A <scp>K</scp>olmogorov‐<scp>B</scp>rutsaert structure function model for evaporation into a turbulent atmosphere

Katul, Gabriel G.; Li, Heping

doi:10.1002/2016wr020006

Cited by 13 publications

(13 citation statements)

References 66 publications

(118 reference statements)

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“…This is justified on the grounds that z 0 m is reasonably described from simplified two‐parameter models (e.g.,

λ_{f}, λ_{p}

), as confirmed here. For a variety of surfaces, including bluff‐rough surfaces, a relation of the form

z_{0 s} / z_{0 m} \sim R e_{*}^{n}

is used (Brutsaert, 1965; 1975b; Zilitinkevich et al ., 2001; Li et al ., 2017; Katul and Liu, 2017; Castellví, 2018). A variety of exponents ( n =0, 1/4 or 1/2) and intercepts have been reported across differing surfaces.…”

Section: Roughness Lengths Determined From Lesmentioning

confidence: 99%

“…The distributional properties of s ,

ϕ (s)

must be externally supplied and are assumed to follow an exponential form (Danckwerts, 1951). Other forms (e.g., log‐normal, power‐law, gamma, inverse‐Gaussian) have also been proposed with various justifications (Katul and Liu, 2017). The choice

ϕ (s) = R \exp (- R s)

is the simplest and most convenient – it defines the probability density function for the rate of occurrence of a surface renewal event and satisfies the normalizing property

\int_{0}^{\infty} ϕ (s) d s = 1

.…”

Section: Scalar Roughness Length From Surface Renewal Theorymentioning

confidence: 99%

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Revisiting the relation between momentum and scalar roughness lengths of urban surfaces

Bou‐Zeid

Grimmond

et al. 2020

Quart J Royal Meteoro Soc

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Large‐Eddy Simulations (LESs) of neutral flow over regular arrays of cuboids are conducted to explore connections between momentum (z0m) and scalar (z0s) roughness lengths in urban environments, and how they are influenced by surface geometry. As LES resolves the obstacles but not the micro‐scale boundary layers attached to them, the aforementioned roughness lengths are analyzed at two distinct spatial scales. At the micro‐scale (roughness of individual facets, e.g., roofs), it is assumed that both momentum and scalar transfer are governed by accepted arguments for smooth walls that form the basis for the LES wall‐model. At the macro‐scale, the roughness lengths are representative of the aggregate effects of momentum and scalar transfer over the resolved roughness elements of the whole surface, and hence they are directly computed from the LES. The results indicate that morphologically based parametrizations for macro‐scale z0m are adequate overall. The relation between the momentum and scalar macro‐roughness values, as conventionally represented by log(z0m/z0s) and assumed to scale with Re∗n (where Re∗ is a roughness Reynolds number), is then interpreted using surface renewal theory (SRT). SRT predicts n = 1/4 when only Kolmogorov‐scale eddies dominate the scalar exchange, whereas n = 1/2 is predicted when large eddies limit the renewal dynamics. The latter is found to better capture the LES results. However, both scaling relations indicate that z0s decreases when z0m increases for typical urban geometries and scales. This is opposite to how their relation is usually modelled for urban canopies (i.e., z0s/z0m is a fixed value smaller than unity).

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“…This is justified on the grounds that z 0 m is reasonably described from simplified two‐parameter models (e.g.,

λ_{f}, λ_{p}

), as confirmed here. For a variety of surfaces, including bluff‐rough surfaces, a relation of the form

z_{0 s} / z_{0 m} \sim R e_{*}^{n}

Section: Roughness Lengths Determined From Lesmentioning

confidence: 99%

“…The distributional properties of s ,

ϕ (s)

ϕ (s) = R \exp (- R s)

is the simplest and most convenient – it defines the probability density function for the rate of occurrence of a surface renewal event and satisfies the normalizing property

\int_{0}^{\infty} ϕ (s) d s = 1

.…”

Section: Scalar Roughness Length From Surface Renewal Theorymentioning

confidence: 99%

Revisiting the relation between momentum and scalar roughness lengths of urban surfaces

