The paper provides an extensive analysis of the use of the free-vortex model for wind turbines in yaw using the actuator disk, actuator disk with rotation, and actuator line formulations. The results demonstrate that these models perform well at reconstructing the flow and are theoretically sound. The paper is generally clear and well written. However, some improvements to the paper could improve its usefulness to readers.

My only significant critique is that it is difficult to follow the equations to compare to other theoretical formulations and papers. More details about the coordinate systems and careful definitions of variables would go a long way in helping readers replicate the results. The yawed wind turbine literature is filled with imprecisely defined variables like induction factor that are not consistent across papers. This makes it very hard to replicate studies and results and has resulted in citation errors. A careful writing would prevent this paper from having that flaw.

I also suggest that more details about the computational cost would help readers understand the best application of this approach. Comparisons to LES and engineering models, for example, could help users weight the costs and benefits. Scaling with number of turbines, domain size, and resolution would also be helpful. 

Some more specific comments are below:

Section 2.2.1: Could you elaborate on the use of the induction factor. Is a measured as streamwise induction or induction normal to the rotor? For ADM-R and ALM, how does a vary with radius?

Section 2.2.2: A few comments on this section:

- The ADM vortex system should be a semi-infinite cylinder. How does the streamwise and azimuthal discretization relate the the streamwise velocity? Does this include induction? Please relate Δt to the streamwise velocity. 

- In what direction is the vorticity pointing? Is it purely azimuthal vorticity? A yawed wind turbine should also generate streamwise vorticity, which can be predicted analysitically. Does your equation provide this vorticity?

Sections 2.2.3 and 2.2.4: I have similar questions in these sections to Section 2.2.2. It is unclear exactly what the coordinate system is, in which direction the vorticity is pointing, and how the system is discretized relative to the streamwise velocity.

Figure 2: How is vortex filament spacing normalized? Is it by delta t? Please put on the axis label. Is the velocity error dimensionless? Equation 18 would have units of velocity. Please note the units in the ordinate label.

Section 3: A few comments on Section 3:

- You could also compare the results to theory since the flow behind an unyawed turbine is well known.

- Please also report results for yawed wind turbines. The unyawed case is much more difficult to reconstruct and errors in the modeling of yaw would not be apparent without this comparison.

- Were these results all using the steady state experiments from Section 4?

- Can you provide an estimate of the computational cost with this scaling and how it compares to other methods (e.g. LES or engineering models).

Section 4.1: Some more repetition of the basics of these experiments here would be useful so the reader does not have to go back to these other papers.

Section 4.1.1 and 4.1.2: Paragraphs typically need 3-4 sentences. I suggest you remove the line breaks and make these entire sections into one paragraph.

See comments attached.