CrossRefGoogle Scholar
Del Álamo, J.C. & Jiménez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor's approximation. J. Fluid Mech. 640, 5–26.CrossRefGoogle Scholar
Del Alamo, J.C., Jiménez, J., Zandonade, P. & Moser, R.D. 2006 Self-similar vortex clusters in the turbulent logarithmic region. J. Fluid Mech. 561, 329–358.CrossRefGoogle Scholar
Deshpande, R., Chandran, D., Monty, J.P. & Marusic, I. 2020 Two-dimensional cross-spectrum of the streamwise velocity in turbulent boundary layers. J. Fluid Mech. 890, R2.CrossRefGoogle Scholar
Deshpande, R., Monty, J.P. & Marusic, I. 2019 Streamwise inclination angle of large wall-attached structures in turbulent boundary layers. J. Fluid Mech. 877, R4.CrossRefGoogle Scholar
Dritselis, C.D. & Vlachos, N.S. 2008 Numerical study of educed coherent structures in the near-wall region of a particle-laden channel flow. Phys. Fluids 20 (5), 055103.CrossRefGoogle Scholar
Dritselis, C.D. & Vlachos, N.S. 2011 Numerical investigation of momentum exchange between particles and coherent structures in low $Re$ turbulent channel flow. Phys. Fluids 23 (2), 025103.CrossRefGoogle Scholar
Duan, Y., Zhang, P., Zhong, Q., Zhu, D. & Li, D. 2020 Characteristics of wall-attached motions in open channel flows. Phys. Fluids 32 (5), 055110.Google Scholar
Ewing, D. & Citriniti, J.H. 1999 Examination of a LSE/POD complementary technique using single and multi-time information in the axisymmetric shear layer. In IUTAM Symposium on Simulation and Identification of Organized Structures in Flows: Proceedings of the IUTAM Symposium held in Lyngby, Denmark, 25–29 May 1997, pp. 375–384. Springer.CrossRefGoogle Scholar
Favre, A., Gaviglio, J. & Dumas, R. 1967 Structure of velocity space-time correlations in a boundary layer. Phys. Fluids 10 (9), S138–S145.CrossRefGoogle Scholar
Ganapathisubramani, B., Longmire, E.K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 35–46.CrossRefGoogle Scholar
Gorlé, C., van Beeck, J., Rambaud, P. & Van Tendeloo, G. 2009 CFD modelling of small particle dispersion: the influence of the turbulence kinetic energy in the atmospheric boundary layer. Atmos. Environ. 43 (3), 673–681.CrossRefGoogle Scholar
Hu, R., Yang, X.I.A. & Zheng, X. 2020 Wall-attached and wall-detached eddies in wall-bounded turbulent flows. J. Fluid Mech. 885, A30.CrossRefGoogle Scholar
Hultmark, M., Vallikivi, M., Bailey, S.C.C. & Smits, A.J. 2012 Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett. 108 (9), 094501.CrossRefGoogle ScholarPubMed
Hutchins, N., Chauhan, K., Marusic, I., Monty, J.P. & Klewicki, J. 2012 Towards reconciling the large-scale structure of turbulent boundary layers in the atmosphere and laboratory. Boundary-Layer Meteorol. 145 (2), 273–306.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Hwang, J., Lee, J.H. & Sung, H.J. 2020 Statistical behaviour of self-similar structures in canonical wall turbulence. J. Fluid Mech. 905, A6.CrossRefGoogle Scholar
Hwang, J. & Sung, H.J. 2018 Wall-attached structures of velocity fluctuations in a turbulent boundary layer. J. Fluid Mech. 856, 958–983.CrossRefGoogle Scholar
Hwang, J. & Sung, H.J. 2019 Wall-attached clusters for the logarithmic velocity law in turbulent pipe flow. Phys. Fluids 31 (5), 055109.CrossRefGoogle Scholar
Hwang, Y. 2015 Statistical structure of self-sustaining attached eddies in turbulent channel flow. J. Fluid Mech. 767, 254–289.CrossRefGoogle Scholar
Jiménez, J. 2012 Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44, 27–45.CrossRefGoogle Scholar
Jiménez, J. 2018 Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842, P1.CrossRefGoogle Scholar
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236.CrossRefGoogle Scholar
Katul, G.G., Porporato, A. & Nikora, V. 2012 Existence of $k^{-1}$ power-law scaling in the equilibrium regions of wall-bounded turbulence explained by Heisenberg's eddy viscosity. Phys. Rev. E 86, 066311.CrossRefGoogle ScholarPubMed
Krug, D., Baars, W.J., Hutchins, N. & Marusic, I. 2019 Vertical coherence of turbulence in the atmospheric surface layer: connecting the hypotheses of Townsend and Davenport. Boundary-Layer Meteorol. 1–16.Google Scholar
