Exploring stratification effects in stable Ekman boundary layers using a stochastic one-dimensional turbulence model
Lehrstuhl Numerische Strömungs- und Gasdynamik, Brandenburgische Technische Universität Cottbus-Senftenberg, Siemens-Halske-Ring 15A, 03046 Cottbus, Germany
Heiko Schmidt
Lehrstuhl Numerische Strömungs- und Gasdynamik, Brandenburgische Technische Universität Cottbus-Senftenberg, Siemens-Halske-Ring 15A, 03046 Cottbus, Germany
Related authors
Marten Klein and Heiko Schmidt
Adv. Sci. Res., 20, 55–64, https://doi.org/10.5194/asr-20-55-2023, https://doi.org/10.5194/asr-20-55-2023, 2023
Short summary
Short summary
Atmospheric boundary layers are inherently unsteady and exhibit processes on multiple scales. A stochastic one-dimensional turbulence model is applied here to periodically forced Ekman flows. These flows are hard to model due to competing laminar and turbulent response mechanisms. It is shown that the model is able to capture parametric dependencies of the near-surface turbulence. The results consolidate improvements seen in a subgrid-scale application of the model within large-eddy simulations.
Marten Klein and Heiko Schmidt
Adv. Sci. Res., 20, 55–64, https://doi.org/10.5194/asr-20-55-2023, https://doi.org/10.5194/asr-20-55-2023, 2023
Short summary
Short summary
Atmospheric boundary layers are inherently unsteady and exhibit processes on multiple scales. A stochastic one-dimensional turbulence model is applied here to periodically forced Ekman flows. These flows are hard to model due to competing laminar and turbulent response mechanisms. It is shown that the model is able to capture parametric dependencies of the near-surface turbulence. The results consolidate improvements seen in a subgrid-scale application of the model within large-eddy simulations.
Cited articles
Ansorge, C. and Mellado, J. P.: Analyses of external and global intermittency
in the surface layer of Ekman flow, J. Fluid Mech., 805, 611–635,
https://doi.org/10.1017/jfm.2016.534, 2016. a, b, c
Ashkenazy, Y., Gildor, H., and Bel, G.: The effect of stochastic wind on the
infinite depth Ekman layer model, Europhys. Lett., 111, 39001,
https://doi.org/10.1209/0295-5075/111/39001, 2015. a
Boyko, V. and Vercauteren, N.: Multiscale shear forcing of turbulence in the
nocturnal boundary layer: a statistical analysis, Bound.-Lay. Meteorol.,
179, 43–72, https://doi.org/10.1007/s10546-020-00583-0, 2021. a
BYUignite: ODT, GitHub [code], https://github.com/BYUignite/ODT, last access: 14 July 2020. a
Cava, D., Mortarini, L., Giostra, U., Acevedo, O., and Katul, G.: Submeso
motions and intermittent turbulence across a nocturnal low-level jet: A
self-organized criticality analogy, Bound.-Lay. Meteorol., 172, 17–43,
https://doi.org/10.1007/s10546-019-00441-8, 2019. a
Chandrakar, K. K., Cantrell, W., Krueger, S., Shaw, R. A., and Wunsch, S.:
Supersaturation fluctuations in moist turbulent Rayleigh–Bénard
convection: a two-scalar transport problem, J. Fluid Mech., 884, A19,
https://doi.org/10.1017/jfm.2019.895, 2020. a
Costa, F. D., Acevedo, O. C., Medeiros, L. E., Maroneze, R., Puhales, F. S.,
Carvalho Jr., A. D., Camponogara, L. F., dos Santos, D. M., and
Mortarini, L.: Stable boundary layer regimes in single-column models, J.
