Tirtha Banerjee

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

u /u∗ 2 = B1 − A1 ln (z/δ) was reported across several high Reynolds number laboratory experiments as predicted from Townsend’s attached eddy hypothesis, whereu∗ is the friction velocity andz is the height normalized by the boundary layer thickness δ. A phenomenological explanation for the origin of this log-law in the intermediate region is provided here based on a solution to a spectral budget where the production and energy transfer terms are modeled. The solution to this spectral budget predicts A1 = (18/55)Co/κ 2/3 and B1 = (2.5)A1, where Co and κ are the Kolmogorov and von K´ arm´ an constants. These predictions hold when very large scale motions do not disturb the k −1 scaling existing across all wavenumbers 1/ δ< k < 1/z in the streamwise turbulent velocity spectrum Eu(k). Deviations from a k −1 scaling along with their effects on A1 and B1 are discussed using published data and field experiments. C 2013 AIP Publishing LLC .[ http://dx.doi.org/10.1063/1.4837876]

Mean Flow Near Edges and Within Cavities Situated Inside Dense Canopies

A streamfunction-vorticity formulation is used to explore the extent to which turbulent and turbulently inviscid solutions to the mean momentum balance explain the mean flow across forest edges and within cavities situated inside dense forested canopies. The turbulent solution is based on the mean momentum balance where first-order closure principles are used to model turbulent stresses. The turbulently inviscid solution retains all the key terms in the mean momentum balance but for the turbulent stress gradients. Both exit and entry versions of the forest edge problem are explored. The turbulent solution is found to describe sufficiently the bulk spatial patterns of the mean flow near the edge including signatures of different length scales reported in canopy transition studies. Next, the ‘clearing inside canopy’ or the so-called ‘cavity’ problem is solved for the inviscid and turbulent solutions and then compared against flume experiments. The inviscid solution describes the bulk flow dynamics in much of the zones within the cavity. In particular, the solution can capture the correct position of the bulk recirculation zone within the cavity, although with a weaker magnitude. The inviscid solution cannot capture the large vertical heterogeneity in the mean velocity above the canopy, as expected. These features are better captured via the first-order closure representation of the turbulent solution. Given the ability of this vorticity formulation to capture the mean pressure variations and the mean advective acceleration terms, it is ideal for exploring the distributions of scalars and roughness-induced flow adjustments on complex topography.

A Spectral Budget Model for the Longitudinal Turbulent Velocity in the Stable Atmospheric Surface Layer

AbstractA spectral budget model is developed to describe the scaling behavior of the longitudinal turbulent velocity variance with the stability parameter and the normalized height in an idealized stably stratified atmospheric surface layer (ASL), where z is the height from the surface, L is the Obukhov length, and δ is the boundary layer height. The proposed framework employs Kolmogorov’s hypothesis for describing the shape of the longitudinal velocity spectra in the inertial subrange, Heisenberg’s eddy viscosity as a closure for the pressure redistribution and turbulent transfer terms, and the Monin–Obukhov similarity theory (MOST) scaling for linking the mean longitudinal velocity and temperature profiles to ζ. At a given friction velocity , reduces with increasing ζ as expected. The model is consistent with the disputed z-less stratification when the stability correction function for momentum increases with increasing ζ linearly or as a power law with the exponent exceeding unity. For the Businger–Dye...

Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis

Expressions for the logarithmic variations of the normalized turbulent longitudinal velocity (u2p¯+)1/p with normalized distance z/δ from a boundary for high-order (p) moments in the intermediate region of wall bounded flows characterized by thickness δ are derived. The ansatz that (u2p¯+)1/p variation in ln(z/δ) originates from a compound effect of random sweeping and -1 power-law scaling in the longitudinal velocity spectrum Eu(k) is discussed, where k is the wavenumber. Using velocity time series sampled above a uniform ice sheet, an Eu(k) ∼ k−1 scaling is confirmed for kz 1. The data were then used to analyze assumptions required for the utility of the random sweeping decorrelation (RSD) hypothesis connecting the k−1 power-law with log-scaling in (u2p¯+)1/p. It has been found out that while the RSD hypothesis is operationally applicable to scales associated with attached eddies bounded by kz 1, significant interactions among high-order turbulent velocity and velocity incremen...

Evaluation of energy balance closure adjustment methods by independent evapotranspiration estimates from lysimeters and hydrological simulations

Karlsruhe Institute of Technology, Institute of Meteorology and Climate Research–Atmospheric Environmental Research, Garmisch‐Partenkirchen, Germany Technical University Dresden, Institute of Hydrology und Meteorology, Dresden, Germany Karlsruhe Institute of Technology, Institute of Geography and Geoecology, Karlsruhe, Germany 4 Institute of Geography, University of Augsburg, Augsburg, Germany Los Alamos National Laboratory, Earth and Environmental Sciences Division, Applied Terrestrial, Energy and Atmospheric Modeling, New Mexico, USA Correspondence Matthias Mauder, KIT/IMK‐IFU, Kreuzeckbahnstraße 19, 82467 Garmisch‐Partenkirchen. Email: matthias.mauder@kit.edu Funding information Helmholtz‐Gemeinschaft, Grant/Award Number: VH‐NG‐843; Helmholtz Association

Effect of Surface Heterogeneity on the Boundary-Layer Height: A Case Study at a Semi-Arid Forest

We investigate the effects of an isolated meso-

Can a simple dynamical system describe the interplay between drag and buoyancy in terrain-induced canopy flows?

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Flume experiments on wind induced flow in static water bodies in the presence of protruding vegetation

γ-scale surface heterogeneity for roughness and albedo on the atmospheric boundary-layer (ABL) height, with a case study at a semi-arid forest surrounded by sparse shrubland (forest area: