# How Taylor frozen hypothesis is used in TurbSim?

Dear Jason and Bonnie,
I am beginner to atmospheric turbulence and trying to understand of the basic theories used in TurbSim.
After reading the User Guide V2.00.00 and some topics on the forum, I know that the velocity spectrum model and spatial coherence model are the two most important parts of the basic theory and I have the following basic understandings:

(1) The turbulent velocity fields are modeled as two separate parts as (1) mean velocity and (2) zero-mean fluctuation velocity.
(2) The mean velocity can be directly determined by the Uref and PLExp .
(3) The velocity spectrum model only determines the magnitude of the fluctuating velocity at each frequency;
(4) The spatial coherence model adds some correlation between the various grid points, otherwise the phases of all grid points could be totally randomized.
(5) Taking the specified velocity spectrum, spatial coherence and random number as input parameters and applying IFFT, we can obtain the time series of the fluctuation velocities at each grid in the vertical slice, namely Ui( t, y, z).

I recently read some papers (about Mann turbulence model and Kaimal model) and get to know that the Taylor frozen turbulence hypothesis is essential in generating turbulent wind fields which assumes all turbulent motions remain unchanged while eddies move with the mean flow. However, Since TubrSim can directly generate time series, it seems there is no need to used Taylor hypothesis in TurbSim ? My questions are :
(1) Does the Taylor hypothesis is used in TurbSim framework?
(2) If so, in which step it is used?
(3) Or the hypothesis is only required by other turbulence models, such as Mann model?

Best regards,
Lin Yang.

Dear @Lin.Yang,

The Taylor frozen turbulence hypothesis is not used by TurbSim or the Mann model. Rather, the Taylor frozen turbulence hypothesis is used by the InflowWind module of OpenFAST in order to make use of inflow data generated by TurbSim or the Mann model. In the case of TurbSim, TurbSim generates a time-dependent 2D grid (in Y and Z) of turbulent inflow data; InflowWind makes use of the Taylor frozen turbulence hypothesis to propagate this 2D grid along X to create a time-dependent 3D grid of turbulent inflow data (essentially relating X and time based on the mean wind speed). In the case of Mann, the Mann model generates a static 3D grid of turbulent wind data; InflowWind makese use of the Taylor frozen turbulence hypothesis to propagate this 3D grid in time to create a time-dependent 3D grid of turbulent inflow data (again, essentially relating X and time based on the mean wind speed).

Best regards,

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Dear Jason,

Thanks for your reply and it becomes much clear to me know.
My current general understanding to TurbSim is as follow:

(1) In real application, FAST needs a 3D time-dependent turbulent wind field at each time step, u(t,x,y,z), v(t,x,y,z), w(t,x,y,z), to interpolate inflow wind velocities at each blade and tower AeroDyn node to calculate AOA.

(2) However, both turbSim and Mann model only generate a 2D+t or static 3D turbulence field, respectively. These fields cannot be directly used by FAST so that the Taylor hypothesis is used to extends the 3D fields (YZ+t or XYZ)to a 4D field(t+XYZ).

(3) Taylor hypothesis assumes a rigid-body translation of the generated turbulent fields, which simply neglects the evolution of turbulence during propagation. This seems very similar as the principle of virtual work in Mechanics.

The following figure shows my overall understanding:

It would be very grateful if you could briefly comment on my cuurent understandings on this issue.

Best regards,
Lin Yang.

Dear @Lin.Yang,

Yes, I agree.

Best regards,