Atmos. Sci., 77, 2039–2054, https://doi.org/10.1175/JAS-D-19-0218.1, 2020. a
Cuxart, J., Holtslag, A. A. M., Beare, R. J., Bazile, E., Beljaars, A., Cheng,
A., Conangla, L., Ek, M., Freedman, F., Hamdi, R., Kerstein, A., Kitagawa,
H., Lenderink, G., Lewellen, D., Mailhot, J., Mauritsen, T., Perov, V.,
Schayes, G., Steeneveld, G.-J., Svensson, G., Taylor, P., Weng, W., Wunsch,
S., and Xu, K.-M.: Single-column model intercomparison for a stably
stratified atmospheric boundary layer, Bound.-Lay. Meteorol., 118,
273–303, 2006. a, b
Deardorff, J. W.: The counter-gradient heat flux in the lower atmosphere and in
the laboratory, J. Atmos. Sci., 23, 503–506,
https://doi.org/10.1175/1520-0469(1966)023<0503:TCGHFI>2.0.CO;2, 1966. a
Dee, D. P., Uppala, S. M., Simmons, A. J., Berrisford, P., Poli, P., Kobayashi,
S., Andrae, U., Balmaseda, M. A., Balsamo, G., Bauer, P., Bechtold, P.,
Beljaars, A. C. M., van de Berg, L., Bidlot, J., Bormann, N., Delsol, C.,
Dragani, R., Fuentes, M., Geer, A. J., Haimberger, L., Healy, S. B.,
Hersbach, H., Hólm, E. V., Isaksen, L., Kållberg, P., Köhler, M.,
Matricardi, M., McNally, A. P., Monge-Sanz, B. M., Morcrette, J.-J., Park,
B.-K., Peubey, C., de Rosnay, P., Tavolato, C., Thépaut, J.-N., and Vitart,
F.: The ERA-Interim reanalysis: configuration and performance of the data
assimilation system, Q. J. Roy. Meteorol. Soc., 137, 553–597,
https://doi.org/10.1002/qj.828, 2011. a
de Silva, C. M., Hutchins, N., and Marusic, I.: Uniform momentum zones in
turbulent boundary layers, J. Fluid Mech., 786, 309–331,
https://doi.org/10.1017/jfm.2015.672, 2016. a
Durre, I., Vose, R. S., and Wuertz, D. B.: Overview of the integrated global
radiosonde archive, J. Climate, 19, 53–68, https://doi.org/10.1175/JCLI3594.1, 2006. a
Fragner, M. M. and Schmidt, H.: Investigating asymptotic suction boundary
layers using a one-dimensional stochastic turbulence model, J. Turbul., 18, 899–928, https://doi.org/10.1080/14685248.2017.1335869, 2017. a, b, c
Freire, L. S. and Chamecki, M.: A one-dimensional stochastic model of
turbulence within and above plant canopies, Agr. Forest Meteorol., 250–251,
9–23, https://doi.org/10.1016/j.agrformet.2017.12.211, 2018. a, b
Freire, L. S. and Chamecki, M.: Large-eddy simulation of smooth and rough
channel flows using a one-dimensional stochastic wall model, Comput. Fluids,
230, 105135, https://doi.org/10.1016/j.compfluid.2021.105135, 2021. a, b
Galperin, B., Sukoriansky, S., and Anderson, P. S.: On the critical
Richardson number in stably stratified turbulence, Atmos. Sci. Lett., 8,
65–69, https://doi.org/10.1002/asl.153, 2007. a, b
Garratt, J. R.: Review: The atmospheric boundary layer, Earth-Sci. Rev., 37,
89–134, https://doi.org/10.1016/0012-8252(94)90026-4, 1994. a
Ghasemi, A., Klein, M., Will, A., and Harlander, U.: Mean flow generation by an
intermittently unstable boundary layer over a sloping wall, J. Fluid Mech.,
853, 111–149, https://doi.org/10.1017/jfm.2018.552, 2018. a
Glawe, C., Medina M., J. A., and Schmidt, H.: IMEX based multi-scale time
advancement in ODTLES, Z. Angew. Math. Mech., 98, 1907–1923,
https://doi.org/10.1002/zamm.201800098, 2018. a, b
Gonzalez-Juez, E. D., Kerstein, A. R., and Shih, L. H.: Vertical mixing in
homogeneous sheared stratified turbulence: A one-dimensional-turbulence
