Logarithmic scaling in the longitudinal velocity variance explained by a spectral budget

Banerjee, Tirtha; Katul, Gabriel G.

doi:10.1063/1.4837876

Cited by 41 publications

(38 citation statements)

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“…A mast was used over the desert and the measurement height was 9 m until 23 August, after which it was changed to 15 m for the remaining period. In this zone of the atmospheric surface layer, the longitudinal and crosswise velocity variances decrease logarithmically with height and the vertical velocity variance shows independence from height (Townsend, 1976;Perry and Chong, 1982;Marusic et al, 2013;Banerjee and Katul, 2013a). High-frequency turbulent data were collected at 20 Hz and 30 min averaging periods were used for both sites.…”

Section: Research Sitementioning

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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Section: Research Sitementioning

confidence: 99%

Turbulent transport of energy across a forest and a semiarid shrubland

et al. 2018

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“…It is worth mentioning here that the exact nature/type of the very large scale structures can not be discerned here -i.e., it cannot be pinpointed at a sea-breeze or other mesoscale events. However, a higher value of α would indicate a stronger large scale motion, the effect of which is to include more large scale low frequency motions in the turbulent spectra (Banerjee and Katul, 2013a).…”

Section: Effect Of Very Large Scale Motions (Vlsm)mentioning

confidence: 99%

“…We seek to quantify the signature of such a mesoscale system on the turbulence above the desert-forest system and 10 a novel technique is used. Banerjee and Katul (2013a) developed a theoretical framework based on spectral theory to describe the scaling law of the longitudinal velocity variance σ 2 u /u 2 * in the surface layer. This scaling law includes a bulk parameter α 13 Atmos.…”

Section: Effect Of Very Large Scale Motions (Vlsm)mentioning

confidence: 99%

“…However, the raising of the mast should not have affected the measurement of turbulent fluxes since it was done within the constant flux layer. In this zone of the atmospheric surface layer, the longitudinal and crosswise velocity variances decrease logarithmically with height and the vertical velocity variance shows an independence with height (Townsend, 1976;Perry and Chong, 1982;Marusic et al, 2013;Banerjee and Katul, 2013a).…”

mentioning

confidence: 99%

“…As a response, the boundary layer heights increased both over the desert and forest. We quantified the first order effect of the very large scale motions (VLSM) through a scaling law that involves the longitudinal turbulent velocity variance developed by Banerjee and Katul (2013a) and found that there are several peaks of a parameter α that contains the bulk effect of all kinds of VLSMs. The VLSMs are found to enhance 20 turbulence fluxes and the nonlocal motions for both the forest and the desert.…”

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confidence: 99%

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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

Banerjee

Katul

Salesky

et al. 2014

Quart J Royal Meteoro Soc

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Because of its non-conformity to Monin-Obukhov Similarity Theory (MOST), the effects of thermal stratification on scaling laws describing the streamwise turbulent intensity σ u normalized by the turbulent friction velocity (u * ) continue to draw research attention. A spectral budget method has been developed to assess the variability of σ u /u * under unstable atmospheric stratification. At least three different length-scales -the distance from the ground (z), the height of the atmospheric boundary layer (δ) and the Obukhov length (L)-are all found to be controlling parameters in the variation of σ u /u * . Analytical models have been developed and supported by experiments for two limiting conditions: z/δ < 0.02, −z/L < 0.5 and 0.02 z/δ < 0.1, −z/L > 0.5. Under the first constraint, the turbulent kinetic energy spectrum is predicted to follow three regimes: k 0 , k −1 and k −5/3 , divided in the last two regimes by a break-point at kz = 1, where k denotes the wave number. The quantity σ u /u * is shown to follow the much discussed logarithmic scaling, reconciled to Townsend's attached eddy hypothesis σ 2 u /u 2 * = B 1 − A 1 log(z/δ), where the coefficients B 1 and A 1 are modified by MOST for mildly unstable stratification. Under the second constraint, the turbulent energy spectrum tends to become quasi-inertial, displaying k 0 and k −5/3 with a break-point predicted to occur at 0.3 < kz < 1. The work here brings together well-established but seemingly unrelated theories of turbulence such as Kolmogorov's hypothesis, Townsend's attached eddy hypothesis, MOST and Heisenberg's eddy viscosity under a common framework.

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Logarithmic scaling in the longitudinal velocity variance explained by a spectral budget

Cited by 41 publications

References 60 publications

Turbulent transport of energy across a forest and a semiarid shrubland

Turbulent transport of energy across a forest and a semiarid shrubland

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

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

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