Kunkel, G.J. & Marusic, I. 2006 Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow. J. Fluid Mech. 548, 375–402.CrossRefGoogle Scholar
Lee, M. & Moser, R.D. 2015 Direct numerical simulation of turbulent channel flow up to ${Re}_{\tau }\approx 5200$. J. Fluid Mech. 774, 395–415.CrossRefGoogle Scholar
Li, J., Wang, H., Liu, Z., Chen, S. & Zheng, C. 2012 An experimental study on turbulence modification in the near-wall boundary layer of a dilute gas-particle channel flow. Exp. Fluids 53, 1385–1403.CrossRefGoogle Scholar
Li, X., Huang, Y., Wang, G. & Zheng, X. 2021 a High-frequency observation during sand and dust storms at the Qingtu Lake observatory. Earth Syst. Sci. Data 13 (12), 5819–5830.CrossRefGoogle Scholar
Li, X., Hutchins, N., Zheng, X., Marusic, I. & Baars, W.J. 2022 a Scale-dependent inclination angle of turbulent structures in stratified atmospheric surface layers. J. Fluid Mech. 942, A38.CrossRefGoogle Scholar
Li, X., Wang, G. & Zheng, X. 2021 b Logarithmic energy profile of the streamwise velocity for wall-attached eddies along the spanwise direction in turbulent boundary layer. Phys. Fluids 33 (10), 105119.Google Scholar
Li, X., Wang, G. & Zheng, X. 2022 b Turbulent/synoptic separation and coherent structures in the atmospheric surface layer for a range of surface roughness. Boundary-Layer Meteorol. 182 (1), 75–93.CrossRefGoogle Scholar
Liu, H., Feng, Y. & Zheng, X. 2022 Experimental investigation of the effects of particle near-wall motions on turbulence statistics in particle-laden flows. J. Fluid Mech. 943, A8.CrossRefGoogle Scholar
Liu, T., et al. 2023 Classification and sources of extremely severe sandstorms mixed with haze pollution in Beijing. Environ. Pollut. 322, 121154.CrossRefGoogle ScholarPubMed
Lozano-Durán, A., Flores, O. & Jiménez, J. 2012 The three-dimensional structure of momentum transfer in turbulent channels. J. Fluid Mech. 694, 100–130.CrossRefGoogle Scholar
Lozano-Durán, A. & Jiménez, J. 2014 Time-resolved evolution of coherent structures in turbulent channels: characterization of eddies and cascades. J. Fluid Mech. 759, 432–471.CrossRefGoogle Scholar
Marusic, I., Baars, W.J. & Hutchins, N. 2017 Scaling of the streamwise turbulence intensity in the context of inner-outer interactions in wall turbulence. Phys. Rev. Fluids 2 (10), 100502.CrossRefGoogle Scholar
Marusic, I. & Heuer, W.D.C. 2007 Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett. 99 (11), 114504.CrossRefGoogle ScholarPubMed
Marusic, I. & Kunkel, G.J. 2003 Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys. Fluids 15 (8), 2461–2464.CrossRefGoogle Scholar
Marusic, I., McKeon, B.J., Monkewitz, P.A. & Nagib, H. 2010 Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22 (6), 65103–65103.CrossRefGoogle Scholar
Marusic, I. & Monty, J.P. 2019 Attached eddy model of wall turbulence. Annu. Rev. Fluid Mech. 51, 49–74.CrossRefGoogle Scholar
Marusic, I., Monty, J.P., Hultmark, M. & Smits, A.J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.CrossRefGoogle Scholar
Meneveau, C. & Marusic, I. 2013 Generalized logarithmic law for high-order moments in turbulent boundary layers. J. Fluid Mech. 719, R1.CrossRefGoogle Scholar
Middleton, N. & Kang, U. 2017 Sand and dust storms: impact mitigation. Sustainability 9 (6), 1053.CrossRefGoogle Scholar
Monin, A. & Obukhov, A.M. 1954 Basic laws of turbulent mixing in the surface layer of the atmosphere. Contrib. Geophys. Inst. Acad. Sci. USSR 151 (163), e187.Google Scholar
Naguib, A.M., Wark, C.E. & Juckenhöfel, O. 2001 Stochastic estimation and flow sources associated with surface pressure events in a turbulent boundary layer. Phys. Fluids 13 (9), 2611–2626.CrossRefGoogle Scholar
Naito, G. & Kondo, J. 1974 Spatial structure of fluctuating components of the horizontal wind speed above the ocean. JMSJ Ser. II 52 (5), 391–399.Google Scholar
Nickels, T.B., Marusic, I., Hafez, S. & Chong, M.S. 2005 Evidence of the $k_1^{-1}$ law in a high-Reynolds-number turbulent boundary layer. Phys. Rev. Lett. 95 (7), 074501.CrossRefGoogle Scholar
Nikora, V. 1999 Origin of the ‘$-1$’ spectral law in wall-bounded turbulence. Phys. Rev. Lett. 83, 734–736.CrossRefGoogle Scholar