study, Phys. Fluids, 23, 055106, https://doi.org/10.1063/1.3592329, 2011a. a
Gonzalez-Juez, E. D., Schmidt, R. C., and Kerstein, A. R.: ODTLES simulations
of wall-bounded flows, Phys. Fluids, 23, 125102, https://doi.org/10.1063/1.3664123,
2011b. a, b
Gonzalez-Juez, E. D., Kerstein, A. R., and Lignell, D. O.: Reactive
Rayleigh–Taylor turbulent mixing: a one-dimensional-turbulence study,
Geophys. Astro. Fluid, 107, 506–525,
https://doi.org/10.1080/03091929.2012.736504, 2013. a, b, c, d
Ha, K.-J. and Mahrt, L.: Simple inclusion of z-less turbulence within and
above the modeled nocturnal boundary layer, Mon. Weather Rev., 129,
2136–2143, https://doi.org/10.1175/1520-0493(2001)129<2136:SIOZLT>2.0.CO;2, 2001. a
Holtslag, A. A. M. and Nieuwstadt, F. T. M.: Scaling the atmospheric boundary
layer, Bound.-Lay. Meteorol., 36, 201–209, https://doi.org/10.1007/BF00117468,
1986. a, b
Howard, L. N.: Note on a paper of John W. Miles, J. Fluid Mech., 10,
509–512, https://doi.org/10.1017/S0022112061000317, 1961. a
Huang, K. Y., Brunner, C. E., Fu, M. K., Kokmanian, K., Morrison, T. J.,
Perelet, A. O., Calaf, M., Pardyjak, E., and Hultmark, M.: Investigation of
the atmospheric surface layer using a novel high-resolution sensor array,
Exp. Fluids, 62, 76, https://doi.org/10.1007/s00348-021-03173-z, 2021. a
Jiménez, M. A. and Cuxart, J.: Large-eddy simulations of the stable boundary
layer using the standard Kolmogorov theory: Range of applicability,
Bound.-Lay. Meteorol., 115, 241–261, https://doi.org/10.1007/s10546-004-3470-4,
2005. a
Kerstein, A. R.: Reduced numerical modeling of turbulent flow with fully
resolved time advancement. Part 1. Theory and physical interpretation,
Fluids, 7, 76, https://doi.org/10.3390/fluids7020076, 2022. a
Kerstein, A. R., Ashurst, W. T., Wunsch, S., and Nilsen, V.: One-dimensional
turbulence: vector formulation and application to free shear flows, J. Fluid
Mech., 447, 85–109, https://doi.org/10.1017/S0022112001005778, 2001. a, b
Klein, M., Zenker, C., and Schmidt, H.: Small-scale resolving simulations of
the turbulent mixing in confined planar jets using one-dimensional
turbulence, Chem. Eng. Sci., 204, 186–202, https://doi.org/10.1016/j.ces.2019.04.024,
2019. a
Krishnamurti, T. N.: Numerical Weather Prediction, Annu. Rev. Fluid Mech., 27,
195–225, https://doi.org/10.1146/annurev.fl.27.010195.001211, 1995. a
Lee, M. and Moser, R. D.: Direct numerical simulation of turbulent channel flow
up to Reτ≈5200, J. Fluid Mech., 774, 395–415,
https://doi.org/10.1017/jfm.2015.268, 2015. a, b
Lignell, D. O., Kerstein, A. R., Sun, G., and Monson, E. I.: Mesh adaption for
efficient multiscale implementation of one-dimensional turbulence, Theor.
Comp. Fluid Dyn., 27, 273–295, https://doi.org/10.1007/s00162-012-0267-9, 2013. a, b, c, d
Lindvall, J. and Svensson, G.: Wind turning in the atmospheric boundary layer
over land, Q. J. Roy. Meteor. Soc., 145, 3074–3088,
https://doi.org/10.1002/qj.3605, 2019. a, b, c, d
Liu, L., Gadde, S. N., and Stevens, R. J. A. M.: Universal wind profile for
conventionally neutral atmospheric boundary layers, Phys. Rev. Lett., 126,
104502, https://doi.org/10.1103/PhysRevLett.126.104502, 2021a. a, b, c
Liu, L., Gadde, S. N., and Stevens, R. J. A. M.: Geostrophic drag law for
conventionally neutral atmospheric boundary layers revisited, Q. J. Roy.
