Neutral turbulent flow over forested hills

Abstract

SUMMARYNumerical simulations of neutral, turbulent flow over periodic forested hills are carried out using a firstorder turbulence closure scheme. The forest is represented by the inclusion in the model of a canopy near the surface where additional drag is exerted on the flow as a result of the trees. Simulations with a more traditional roughness-length parametrization of the surface, which does not explicitly model the flow within the forest, are also carried out for comparison. Comparison of simulations with existing wind-tunnel data shows that the simple mixing-length canopy closure scheme provides a good estimate of the mean flow over a forested hill and is a significant improvement on a traditional roughness-length parametrization in this case.The numerical results are seen to be in close agreement with existing linear analytical solutions for flow over a low and wide forested hill. The model is used to investigate the breakdown of the analytical solution when the hill becomes steep and the perturbations to the flow are no longer linear. Even in the case of a gentle slope, the analytical solution can break down when the hill is narrow or the canopy is deep and the vertical velocities near the top of the canopy become large. This leads to a downwind shift in the surface pressure perturbation and an enhanced drag compared to a roughness-length model. Model results also show enhanced flow separation in the presence of a canopy. These results are important for a range of meteorological problems including the interpretation of flux measurements, parametrization of orographic drag, predicting wind damage to trees and calculating the yield from wind turbines.

First‐order turbulence closure for modelling complex canopy flows

“…The Finnigan and Belcher (2004) group of models (Ross and Vosper 2005;Ross, 2011;Finnigan 2010, 2013) for canopy flow in complex terrain utilise this approach. While the concept of an eddy diffusivity dates back to Boussinesq (1877), a physical model for K awaited the introduction of mixing length closures by Prandtl (1925) (based on momentum) and Taylor (1932) (based on vorticity).…”

Stably stratified canopy flow in complex terrain

“…There are many challenges to face when pursuing this goal. First, the mixing-length theory and K theory that are widely used as closure approaches to momentum equations (Wilson et al, 1998;Pinard and Wilson, 2001;Ross and Vosper, 2005;Katul et al, 2006) have been shown to have questionable validity within a forest canopy layer both theoretically (Yi, 2008) and observationally (Denmead and Bradley, 1985). Second, the analytical model (Finnigan and Belcher, 2004) is limited to neutral condition and hills of gentle slope.…”

“…The analytical model is developed based on the linearized perturbation theory for the flow over a rough hill (Jackson and Hunt, 1975), which assumes that the mean flow perturbations caused by the hill are small in comparison to the upwind flow. Poggi and Katul (2007b) and Ross and Vosper (2005) have shown that the analytical model fails to model the flow pattern on dense canopies on narrow hills. Third, even though turbulence closure models and large eddy simulation models have been used to simulate flow within and above the canopy in numerous published studies, most numerically reproduced canopy flow is confined to idealized cases: either neutral (Ross and Vosper, 2005;Dupont et al, 2008;Ross, 2008) or weakly unstable (Wang, 2010) atmospheric conditions, or flat terrain with a homogeneous and extensive canopy (Huang et al, 2009;Dupont et al, 2010).…”

Modelling Three-Dimensional Winds on a NW Pacific Region of Mexico Using Boundary-Fitted Grids

“…Previous research has focused on many aspects of idealized low-level three-dimensional flow in the vicinity of isolated topography [1] [2] [3] and associated downstream wake dynamics [4] [5] [6], while studies on realistic topography have been performed in other parts of the world by several authors such as [7]- [12] among others. Regionally, while a great deal of attention has been paid to modeling wind driven ocean currents, the related problem of marine air flow over land has received considerably less attention.…”