Revisiting the formulations for the longitudinal velocity variance in the unstable atmospheric surface layer

Banerjee, Tirtha; Katul, Gabriel G.; Salesky, Scott T.; Chamecki, Marcelo

doi:10.1002/qj.2472

Cited by 45 publications

(40 citation statements)

References 78 publications

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“…This aforementioned determination of Q must be viewed as a simplification whose (minor) consequences are explored in . In addition, the budget equation for the turbulent kinetic energy is assumed to be in equilibrium (Katul et al , , ; Li et al , ) so that φ ε ( ζ ) = φ m ( ζ ) − ζ (Banerjee et al , , gives experimental evaluation of this assumption). The

φ_{a_{3}}

is determined for reference so that φ a , the sum of

φ_{a_{1}}

φ_{a_{2}}

and

φ_{a_{3}}

, is 0.9 consistent with the value in Figures and .…”

Section: Resultsmentioning

confidence: 99%

“…is:

\begin{matrix} alignleft \\ align-1 \frac{\int_{z^{- 1}}^{\infty} TR (k^{'}) d k^{'}}{D_{m} \int_{0}^{z^{- 1}} k^{' 2} E_{TT} (k^{'}) d k^{'}} & align-2 = \frac{\int_{z^{- 1}}^{\infty} D_{t} (k^{'}) d k^{'}}{D_{m}} \\ align-1 & align-2 = \frac{3}{4} C_{H} C_{o}^{\frac{1}{2}} κ_{v}^{- \frac{1}{3}} \frac{ν_{m}}{D_{m}} P r_{t}^{- 1} φ_{ε}^{1 / 3} Re, \end{matrix}

where Re = u ∗ z / ν m is the Reynolds number, ν m is the kinematic molecular viscosity and

φ_{ε} = ε κ_{v} z / u_{*}^{3}

is the normalized dissipation rate for turbulent kinetic energy. For a sufficiently high Re , the molecular dissipation term is much smaller than the transfer term and hence can be ignored at k = 1/ z (Banerjee and Katul, ; Banerjee et al , ).…”

Section: Theorymentioning

confidence: 99%

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The k⁻¹ scaling of air temperature spectra in atmospheric surface layer flows

Katul

Gentine

2015

Quart J Royal Meteoro Soc

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A number of atmospheric surface layer (ASL) experiments reported a k−1 scaling in air temperature spectra ETT(k) at low wavenumber k but other experiments did not. Occurrence of this scaling law in ETT(k) in an idealized ASL flow across a wide range of atmospheric stability regimes is investigated theoretically and experimentally using measurements collected above a lake and a grass surface. Experiments reveal a k−1 scaling persisted across different atmospheric stability parameter values (ζ) ranging from mildly unstable to mildly stable conditions (−0.1 < ζ < 0.2). As instability increases, the k−1 scaling vanishes. Based on simplified spectral and co‐spectral budgets and using a Heisenberg eddy viscosity as a closure to the spectral flux transfer term, conditions promoting a k−1 scaling in ETT(k) are identified. Existence of a k−1 scaling is shown to be primarily linked to an imbalance between the production and dissipation rates of half the temperature variance. When −0.1 < ζ < 0.2, such imbalance exhibits weak dependence on ζ and hence z, which is shown to be the main cause for a −1 scaling at low k. As the atmosphere becomes more unstable, the imbalance determined from experiments here are not significantly affected by ζ, thereby negating conditions promoting a −1 scaling in ETT(k). The role of the imbalance between the production and dissipation rates of half the temperature variance in controlling the existence of a −1 scaling suggests that the −1 scaling in ETT(k) does not necessarily concur with the −1 scaling in the spectra of longitudinal velocity Euu(k). This finding explains why some ASL experiments reported k−1 in Euu(k) but not in ETT(k).

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φ_{a_{3}}

is determined for reference so that φ a , the sum of

φ_{a_{1}}

φ_{a_{2}}

and

φ_{a_{3}}

, is 0.9 consistent with the value in Figures and .…”

Section: Resultsmentioning

confidence: 99%

“…is:

\begin{matrix} alignleft \\ align-1 \frac{\int_{z^{- 1}}^{\infty} TR (k^{'}) d k^{'}}{D_{m} \int_{0}^{z^{- 1}} k^{' 2} E_{TT} (k^{'}) d k^{'}} & align-2 = \frac{\int_{z^{- 1}}^{\infty} D_{t} (k^{'}) d k^{'}}{D_{m}} \\ align-1 & align-2 = \frac{3}{4} C_{H} C_{o}^{\frac{1}{2}} κ_{v}^{- \frac{1}{3}} \frac{ν_{m}}{D_{m}} P r_{t}^{- 1} φ_{ε}^{1 / 3} Re, \end{matrix}

where Re = u ∗ z / ν m is the Reynolds number, ν m is the kinematic molecular viscosity and

φ_{ε} = ε κ_{v} z / u_{*}^{3}

Section: Theorymentioning

confidence: 99%

The k⁻¹ scaling of air temperature spectra in atmospheric surface layer flows

Katul

Gentine

2015

Quart J Royal Meteoro Soc

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“…2 in the inertial subrange (Salesky et al, 2013;Banerjee et al, 2015Banerjee et al, , 2016Li et al, 2016)…”

