Idealized models of the atmospheric boundary layer (ABL) can be used to leverage understanding of the interaction between the ABL and wind farms towards the improvement of wind farm flow modeling. We propose a pressure-driven one-dimensional ABL model without wind veer, which can be used as an inflow model for three-dimensional wind farm simulations to separately demonstrate the impact of wind veer and ABL depth. The model is derived from the horizontal momentum equations and follows both Rossby and Reynolds number similarity; use of such similarity reduces computation time and allows rational comparison between different conditions. The proposed ABL model compares well with solutions of the mean momentum equations that include wind veer if the forcing variable is employed as a free parameter.

The interaction between the atmospheric boundary layer (ABL) and wind farms is important for wind energy, because it influences the energy yield and wind turbine lifetime.
Many models of the ABL exist; these range from mesoscale models like the Weather Research and Forecasting (WRF) Model

Notably, various planetary boundary layer (PBL) schemes are available to choose from in WRF, each of which models the ABL in a manner analogous to so-called single-column models (SCMs) that are one-dimensional parameterizations of the ABL.

to microscale models such as large-eddy simulation (LES)The use of higher-fidelity ABL inflow models in RANS for wind farm flows is a research area of both practical and academic interest.
One can include the effects of surface layer atmospheric stability on a wind turbine wake using analytical profiles following Monin–Obukhov similarity theory

In this article, we present a new pressure-driven ABL model, which can be employed to follow both Reynolds and Rossby similarity.
The ABL profiles of the proposed model are very similar to the ABL model of

A steady-state idealized atmospheric boundary layer can be modeled by the incompressible RANS equations of momentum when considering homogeneous terrain and neglecting mesoscale effects:

Our goal is to develop a pressure-driven one-dimensional model of the idealized ABL in terms of wind speed but without wind veer.
One can derive such a model by combining the momentum equations of

In meteorology

With the neglect of

Analytic solutions with and without wind veer.

Analytic solutions of the wind speed profile can be derived from Eq. (

The analytical solutions corresponding to a constant and a linear

The methodology of the numerical one-dimensional simulations of the present article is very similar to that performed in

Rossby number similarity of the proposed ABL model without wind veer for two turbulence closures.

The ABL model including wind veer follows a Rossby similarity as shown in previous work

Reynolds number similarity of the proposed ABL model without wind veer for two turbulence closures.

If all external forces in the momentum equations scale by

Comparison of

In this section, one-dimensional RANS simulations are performed to compare the proposed ABL model without wind veer to the ABL model including wind veer, and we investigate the application to use the model as an inflow model.
Three-dimensional RANS simulations are not performed in this article and will be carried out in future work.
In addition, the

Figure ^{-1}, and a Coriolis parameter of

It is possible to use

Comparison of

Summary of input and derived parameters for ABL models.

In previous work, the

It should be noted that both

We have proposed a pressure-driven model of the mean ABL without wind veer, based on the streamwise (scalar) momentum equation.
One-dimensional RANS simulations of the pressure-driven ABL model are performed to show that the model follows both Rossby and Reynolds number similarity.
The similarities can be employed to quickly find a desired ABL profile based on a pre-calculated library of ABL profiles, which can be used as an inflow profile for three-dimensional RANS simulations of wind farms.
The pressure-driven ABL model compares well with an ABL model including wind veer if the forcing variable

The results of the

Simulate non-dimensional libraries of ABL profiles for both models (with and without wind veer) based on the two Rossby numbers (i.e., both

Set

Find

For each (

Curve

Curve

Calculate

Find

Example of obtaining a set of Rossby numbers from an ABL library with wind veer, Step 3d.

The numerical results are generated with DTU's proprietary software, although the data presented can be made available by contacting the corresponding author.

MPvdL performed the simulations, proposed the pressure-driven ABL model, obtained the model-based Rossby and Reynolds number similarity, and produced all figures. All authors have contributed to the derivation and development of the pressure-driven ABL model and article writing.

The authors declare that they have no conflict of interest.

This paper was edited by Raúl Bayoán Cal and reviewed by Javier Sanz Rodrigo and one anonymous referee.