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A spectral model for stably stratied turbulence
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, LUVAL.
(English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645Article in journal (Refereed) Submitted
Abstract [en]

A solution of the inviscid rapid distortion equations of a stratied flow with homogeneous shear is proposed, extending the work of Hanazaki and Hunt (J. Fluid Mech., 2004,vol. 507, pp. 1-42) to the two horizontal velocity components. The analytical solution allowed the determination of the spectral tensor evolution at any given time starting from a known initial condition. By following the same approach adopted by Mann (J.Fluid Mech., 1994, vol. 273, pp. 141-168), a model for the velocity spectral tensor in the atmospheric boundary layer is obtained where the spectral tensor, assumed to be isotropic at the initial time, evolves until the break-up time where the spectral tensor is supposed to achieve its final state observed in the boundary layer. The model predictions are compared with atmospheric measurements obtained over a forested area, giving the opportunity to calibrate the model parameters and further validation is provided by lowroughness data. Characteristic values of the model coffecients and their dependence on the Richardson number are proposed and discussed.

National Category
Meteorology and Atmospheric Sciences
URN: urn:nbn:se:uu:diva-237761OAI: oai:DiVA.org:uu-237761DiVA: diva2:768811
Available from: 2014-12-04 Created: 2014-12-04 Last updated: 2015-03-09
In thesis
1. Mean Wind and Turbulence Conditions in the Boundary Layer above Forests
Open this publication in new window or tab >>Mean Wind and Turbulence Conditions in the Boundary Layer above Forests
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

As wind turbines have grown, new installation areas become possible. Placing wind turbines in forested landscapes introduce uncertainties to the wind resource estimation. Even though close-to-canopy processes have been studied intensively during the last thirty years, the focus has mostly been on exchange processes and the height span of the studies has been below the rotor of a modern wind turbine.

This thesis contains analysis of new measurements from a 138 m high tower in a forested landscape. The previous knowledge of near-canopy processes is extended to the region above the roughness sublayer. It is shown that above the roughness sublayer, the surface layer behaves as over low vegetation, and Monin-Obukhov similarity is shown to hold for several variables. However, in stable stratification, effects that could be linked to the boundary layer depth are shown to be present in the measurements. These include wind turning with height, the behaviour of the turbulence length scale and the curvature of the wind profile.

Two new analytical models are presented in the thesis. One is a flux-profile expression in the roughness sublayer, which allows for analytical integration of the wind gradient. The model suggests that the roughness-sublayer effect depends on stratification and that the aerodynamic roughness length changes with stability. A decrease of roughness length in stable stratification is confirmed with a new method to determine the roughness length using measurements from the 138 m tower.

The other model determines the spectral tensor in stable stratification using analytical solution to the rapid distortion equations for stratified shear flow, with homogeneous stratification and shear. By using a formulation for the integration time of the distortions of an isotropic spectrum, a model is derived which provides the cross spectra of velocity and temperature at any two given points in space.

Finally the existence of waves in the wind over forests is investigated and it is concluded that the Kelvin-Helmholtz instability can create waves which are coherent in time and exist over the entire height span of wind turbine rotors. Linear wave theory is shown to be able to explain certain features of the waves.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2015. 47 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1212
Wind power, Forest, Turbulence, Waves, Spectra, Wind model, Atmospheric stability, Vindkraft, Skog, Turbulens, Vågor, Spektra, Modell, Atmosfärisk stabilitet
National Category
Meteorology and Atmospheric Sciences
urn:nbn:se:uu:diva-237764 (URN)978-91-554-9123-9 (ISBN)
Public defence
2015-02-06, Ekmansalen, EBC, Norbyvägen 14, Uppsala, 13:00 (English)
Vindforsk III, Wind power in forestsVindforsk IV, Forest wind
Swedish Energy Agency
Available from: 2015-01-16 Created: 2014-12-04 Last updated: 2015-03-09

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