# An analytical model for a full wind turbine wake

## TL;DR

This paper introduces an analytical wind turbine wake model that predicts velocity distribution at all distances downwind, improving upon existing models by incorporating physical principles and a double-Gaussian velocity deficit distribution.

## Contribution

It generalizes the Jensen and Bastankhah-Porte-Agel models by deriving a comprehensive wake model based on conservation laws and actuator disk theory.

## Key findings

- The model accurately predicts velocity deficits in the near- and far-wake regions.
- It incorporates a double-Gaussian distribution for velocity deficits.
- The model provides a physically consistent solution for wind turbine wakes.

## Abstract

An analytical wind turbine wake model is proposed to predict the wind velocity distribution for all distances downwind of a wind turbine, including the near-wake. This wake model augments the Jensen model and subsequent derivations thereof, and is a direct generalization of that recently proposed by Bastankhah and Porte-Agel. The model is derived by applying conservation of mass and momentum in the context of actuator disk theory, and assuming a distribution of the double-Gaussian type for the velocity deficit in the wake. The physical solutions are obtained by appropriate mixing of the waked- and freestream velocity deficit solutions, reflecting the fact that only a portion of the fluid particles passing through the rotor disk will interact with a blade.