pyts.specModels package

Submodules

pyts.specModels.api module

PyTurbSim turbulence ‘spectra models’ API.

Available spectral models

nwtc.smooth() (alias: smooth)
The nwtc ‘smooth’ spectral model.
nwtc.nwtcup() (alias: nwtcup)
The nwtc ‘upwind’ spectral model.
hydro.tidal (alias: tidal)
The hydro ‘tidal’ spectral model.
hydro.river (alias: river)
The hydro ‘river’ spectral model.
iec.ieckai (alias: ieckai)
The IEC ‘Kaimal’ spectral model.
iec.iecvkm (alias: iecvkm)
The IEC ‘Von-Karman’ spectral model.
specModelBase
This is the base class for spectral models. To create a new spectral model, subclass this class or subclass and modify an existing spectal model.
specObj
This is the ‘spectral object’ class. All spectral model __call__ methods must take a tsrun as input and return this class.

Example usage

>>> import pyts.specModels.api as sm

Create a smooth spectral model with friction velocity Ustar=1m/s and Richardson number Ri=0.6:

>>> my_spec_model=sm.smooth(1.0,0.6)

Now set a pyts.main.tsrun instance to use this spectral model:

>>> tsrun.spec=my_spec_model(tsrun)

Notes

For a description of the difference between ‘spectral models’ (e.g. ‘my_spec_model’ in example above) and the spectral array they output (tsrun.spec), see the Code Framework section of the PyTurbSim documentation.

pyts.specModels.base module

This is the turbulence spectrum package’s base module.

class pyts.specModels.base.specModelBase[source]

Bases: pyts.base.modelBase

A base class for TurbSim spectral models.

pow2_3 = 0.6666667
pow5_3 = 1.6666666
class pyts.specModels.base.specObj(tsrun)[source]

Bases: pyts.base.gridProps, pyts.base.calcObj

Spectral objects contain the array (self.array) of turbulence spectra values for a specific PyTurbSim run. This class defines various shortcuts to the data.

Parameters:

tsrun : tsrun type

The PyTurbSim run object in which the spectra will be used.
Suu

This is the u-component of the TKE spectrum.

Svv

This is the v-component of the TKE spectrum.

Sww

This is the w-component of the TKE spectrum.

flat

Return the partially-flattened spectral array. This flattens the spatial dimensions of the spectral array (component and frequency dimensions are retained).

For example, for a 5 x 4 spatial grid (nz=5,ny=4) with 1000 frequency values, the size of the array in this spectral object will be 3 x 5 x 4 x 1000. Performing this flatten operation will return a 3 x 20 x 1000 shaped spectral array. The ordering (row-major or column-major) is defined in the spatial grid class.

This is used for input into the functions that calculate the coherence.

tke

This is the component-wise turbulent kinetic energy.

pyts.specModels.hydro module

This module contains the turbulence models for the aquatic environment.

class pyts.specModels.hydro.river(Ustar, Zref)[source]

Bases: pyts.specModels.hydro.tidal

River turbulence spectral model.

This model is based on measurements from the East River, in New York City. It is identical to the tidal model, but uses different values for coef.

coef = array([[1.057, 3.432], [0.351, 0.546], [0.265, 0.341]], dtype=float32)
class pyts.specModels.hydro.tidal(Ustar, Zref)[source]

Bases: pyts.specModels.base.specModelBase

Tidal Channel spectral model.

The tidal spectral model is based on measurements from Admiralty Inlet, in Puget Sound, WA.

Parameters:

Ustar : float

bottom boundary friction velocity [m/s].

Zref : float

Reference height at which u’w’ stress nears zero [m].

See also

coef
The ‘fit coefficients’

Notes

This model is similar to NWTC_stable, but uses different values for coef, and does not support new fit-coefficients. The form of this model is:

\[S_k(f) = \frac{\sigma_k^2 \mathrm{coef}[k,0]}{1+\mathrm{coef}[k,1](f/\hat{f})^{5/3}} \qquad k=0,1,2\ (u,v,w)\]

Where,

\(\hat{f}=\frac{\partial \bar{u}}{\partial z}\)

\(\bar{u}\) is the mean velocity from the profObj.

\(\sigma_k^2 = U_{*}^2 \alpha_k exp(-2 z/Zref)\)

\(\alpha_k = (4.4,2.25,0.9)\)

__call__(tsrun)[source]

Create the spectral object for tsrun.

Parameters:

tsrun : tsrun

A TurbSim run object.
Returns:

out : specObj

An IEC spectral object for the grid in tsrun.
coef = array([[1.21, 4.3 ], [0.33, 0.5 ], [0.23, 0.26]], dtype=float32)

pyts.specModels.iec module

This module contains the IEC turbulence models.

