On the linkage between the <i>k</i>−5/3 spectral and <i>k</i>−7/3 cospectral scaling in high-Reynolds number turbulent boundary layers

Li, Dan; Katul, Gabriel G.

doi:10.1063/1.4986068

Cited by 11 publications

(3 citation statements)

References 48 publications

(69 reference statements)

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“…The cospectral budget model was then developed to rectify this limitation, allowing for a new representation of the multiscale nature of turbulent transfer. The cospectral budget model recovers and refines the results obtained previously by the spectral link such as the mean velocity profile above a smooth surface (G. Katul & Manes, ; McColl, Katul, Gentine, & Entekhabi, ) and enables extensions to more complex situations as well as to scalar transport (G. Katul, Porporato, Shah, & Bou‐Zeid, ; Li, Katul, & Bou‐Zeid, ; Li, Katul, & Zilitinkevich, ; G. Katul, Li, Liu, & Assouline, ; Li et al, ; Li & Katul, ; McColl, van Heerwaarden, Katul, Gentine, & Entekhabi, ). It also offered a new perspective on the debate about the shape of the mean velocity profile (power‐law versus log‐law) as discussed elsewhere (G. G. Katul, Porporato, et al, ).…”

Section: Further Readingsupporting

confidence: 73%

A primer on turbulence in hydrology and hydraulics: The power of dimensional analysis

Katul

Manes

2019

WIREs Water

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The apparent random swirling motion of water is labeled “turbulence,” which is a pervasive state of the flow in many hydrological and hydraulic transport phenomena. Water flow in a turbulent state can be described by the momentum conservation equations known as the Navier–Stokes (NS) equations. Solving these equations numerically or in some approximated form remains a daunting task in applications involving natural systems thereby prompting interest in alternative approaches. The apparent randomness of swirling motion encodes order that may be profitably used to describe water movement in natural systems. The goal of this primer is to illustrate the use of a technique that links aspects of this ordered state to conveyance and transport laws. This technique is “dimensional analysis”, which can unpack much of the complications associated with turbulence into surprisingly simplified expressions. The use of this technique to describing water movement in streams as well as water vapor movement in the atmosphere is featured. Particular attention is paid to bulk expressions that have received support from a large body of experiments such as flow‐resistance formulae, the Prandtl‐von Karman log‐law describing the mean velocity shape, Monin‐Obukhov similarity theory that corrects the mean velocity shape for thermal stratification, and evaporation from rough surfaces. These applications illustrate how dimensional analysis offers a pragmatic approach to problem solving in sciences and engineering. This article is categorized under: Science of Water > Methods Science of Water > Hydrological Processes

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Section: Further Readingsupporting

confidence: 73%

A primer on turbulence in hydrology and hydraulics: The power of dimensional analysis

Katul

Manes

2019

WIREs Water

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“…In this paper, we use the model of Massman and Clement () for illustration purposes, as follows:

F_{wθ} ((), k) = \frac{A}{k_{p} {[1 + m {((), \frac{k}{k_{p}})}^{2 μ}]}^{\frac{1}{2 μ} \cdot \frac{m + 1}{m}}},

where A is a normalization parameter and m and μ are the (inertial subrange) slope parameter and broadness parameter, respectively. When m = 3/4, equation reproduces the −7/3 power law of F wθ in the inertial subrange (Li & Katul, ; Lumley, ). When μ = 0.5, equation reproduces the observed cospectrum from the famous Kansas experiment (Kaimal et al, ), which is commonly used as the standard in the cospectral correction of EC observations (Moore, ).…”

Section: Methodsmentioning

confidence: 82%

The Effects of Surface Heterogeneity Scale on the Flux Imbalance under Free Convection