Meteor. Soc., 147, 847–857, https://doi.org/10.1002/qj.3949, 2021b. a
Lonardi, M., Pilz, C., Akansu, E. F., Dahlke, S., Egerer, U., Ehrlich, A.,
Griesche, H., Heymsfield, A. J., Kirbus, B., Schmitt, C. G., Shupe, M. D.,
Siebert, H., Wehner, B., and Wendisch, M.: Tethered balloon-borne profile
measurements of atmospheric properties in the cloudy atmospheric boundary
layer over the Arctic sea ice during MOSAiC: Overview and first results,
Elementa, 10, 000120, https://doi.org/10.1525/elementa.2021.000120, 000120, 2022. a
Lüpkes, C. and Schlünzen, K. H.: Modelling the arctic convective
boundary-layer with different turbulence parameterizations, Bound.-Lay.
Meteorol., 79, 107–130, https://doi.org/10.1007/BF00120077, 1996. a
Mahrt, L.: Stratified atmospheric boundary layers, Bound.-Lay. Meteorol.,
90, 375–396, https://doi.org/10.1023/A:1001765727956, 1999. a
Mahrt, L.: Stably stratified atmospheric boundary layers, Annu. Rev. Fluid
Mech., 46, 23–45, https://doi.org/10.1146/annurev-fluid-010313-141354, 2014. a, b
Medina M., J. A., Klein, M., and Schmidt, H.: One-dimensional turbulence
investigation of variable density effects due to heat transfer in a low
Mach number internal air flow, Int. J. Heat Fluid Fl., 80, 108481,
https://doi.org/10.1016/j.ijheatfluidflow.2019.108481, 2019. a
Meneveau, C. and Marusic, I.: Generalized logarithmic law for high-order
moments in turbulent boundary layers, J. Fluid Mech., 719, R1,
https://doi.org/10.1017/jfm.2013.61, 2013. a
Miles, J. W.: On the stability of heterogeneous shear flows, J. Fluid Mech.,
10, 496–508, https://doi.org/10.1017/S0022112061000305, 1961. a
Monson, E., Lignell, D. O., Finney, M., Werner, C., Jozefik, Z., Kerstein,
A. R., and Hintze, R.: Simulation of ethylene wall fires using the
spatially-evolving one-dimensional turbulence model, Fire Tech., 52,
167–196, https://doi.org/10.1007/s10694-014-0441-2, 2016. a
Owinoh, A. Z., Hunt, J. C. R., Orr, A., Clark, P., Klein, R., Fernando, H.
J. S., and Nieuwstadt, F. T. M.: Effects of changing surface heat flux on
atmospheric boundary-layer flow over flat terrain, Bound.-Lay. Meteorol.,
116, 331–361, https://doi.org/10.1007/s10546-004-2819-z, 2005. a
Pedlosky, J.: Geophysical Fluid Dynamics, Springer-Verlag,
https://doi.org/10.1007/978-1-4684-0071-7, 1979. a, b, c, d
Pope, S.: Turbulent Flows, Cambridge University Press, https://doi.org/10.1017/CBO9780511840531, 2000. a, b
Rakhi, Klein, M., Medina Méndez, J. A., and Schmidt, H.: One-dimensional
turbulence modelling of incompressible temporally developing turbulent
boundary layers with comparison to DNS, J. Turbul., 20, 506–543,
https://doi.org/10.1080/14685248.2019.1674859, 2019. a, b, c, d
Schmidt, R. C., Kerstein, A. R., Wunsch, S., and Nilsen, V.: Near-wall LES
closure based on one-dimensional turbulence modeling, J. Comput. Phys., 186,
317–355, https://doi.org/10.1016/S0021-9991(03)00071-8, 2003. a, b
Seidel, D. J., Zhang, Y., Beljaars, A., Golaz, J.-C., Jacobson, A. R., and
Medeiros, B.: Climatology of the planetary boundary layer over the
continental United States and Europe, J. Geophys. Res.-Atmos., 117, D17106, https://doi.org/10.1029/2012JD018143, 2012. a
Steeneveld, G.-J.: Current challenges in understanding and forecasting stable
