Coherent Structures Modulate Atmospheric Surface Layer Flux-Gradient Relationships

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Coherent Structures Modulate Atmospheric Surface Layer Flux-Gradient Relationships

S. T. Salesky and W. Anderson

Phys. Rev. Lett. 125, 124501 – Published 16 September 2020

Abstract

Since its inception in the 1940s, Monin-Obukhov similarity theory (MOST), which relates turbulent fluxes to mean vertical gradients in the lower atmosphere, has become ubiquitous for predicting surface fluxes of quantities transported by the flow in numerical weather, climate, and hydrological forecasting models. Despite its widespread use, MOST does not account for the effects of large coherent structures in the flow, which modulate the amplitude of turbulent fluctuations, and are responsible for a large fraction of the total transport. Herein, we demonstrate that the incorporation of the large-scale streamwise velocity $u_{l} (x, t) = G_{δ} ⋆ u (x, t)$ , where $G_{δ}$ is a low-pass filtering kernel, into dimensional analysis leads to an additional dimensionless parameter $α (x, t)$ , which captures the modulating influence of these structures on flux-gradient relationships. Atmospheric observations and large-eddy simulations are used to demonstrate that observed deviations from MOST can indeed be explained by this new parameter; coherent structures induce an alternating loading and unloading of the mean velocity gradient near the surface.

Received 31 January 2020
Revised 6 March 2020
Accepted 24 August 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.124501

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Atmospheric fluid dynamics Structure & turbulence of boundary layers Turbulence

Fluid Dynamics

Authors & Affiliations

S. T. Salesky ^*

School of Meteorology, The University of Oklahoma, Norman, Oklahoma 73072, USA

W. Anderson

Mechanical Engineering Department, The University of Texas at Dallas, Richardson, Texas 75080, USA

^*salesky@ou.edu

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Issue

Vol. 125, Iss. 12 — 18 September 2020

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Images

Figure 1
Statistics from LES of the neutrally stratified ABL and AHATS data [9, 47]. (a) Premultiplied spectrogram of streamwise velocity, $π λ_{x}^{- 1} u_{τ}^{- 2} E_{⟨ u^{'} (x, t)^{2} ⟩_{t}} (λ_{x}, z)$ , plotted versus dimensionless wall-normal distance ( $z / δ$ ) and streamwise wavelength ( $λ_{x} / δ$ ); (b) vertical profile of the similarity parameter $⟨ α (z) ⟩_{x y t}$ , recovered from integrating the low-wave-number range of the spectrum [Eq. (11)]. (c),(d) Time-variable nondimensional velocity gradient attributes. Abscissa and ordinate in (c) are $α (x, t)$ [Eq. (2)] and nondimensional velocity gradient variability, respectively [Eq. (4)]; data points shown based on AHATS tower measurement heights denoted on legend, while linear fit represents the right-hand side of Eq. (4). (d) Results of generalized empirical curves [solid curves; Eq. (6)], generalized O’KEYPS model [dashed curves; Eq. (7)], and data points from AHATS. (e) Time series of large-scale velocity gradient (red) and nondimensional parameter, $α (x, t)$ (black) from AHATS data; gray panels denote elevated gradient due to $α (x, t) > 0$ , where the correlation coefficient is $ρ = 0.71$ . (f) Vertical profile of large-scale gradient and $α (x, t)$ correlation from the AHATS data; red markers denote mean value and gray bands denote standard deviation. (g),(h) Idealized large-scale velocity and velocity gradient with respect to ensemble-mean value, respectively, where the influence of unloading and loading is shown.
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Figure 2
Contours of dimensionless streamwise velocity ( $\tilde{u} / u_{τ}$ ) as a function of dimensionless time $t u_{τ} δ^{- 1}$ and height $z / δ$ from (a) neutrally stratified LES and (c) PDE solution. Heavy black lines indicate inclination angles, $θ = \tan^{- 1} [- U_{0} u_{τ}^{- 1} \tan (γ)]$ , where $γ = 17 °$ is the spatial inclination angle for LSMs and $U_{0}$ is the advection velocity; thin black lines in (a) denote interfaces between uniform momentum zones (UMZ). A dimensionless frequency of $\hat{ω} = (U_{0} δ) (u_{τ} λ_{x})^{- 1}$ is used when computing the PDE solution in (c), with an LSM wavelength of $λ_{x} = π δ$ . Vertical lines on (a) and (c) denote sampling times, with the corresponding profiles superimposed on (b) and (d), respectively; the LES profiles reveal the “staircaselike” pattern associated with UMZs [52, 53].
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Figure 3
(a)–(d) Conditionally sampled mean velocity profiles, i.e., $⟨ \tilde{u} / u_{τ} | α (x, t) ⟩_{x y t}$ from neutrally stratified LES. (e)–(h) Velocity profiles $U / u_{τ}$ from PDE solution for a range of $S$ values. (a),(e) $- δ / L = 0$ ; (b),(f) $- δ / L = 3.16$ ; (c),(g) $- δ / L = 17.7$ ; (d),(h) $- δ / L = 80.3$
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