Implications of Nonlocal Transport and Conditionally Averaged Statistics on Monin–Obukhov Similarity Theory and Townsend’s Attached Eddy Hypothesis

Qi Li Department of Earth and Environmental Engineering, Columbia University, New York, New York

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Pierre Gentine Department of Earth and Environmental Engineering, Columbia University, New York, New York

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Juan Pedro Mellado Max Planck Institute for Meteorology, Hamburg, Germany

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Kaighin A. McColl Harvard John A. Paulson School of Engineering and Applied Sciences, and Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts

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Abstract

According to Townsend’s hypothesis, so-called wall-attached eddies are the main contributors to turbulent transport in the atmospheric surface layer (ASL). This is also one of the main assumptions of Monin–Obukhov similarity theory (MOST). However, previous evidence seems to indicate that outer-scale eddies can impact the ASL, resulting in deviations from the classic MOST scaling. We conduct large-eddy simulations and direct numerical simulations of a dry convective boundary layer to investigate the impact of coherent structures on the ASL. A height-dependent passive tracer enables coherent structure detection and conditional analysis based on updrafts and subsidence. The MOST similarity functions computed from the simulation results indicate a larger deviation of the momentum similarity function ϕm from classical scaling relationships compared to the temperature similarity function ϕh. The conditional-averaged ϕm for updrafts and subsidence are similar, indicating strong interactions between the inner and outer layers. However, ϕh conditioned on subsidence follows the mixed-layer scaling, while its updraft counterpart is well predicted by MOST. Updrafts are the dominant contributors to the transport of momentum and temperature. Subsidence, which comprises eddies that originate from the outer layer, contributes increasingly to the transport of temperature with increasing instability. However, u′ of different signs are distributed symmetrically in subsidence unlike the predominantly negative θ′ as instability increases. Thus, the spatial patterns of uw′ differ compared to θw′ in regions of subsidence. These results depict the mechanisms for departure from the MOST scaling, which is related to the stronger role of subsidence.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Qi Li, liqi1026@gmail.com

Abstract

According to Townsend’s hypothesis, so-called wall-attached eddies are the main contributors to turbulent transport in the atmospheric surface layer (ASL). This is also one of the main assumptions of Monin–Obukhov similarity theory (MOST). However, previous evidence seems to indicate that outer-scale eddies can impact the ASL, resulting in deviations from the classic MOST scaling. We conduct large-eddy simulations and direct numerical simulations of a dry convective boundary layer to investigate the impact of coherent structures on the ASL. A height-dependent passive tracer enables coherent structure detection and conditional analysis based on updrafts and subsidence. The MOST similarity functions computed from the simulation results indicate a larger deviation of the momentum similarity function ϕm from classical scaling relationships compared to the temperature similarity function ϕh. The conditional-averaged ϕm for updrafts and subsidence are similar, indicating strong interactions between the inner and outer layers. However, ϕh conditioned on subsidence follows the mixed-layer scaling, while its updraft counterpart is well predicted by MOST. Updrafts are the dominant contributors to the transport of momentum and temperature. Subsidence, which comprises eddies that originate from the outer layer, contributes increasingly to the transport of temperature with increasing instability. However, u′ of different signs are distributed symmetrically in subsidence unlike the predominantly negative θ′ as instability increases. Thus, the spatial patterns of uw′ differ compared to θw′ in regions of subsidence. These results depict the mechanisms for departure from the MOST scaling, which is related to the stronger role of subsidence.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Qi Li, liqi1026@gmail.com
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