Bou‐Zeid

Grimmond

et al. 2020

Quart J Royal Meteoro Soc

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“…The Surface Renewal (SR) theory is a simplification of surface turbulent flow exchange proposed by Higbie (1935) and subsequently modified by Danckwerts (1951), to study liquid-gas interfacial heat transfer in chemical engineering. The SR theory was the basis to derive new schemes and models to explain scalar exchange near-wall turbulent flows (Brutsaert, 1965;Bullin & Dukler, 1972;Harriot, 1962;Meek & Baer, 1970;Seo & Lee, 1988, among others), such as evaporation rates from different kind of surfaces (e.g., free water surfaces, rough surfaces, and porous media) (Brustasert, 1965(Brustasert, , 1975Haghighi & Or, 2013;Katul & Liu, 2017). In conjunction with the analysis of scalar concentration time series sampled at high frequency, based on the role of large coherent motions, a different SR-based depiction was introduced by Paw U et al (1995) for estimating the eddy flux of a scalar over agricultural and forest surfaces without requiring measurements of the wind speed and estimation of canopy parameters (known as SR analysis).…”

Section: Introductionmentioning

confidence: 99%

An Advanced Method Based on Surface Renewal Theory to Estimate the Friction Velocity and the Surface Heat Flux

Castellvı́

2018

Water Resources Research

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The earlier formulation based on surface renewal (SR) analysis for estimating the sensible (or buoyant) heat flux (H) of a surface without requiring calibration involved canopy parameters to simultaneously estimate H and the friction velocity (u * ). A SR-based formulation is derived that allows estimating u * and subsequently H that, at most, involves the zero-plane displacement. Regardless of the measurement height above the canopy and the stability case, u * and H estimates were closed to values measured using the eddy covariance method for either homogeneous or sparse (orchards) canopies. The proposed SR analysis can be potentially considered for gap filling in half-hourly eddy covariance series of u * and H and to estimate parameters useful for land surface modeling, such as the roughness length for momentum, the roughness lengths for momentum, and heat and the turbulent Prandtl number. CASTELLVÍ10,134

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“…As discussed elsewhere (Katul & Liu, 2017a, 2017bKomori et al, 1990), surface renewal theory predicts…”

Section: Surface Renewal Schemes: Large-and Micro-eddy Modelsmentioning

confidence: 86%

“…As discussed elsewhere (Katul & Liu, , ; Komori et al, ), surface renewal theory predicts

k_{L} \propto \sqrt{D_{m} \frac{σ_{t}}{L_{I}}},

where σ t is a characteristic turbulent velocity and L I is a length scale describing the upwelling eddy sizes penetrating the viscous sublayer and efficiently exchanging mass with the air‐water interface via molecular diffusion. Two types of models have been proposed to estimate σ t and L I : the so‐called microeddy approach (Lamont & Scott, ) and the energy‐containing eddy approach (Fortescue & Pearson, ; Komori et al, ).…”

Section: Theorymentioning

confidence: 87%

A Structure Function Model Recovers the Many Formulations for Air‐Water Gas Transfer Velocity

Katul

Mammarella

Grönholm

et al. 2018

Water Resources Research

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Two ideas regarding the structure of turbulence near a clear air‐water interface are used to derive a waterside gas transfer velocity kL for sparingly and slightly soluble gases. The first is that kL is proportional to the turnover velocity described by the vertical velocity structure function Dww(r), where r is separation distance between two points. The second is that the scalar exchange between the air‐water interface and the waterside turbulence can be suitably described by a length scale proportional to the Batchelor scale lB=ηSc−1/2, where Sc is the molecular Schmidt number and η is the Kolmogorov microscale defining the smallest scale of turbulent eddies impacted by fluid viscosity. Using an approximate solution to the von Kármán‐Howarth equation predicting Dww(r) in the inertial and viscous regimes, prior formulations for kL are recovered including (i) kL=2false/15Sc−1false/2vK, vK is the Kolmogorov velocity defined by the Reynolds number vKη/ν = 1 and ν is the kinematic viscosity of water; (ii) surface divergence formulations; (iii) kL∝Sc−1false/2u∗, where u∗ is the waterside friction velocity; (iv) kL∝Sc−1false/2gνfalse/u∗ for Keulegan numbers exceeding a threshold needed for long‐wave generation, where the proportionality constant varies with wave age, g is the gravitational acceleration; and (v) kL=2false/15Sc−1false/2false(νgβoqofalse)1false/4 in free convection, where qo is the surface heat flux and βo is the thermal expansion of water. The work demonstrates that the aforementioned kL formulations can be recovered from a single structure function model derived for locally homogeneous and isotropic turbulence.

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A Kolmogorov‐Brutsaert structure function model for evaporation into a turbulent atmosphere

Cited by 13 publications

References 66 publications

Revisiting the relation between momentum and scalar roughness lengths of urban surfaces

Revisiting the relation between momentum and scalar roughness lengths of urban surfaces

An Advanced Method Based on Surface Renewal Theory to Estimate the Friction Velocity and the Surface Heat Flux

A Structure Function Model Recovers the Many Formulations for Air‐Water Gas Transfer Velocity

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