boundary layers over land and ice, Front. Environ. Sci., 2, 41,
https://doi.org/10.3389/fenvs.2014.00041, 2014. a
Stephens, V. B. and Lignell, D. O.: One-dimensional turbulence (ODT):
Computationally efficient modeling and simulation of turbulent flows,
SoftwareX, 13, 100641, https://doi.org/10.1016/j.softx.2020.100641,
2021. a
Sullivan, P. P., Weil, J. C., Patton, E. G., Jonker, H. J. J., and Mironov,
D. V.: Turbulent winds and temperature fronts in large-eddy simulations of
the stable atmospheric boundary layer, J. Atmos. Sci., 73, 1815–1840,
https://doi.org/10.1175/JAS-D-15-0339.1, 2016. a
Townsend, A. A.: The Structure of Turbulent Shear Flow, 2nd edition, Cambridge University Press, in: Cambridge Monographs on Mechanics, edited by: Bathchelor, G. K. and Miles, J. W., ISBN 978-0-521-29819-3,1976. a
van de Wiel, B. J. H., Moene, A., Jonker, H. J. J., Baas, P., Basu, S., Donda,
J. M. M., Sun, J., and Holtslag, A. A. M.: The minimum wind speed for
sustainable turbulence in the nocturnal boundary layer, J. Atmos. Sci., 69,
3116–3127, https://doi.org/10.1175/JAS-D-12-0107.1, 2012. a, b
Vincze, M., Fenyvesi, N., Klein, M., Sommeria, J., Viboud, S., and Ashkenazy,
Y.: Evidence for wind-induced Ekman layer resonance based on rotating tank
experiments, Europhys. Lett., 125, 44001, https://doi.org/10.1209/0295-5075/125/44001, 2019. a
Wang, L. and Geller, M. A.: Morphology of gravity-wave energy as observed from
4 years (1998–2001) of high vertical resolution U.S. radiosonde data, J.
Geophys. Res. Atmos., 108, 4489, https://doi.org/10.1029/2002JD002786,
2003. a
Warner, T. T.: Numerical Weather and Climate Prediction, Cambridge University Press, ISBN 978-0-521-51389-0, 2011. a
Wunsch, S. and Kerstein, A. R.: A model for layer formation in stably
stratified turbulence, Phys. Fluids, 13, 702–712, https://doi.org/10.1063/1.1344182,
2001. a
Wunsch, S. and Kerstein, A. R.: A stochastic model for high-Rayleigh-number
convection, J. Fluid Mech., 528, 173–205, https://doi.org/10.1017/S0022112004003258,
2005. a
Zilitinkevich, S. S., Gryanik, V. M., Lykossov, V. N., and Mironov, D. V.:
Third-order transport and nonlocal turbulence closures for convective
boundary layers, J. Atmos. Sci., 56, 3463–3477,
https://doi.org/10.1175/1520-0469(1999)056<3463:TOTANT>2.0.CO;2, 1999.
a
Zilitinkevich, S. S., Elperin, T., Kleeorin, N., Rogachevskii, I., and Esau,
I.: A Hierarchy of energy- and flux-budget (EFB) turbulence closure models
for stably-stratified geophysical flows., Bound.-Lay. Meteorol., 146,
341–373, https://doi.org/10.1007/s10546-012-9768-8, 2013. a, b
Short summary
We study the flow in the lower atmosphere in response to a sudden surface cooling. Our numerical approach aims to resolve all relevant scales of the flow but only along a vertical column. Complex turbulent motions are modeled by simple random mappings. We show that the numerical model accurately captures some relevant features of near-surface turbulent winds and temperature fluctuations. The model offers new opportunities for atmospheric chemistry and polar boundary layer application cases.
We study the flow in the lower atmosphere in response to a sudden surface cooling. Our numerical...