Interactions between boundary layer flow and gentle topography covered by vegetation

The interaction between gentle topography and boundary layer flow plays a critical role in a range of applications, including numerical weather prediction, wind energy applications including turbine siting and output prediction and atmospheric dispersion. The interaction between topography and boundary layer flows also plays a role in the interpretation of eddy covariance measurement over canopies. In addition to the well-known thermotopographic flows, the systematic impacts of even gentle topography on turbulence can lead to substantial spatial variations in the measured eddy flux of passive scalars even in neutral and near-neutral conditions, with the potential to impose biases on the inferred source/sink strengths in the various biogeochemical cycles.

Linearised perturbation theory for the flow over gentle topography has been extended (Finnigan and Belcher, 2004) to account for the role of the canopy in determining the flow and transport characteristics. However, comparisons with flume and wind tunnel experiments and Large Eddy Simulations indicate that while the theory provides good qualitative agreement, the quantitative agreement is less satisfactory. This includes important features of the flow such as the driving pressure perturbation and associated form drag, the depth scales of the flow structure, and the presence (or lack of) and location of recirculating flow which are important for near-surface dispersion. If the role of the interactions between gentle topography, canopies and boundary layer flow is to be rigorously incorporated into larger scale models then reasonable quantitative agreement between the observations, the theory and any parameterisation based on these, including the scaling, must be achieved.

We consider the quantitative agreement between the linearised perturbation theory and recent LES experiments (Patton and Katul, 2009) for two cases which lie outside the strict bounds of the perturbation theory. Careful analysis allows the identification of the important physical processes present in the LES which are not incorporated in the theory. Extensions to the theory, some exact and some necessarily approximate, then allow substantially better agreement between theory and the LES. In particular we will discuss how the magnitude and phase of the driving pressure perturbation can be handled within the framework of the linearised theory to match the LES results better and the physical interpretation of such modifications.

We will also comment pm how this analysis can be extended to 3-dimensional topography and how the theory can be used to provide insight as to the existence and magnitude of the potential bias in eddy flux measurements taken in neutral flow conditions at sites in complex terrain.