Zhou

2019

JGR Atmospheres

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It is well known that the available energy (i.e., the net radiation minus the ground heat flux) is often 10-30% larger than the sum of turbulent fluxes measured by the eddy-covariance method. Although field observations and previous large-eddy simulation studies have shown that surface heterogeneity can induce flux imbalance, the relationship between the flux imbalance magnitude and the surface heterogeneity scale remains to be investigated in more detail. Here we examine the flux imbalance over landscapes characterized by different surface heterogeneity scales in a dry freely convective boundary layer. We reveal that the flux imbalance initially increases with increasing surface heterogeneity scale. However, when the surface heterogeneity scale becomes larger than the boundary layer height, the surface starts to behave locally homogeneous, which leads to a lower flux imbalance. Based on large-eddy simulation results, we propose a conceptual model to explain how the domain average flux imbalance is influenced by surface heterogeneity. The flux imbalance is found to be controlled by the ratio of the boundary layer height to the Obukhov length (−z i /L), the integral length scale of vertical velocity (l w ), the mean horizontal speed (U), and the time averaging interval (T). Among these four variables, l w determines the size of turbulent coherent structures (i.e., large eddies), whereas −z i /L affects the form of these large eddies. Meanwhile, the U and T determine how many these large eddies can be sampled by the eddy covariance. This finding indicates that it may be possible to diagnose the flux imbalance using these four variables under convective conditions. Key Points: • The relation between flux imbalance and surface heterogeneity scale is investigated using large-eddy simulations and a cospectral model • A diagnostic equation for flux imbalance is proposed • The qualitative relations between flux imbalance and various factors reported in the literature can be explained by this equation

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“…where sðkÞ ¼ ae À1=3 k À2=3 is the relaxation time at k associated with turbulent stress de-correlation, 53,54,66,70 and a is a proportionality constant of order unity. Upon integrating Eq.…”

Section: Model 2: the Co-spectral Budget (Csb) Modelmentioning

confidence: 99%

Adjustments to the law of the wall above an Amazon forest explained by a spectral link

et al. 2023

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Modification to the law-of-the wall represented by a dimensionless correction function $\phi_{RSL}(z/h)$ is derived using near-neutral atmospheric turbulence measurements collected at two sites in the Amazon in near-neutral stratification, where $z$ is the distance from the forest floor and $h$ is the mean canopy height. The sites are the Amazon Tall Tower Observatory (ATTO) for $z/h\in [1,2.3]$ and the Green Ocean Amazon (GoAmazon) site for $z/h\in[1,1.4]$. A link between the vertical velocity spectrum $E_{ww}(k)$ ($k$ is the longitudinal wavenumber) and $\phi_{RSL}$ is then established using a co-spectral budget (CSB) model interpreted by the moving-equilibrium hypothesis (MEH). The key finding is that $\phi_{RSL}$ is determined by the ratio of two turbulent viscosities and is given as $\nu_{t,BL}/\nu_{t,RSL}$, where $\nu_{t,RSL}=(1/A)\int_{0}^{\infty}\tau(k) E_{ww}(k)dk$, $\nu_{t,BL}=\kappa (z-d) u_*$, $\tau(k)$ is a scale-dependent decorrelation time scale between velocity components, $A=C_R/(1-C_I)=4.5$ is predicted from the Rotta constant $C_R=1.8$ and the isotropization of production constant $C_I=3/5$ given by Rapid Distortion Theory, $\kappa$ is the von K\'arm\'an constant, $u_*$ is the friction velocity at the canopy top, and $d$ is the zero-plane displacement. Because the transfer of energy across scales is conserved in $E_{ww}(k)$ and is determined by the turbulent kinetic energy dissipation rate ($\epsilon$), the CSB model also predicts that $\phi_{RSL}$ scales with $L_{BL}/L_d$, where $L_{BL}$ is the length scale of attached eddies to $z=d$, $L_d=u_*^3/\epsilon$ is a macro-scale dissipation length.

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On the linkage between the k−5/3 spectral and k−7/3 cospectral scaling in high-Reynolds number turbulent boundary layers

Cited by 11 publications

References 48 publications

A primer on turbulence in hydrology and hydraulics: The power of dimensional analysis

A primer on turbulence in hydrology and hydraulics: The power of dimensional analysis

The Effects of Surface Heterogeneity Scale on the Flux Imbalance under Free Convection

Adjustments to the law of the wall above an Amazon forest explained by a spectral link

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