Obukhov, A.M. 1946 Turbulence in an atmosphere with inhomogeneous temperature, TR. Inst. Teor. Geofis. Akad. Nauk SSSR 1, 95–115.Google Scholar
Perry, A.E. & Abell, C.J. 1977 Asymptotic similarity of turbulence structures in smooth- and rough-walled pipes. J. Fluid Mech. 79 (04), 785–799.CrossRefGoogle Scholar
Perry, A.E. & Chong, M.S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217.CrossRefGoogle Scholar
Perry, A.E., Henbest, S. & Chong, M.S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163–199.CrossRefGoogle Scholar
Perry, A.E. & Marusic, I. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis. J. Fluid Mech. 298, 361–388.CrossRefGoogle Scholar
Pielke, R.A. & Panofsky, H.A. 1970 Turbulence characteristics along several towers. Boundary-Layer Meteorol. 1, 115–130.CrossRefGoogle Scholar
Robinson, S.K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601–639.CrossRefGoogle Scholar
Rosenberg, B.J., Hultmark, M., Vallikivi, M., Bailey, S.C.C. & Smits, A.J. 2013 Turbulence spectra in smooth- and rough-wall pipe flow at extreme Reynolds numbers. J. Fluid Mech. 731, 46–63.CrossRefGoogle Scholar
Salesky, S.T. & Anderson, W. 2020 Coherent structures modulate atmospheric surface layer flux-gradient relationships. Phys. Rev. Lett. 125 (12), 124501.CrossRefGoogle ScholarPubMed
Sillero, J.A., Jiménez, J. & Moser, R.D. 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to $\delta ^+\approx 2000$. Phys. Fluids 25 (10), 105102.CrossRefGoogle Scholar
Sivakumar, M.V.K. 2005 Impacts of sand storms/dust storms on agriculture. In Natural Disasters and Extreme Events in Agriculture: Impacts and Mitigation, pp. 159–177. Springer.CrossRefGoogle Scholar
Song, L., Bi, X., Zhang, Z., Li, L., Dai, Q., Zhang, W., Li, H., Wang, X., Liang, D. & Feng, Y. 2022 Impact of sand and dust storms on the atmospheric environment and its source in Tianjin-China. Sci. Total Environ. 825, 153980.CrossRefGoogle Scholar
Stevens, R.J.A.M., Wilczek, M. & Meneveau, C. 2014 Large-eddy simulation study of the logarithmic law for second- and higher-order moments in turbulent wall-bounded flow. J. Fluid Mech. 757, 888–907.CrossRefGoogle Scholar
Sun, J., Mahrt, L., Nappo, C. & Lenschow, D.H. 2015 Wind and temperature oscillations generated by wave–turbulence interactions in the stably stratified boundary layer. J. Atmos. Sci. 72 (4), 1484–1503.CrossRefGoogle Scholar
Taylor, G.I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A Math. Phys. Sci. 164 (919), 476–490.Google Scholar
Terradellas, E., Soler, M.R., Ferreres, E. & Bravo, M. 2005 Analysis of oscillations in the stable atmospheric boundary layer using wavelet methods. Boundary-Layer Meteorol. 114 (3), 489–518.CrossRefGoogle Scholar
Tinney, C.E., Coiffet, F., Delville, J., Hall, A.M., Jordan, P. & Glauser, M.N. 2006 On spectral linear stochastic estimation. Exp. Fluids 41, 763–775.CrossRefGoogle Scholar
Tomkins, C.D. & Adrian, R.J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74.CrossRefGoogle Scholar
Townsend, A.A.R. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Wang, G., Gu, H. & Zheng, X. 2020 Large scale structures of turbulent flows in the atmospheric surface layer with and without sand. Phys. Fluids 32 (10), 106604.CrossRefGoogle Scholar
Wang, G. & Zheng, X. 2016 Very large scale motions in the atmospheric surface layer: a field investigation. J. Fluid Mech. 802, 464–489.CrossRefGoogle Scholar
Wark, C.E. & Nagib, H.M. 1991 Experimental investigation of coherent structures in turbulent boundary layers. J. Fluid Mech. 230, 183–208.CrossRefGoogle Scholar
Yoon, M., Hwang, J., Yang, J. & Sung, H.J. 2020 Wall-attached structures of streamwise velocity fluctuations in an adverse-pressure-gradient turbulent boundary layer. J. Fluid Mech. 885, A12.CrossRefGoogle Scholar
Zhang, Y., Hu, R. & Zheng, X. 2018 Large-scale coherent structures of suspended dust concentration in the neutral atmospheric surface layer: a large-eddy simulation study. Phys. Fluids 30 (4), 046601.CrossRefGoogle Scholar
Zhao, L.H., Andersson, H.I. & Gillissen, J.J.J. 2010 Turbulence modulation and drag reduction by spherical particles. Phys. Fluids 22 (8), 081702.CrossRefGoogle Scholar