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Calculation of momentum flux using Monin–Obukhov similarity theory over forested areas is well known to underestimate the flux. Several suggestions of corrections to the standard flux-profile expression have been proposed in order to increase the magnitude of turbulent flux. The aim of this article is to find a simple, analytical representation for the characteristics of the flow within the canopy layer and the surface layer, including the roughness sublayer. A new form of the roughness sublayer correction is proposed, based on the desire to connect the shape of the roughness sublayer correction to forest characteristics. The new flux-profile relation can be used to find the flux or the wind profile whenever simple and fast estimations are needed, as for mesoscale modelling, scalar transport models, or sound propagation models.

An analysis and interpretation of measurements from a 138-m tall tower located in a forested landscape is presented. Measurement errors and statistical uncertainties are carefully evaluated to ensure high data quality. A 40∘ wide wind-direction sector is selected as the most representative for large-scale forest conditions, and from that sector first-, second- and third-order statistics, as well as analyses regarding the characteristic length scale, the flux-profile relationship and surface roughness are presented for a wide range of stability conditions. The results are discussed with focus on the validity of different scaling regimes. Significant wind veer, decay of momentum fluxes and reduction in shear length scales with height are observed for all stability classes, indicating the influence of the limited depth of the boundary layer on the measured profiles. Roughness sublayer characteristics are however not detected in the presented analysis. Dimensionless gradients are shown to follow theoretical curves up to 100 m in stable conditions despite surface-layer approximations being invalid. This is attributed to a balance of momentum decay and reduced shear length scale growth with height. The wind profile shows a strong stability dependence of the aerodynamic roughness length, with a 50 % decrease from neutral to stable conditions.

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.

In this paper the existence of canopy waves is examined using measurements from a 138 m high tower placed in a forest. Characteristics of the waves are examined in relation to wind energy. Using wavelet analysis it is shown that when the wave signal is clear, the phase lag between horizontal and vertical velocity is close to 90 degrees, which limits the contribution of the waves to themomentum flux. Results from numerical solution of linear wave equations is shown to agree with measurements in terms of wave period and the vertical shape of the wave amplitude. Linear analysis and measurements suggests that Kelvin-Helmholtz instability causes unstable wave growth and that the most unstable wave number normally has a period of 10-100 s. In addition to the Kelvin-Helmholtz instability, the linear analysis predicts that instabilities of the Holmboe kind, with higher frequency, can develop over forests in certain conditions.