Theory error in Gaussian wake models

Gaussian wake models have 2 errors that do not align with theory

This doesn't fit the typical issue template since it is just comparing code with theory. I will do my best to justify everything with references.

The first reference is the research paper that the Gaussian wake model is based off of:

Bastankhah, Majid, and Fernando Porté-Agel. 
"Experimental and theoretical study of wind turbine wakes in yawed conditions." 
Journal of Fluid Mechanics 806 (2016): 506-541.

which may be accessed publicly here. The main equations I am looking at are Eq. (6.4)
$$\frac{u_R}{u_\infty} = \frac{C_T \cos \gamma}{2 ( 1 - \sqrt{1-C_T \cos \gamma} )}$$
and Eq. (6.16)
$$\frac{x_0}{D} = \frac{\cos \gamma (1+\sqrt{1-C_T})}{\sqrt{2} [ 4 \alpha I + 2 \beta (1-\sqrt{1-C_T})]}$$

I am specifically referencing the code within the following files:

floris/simulation/wake_velocity/gauss.py

(herein referred to as wake_velocity) and

floris/simulation/wake_deflection/gauss.py

(herein referred to as wake_deflection)

Error 1 in wake_velocity

The first error occurs in wake_velocity, with respect to Eq. (6.4) where $u_R$ is calculated on line 87.

        uR = u_initial * ct_i / ( 2.0 * (1 - np.sqrt(1 - ct_i) ) )

This equation does not match up with Eq. (6.4), and it should be

        uR = u_initial * ct_i * cosd(yaw_angle) / ( 2.0 * (1 - np.sqrt(1 - ct_i) ) )

(note that cosine is multiplied in the numerator)

For additional verification, I also noticed that in wake_deflection lines 150-156, $u_R$ is calculated by

        uR = (
            freestream_velocity
          * ct_i
          * cosd(tilt)
          * cosd(yaw_i)
          / (2.0 * (1 - np.sqrt(1 - (ct_i * cosd(tilt) * cosd(yaw_i)))))
        )

further confirming the inconsistency with theory.

Error 2 in wake_deflection

The first error occurs in wake_deflection, with respect to Eq. (6.16) where $x_0$ is calculated on lines 160-166.

        x0 = (
            rotor_diameter_i
            * (cosd(yaw_i) * (1 + np.sqrt(1 - ct_i * cosd(yaw_i))))
            / (np.sqrt(2) * (
                4 * self.alpha * turbulence_intensity_i + 2 * self.beta * (1 - np.sqrt(1 - ct_i))
            )) + x_i
        )

This equation does not match up with Eq. (6.16), and it should be

        x0 = (
            rotor_diameter_i
            * (cosd(yaw_i) * (1 + np.sqrt(1 - ct_i)))
            / (np.sqrt(2) * (
                4 * self.alpha * turbulence_intensity_i + 2 * self.beta * (1 - np.sqrt(1 - ct_i))
            )) + x_i
        )

(note that cosine is removed within the square root)

For additional verification, I also noticed that in wake_velocity line 102, $x_0$ is calculated by

        x0 *= rotor_diameter_i * cosd(yaw_angle) * (1 + np.sqrt(1 - ct_i) )

further confirming the inconsistency with theory.

Floris version

v3.4 (latest)
I installed by

git clone git@github.com:NREL/floris.git

Before submitting I made sure to git pull and it appears this has not yet been spotted.