Section: Theorymentioning

confidence: 99%

Turbulent transport of energy across a forest and a semiarid shrubland

et al. 2018

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Abstract. The role of secondary circulations has recently been studied in the context of well-defined surface heterogeneity in a semiarid ecosystem where it was found that energy balance closure over a desert-forest system and the structure of the boundary layer was impacted by advection and flux divergence. As a part of the CliFF ("Climate feedbacks and benefits of semi-arid forests", a collaboration between KIT, Germany, and the Weizmann Institute, Israel) campaign, we studied the boundary layer dynamics and turbulent transport of energy corresponding to this effect in Yatir Forest situated in the Negev Desert in Israel. The forest surrounded by small shrubs presents a distinct feature of surface heterogeneity, allowing us to study the differences between their interactions with the atmosphere above by conducting measurements with two eddy covariance (EC) stations and two Doppler lidars. As expected, the turbulence intensity and vertical fluxes of momentum and sensible heat are found to be higher above the forest compared to the shrubland. Turbulent statistics indicative of nonlocal motions are also found to differ over the forest and shrubland and also display a strong diurnal cycle. The production of turbulent kinetic energy (TKE) over the forest is strongly mechanical, while buoyancy effects generate most of the TKE over the shrubland. Overall TKE production is much higher above the forest compared to the shrubland. The forest is also found to be more efficient in dissipating TKE. The TKE budget appears to be balanced on average both for the forest and shrubland, although the imbalance of the TKE budget, which includes the role of TKE transport, is found to be quite different in terms of diurnal cycles for the forest and shrubland. The difference in turbulent quantities and the relationships between the components of TKE budget are used to infer the characteristics of the turbulent transport of energy between the desert and the forest.

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“…are common sources of such uncertainties that give rise to nonlocal motions and secondary circulations. These secondary 5 circulations can occur not only in forests but are generic characteristics of boundary layer flows over natural and man made landscapes with discongruity of land use types, surface moisture or temperature etc. (Higgins et al, 2013;Eder et al, 2015).…”

mentioning

confidence: 99%

“…We use eddy covariance 5 and Doppler LiDAR measurements at two sites over the shrubland and the Yatir forest 4.3 km apart, where the shrubland is upwind of the forest in the path of the principal wind direction (there exists a heat induced low pressure system to the east, resulting in the main wind direction from the north west). We investigate the individual components of the turbulent kinetic energy budget, as well as the nature of advection and turbulent transport over the forest and desert and determine if there is a relationship between them.…”

mentioning

confidence: 99%

Turbulent transport of energy across a forest and a semi-arid shrubland

Banerjee¹,

Brugger²,

Roo³

et al. 2017

Preprint

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Abstract. The role of secondary circulations has recently been studied in the context of well defined surface heterogeneity in a semi-arid ecosystem where it was found that energy balance closure over a desert-forest system and the structure of the boundary layer was impacted by advection and flux divergence. As a part of the CliFF (Climate Feedbacks and benefits of semiarid forests, a collaboration between KIT, Germany and the Weizmann Institute, Israel) campaign, we studied the boundary layer dynamics and turbulent transport of energy corresponding to this effect in the Yatir forest situated in the Negev desert 5 in Israel. The forest surrounded by small shrubs presents a distinct feature of surface heterogeneity, allowing us to study the differences between their interactions with the atmosphere above by conducting measurements with two EC stations and two Doppler LiDARs. As expected, the turbulence intensity and vertical fluxes of momentum and sensible heat are found to be higher above the forest compared to the shrubland. Turbulent statistics indicative of nonlocal motions are also found to differ over the forest and shrubland and also display a strong diurnal cycle. The production of turbulent kinetic energy (TKE) over the 10 forest is strongly mechanical, while buoyancy effects generate most of the TKE over the shrubland. Overall TKE production is much higher above the forest compared to the shrubland. The forest is also found to be more efficient in dissipating TKE.The TKE budget appears to be balanced on average both for the forest and shrubland, although the imbalance of the TKE budget, which contains the role of TKE transport, is found to be quite different in terms of their variation with atmospheric stability and diurnal cycles for the forest and shrubland. The effect of very large mesoscale motions is also directly quantified 15 following a recent formulation by Banerjee and Katul, 2013, using the measured longitudinal velocity variances and boundary layer heights. The difference of turbulent quantities and the relationships between the components of TKE budget are used to infer the characteristics of turbulent transport of energy between the desert and the forest.

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Revisiting the formulations for the longitudinal velocity variance in the unstable atmospheric surface layer

Cited by 45 publications

References 78 publications

The k⁻¹ scaling of air temperature spectra in atmospheric surface layer flows

The k⁻¹ scaling of air temperature spectra in atmospheric surface layer flows

Turbulent transport of energy across a forest and a semiarid shrubland

Turbulent transport of energy across a forest and a semi-arid shrubland

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Revisiting the formulations for the longitudinal velocity variance in the unstable atmospheric surface layer

Cited by 45 publications

References 78 publications

The k−1 scaling of air temperature spectra in atmospheric surface layer flows

The k−1 scaling of air temperature spectra in atmospheric surface layer flows

Turbulent transport of energy across a forest and a semiarid shrubland

Turbulent transport of energy across a forest and a semi-arid shrubland

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Product

Resources

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The k⁻¹ scaling of air temperature spectra in atmospheric surface layer flows

The k⁻¹ scaling of air temperature spectra in atmospheric surface layer flows