See the Original-TurbSim user manual for more info on IEC spectral models.

class pyts.specModels.iec.IECKai(IECwindtype, IECstandard, IECedition, IECturbc, ETMc=None)[source]

Bases: pyts.specModels.iec.iecbase

IEC Kaimal spectral model.

Notes

The form of this model is,

\[S_k(f) = \frac{4 \sigma_k^2/\hat{f}_k}{(1+6 f/\hat{f}_k )^{5/3}} \qquad \mathrm{for}\ k=u,v,w\]

Where,

\(\hat{f}_k = \alpha_k \bar{u}_{hub}/\Lambda\)

\(\alpha_k =\) (8.1,2.7,0.66) for k= (u,v,w)

\(\sigma_u\) is defined in IEC_Sigma

\(\sigma_v=0.8\sigma_u\) and \(\sigma_w=0.5\sigma_u\)

\(\Lambda\) is defined in Lambda

__call__(tsrun)[source]

Create the spectral object for a tsrun instance.

Parameters:

tsrun : tsrun

A TurbSim run object.
Returns:

out : specObj

An IEC spectral object for the grid in tsrun.
class pyts.specModels.iec.IECVKm(IECwindtype, IECstandard, IECedition, IECturbc, ETMc=None)[source]

Bases: pyts.specModels.iec.iecbase

IEC Von-Karman spectral model

Notes

The form of this model is,

\[ \begin{align}\begin{aligned}S_u(f) = \frac{4 \sigma^2/\hat{f}}{(1+71(f/\hat{f})^2)^{5/6}}\\S_v(f) = S_w(f) = (1+189(f/\hat{f})^2\frac{2\sigma^2/\hat{f}} {(1+71 (f/\hat{f})^2)^{11/6}}\end{aligned}\end{align} \]

Where,

\(\hat{f} = \bar{u}_{hub}/\Lambda\)

\(\sigma\) is defined in IEC_Sigma

\(\Lambda\) is defined in Lambda

__call__(tsrun)[source]

Create and calculate the spectral object for a tsrun instance.

Parameters:

tsrun : tsrun

A TurbSim run object.
Returns:

out : specObj

An IEC spectral object for the grid in tsrun.
class pyts.specModels.iec.iecbase(IECwindtype, IECstandard, IECedition, IECturbc, ETMc=None)[source]

Bases: pyts.specModels.base.specModelBase

This is a base class for the IEC spectral models (IECKAI and IECVKM).

Parameters:

IECwindtype : str {‘NTM’=normal,

‘xETM’=extreme turbulence, ‘xEWM1’=extreme 1-year wind, ‘xEWM50’=extreme 50-year wind, where x=wind turbine class 1, 2, or 3}

IECstandard : int {1}

Currently this only supports IECstandard==1. IECstandard == 2 and 3 correspond to small and offshore wind, respectively, and have not yet been implemented here.

IECedition : int {2,3}

This is the ‘edition’ number of the -1 standard.

IECturbc : str | float {‘A’,’B’,’C’}

The string form correspodes to the IEC turbulence ‘categories’. If a float is provided, it specifies a specific value of Turbulence Intensity.

ETMc : float, optional (2.0)

ETMc specifies the value of the ‘c’ parameter in the equation for \(\sigma_u\). It is only used when IECwindtype`=`xETM.

Notes

For further details on the IEC spectral models see the Original-TurbSim user manual.

IEC_Sigma(uhub)[source]

Calculate the default value of the standard deviation of u-component wind speed, \(\sigma\) or \(\sigma_u\).

Notes

For input IECturbc a numeric value, it simply specifies the turbulence intensity. That is,

\[\sigma = \mathrm{IECturbc}\times u_{hub}\]

Otherwise only IECversion == 1 is supported. In that case:

  • For IECedition == 2 the windtype must be ‘NTM’, in that case:

    \[\sigma = Ti (\frac{15+\beta u_{hub}}{\beta + 1})\]

    Where,

    Ti = (0.18,0.16) for input variable IECturbc = (‘a’,’b’), respectively.

    \(\beta\) = (2.0,3.0) for input variable IECturbc = (‘a’,’b’), respectively.

  • For IECedition == 3, Ti=(0.16,0.14,0.12) for IECturbc=(a,b,c), respectively. In this case, different formulations are used for different IECwindtype.

    • For IECwindtype == ‘NTM’:

      \[\sigma = Ti(0.75u_{hub} + 5.6)\]

    • For IECwindtype == ‘xETM’, the value of ‘x’ in that string provides another input variable, Vref=(50,42.5,37.5) for x=1,2,3.

      \[\sigma = \mathrm{ETMc} \times Ti (0.072(0.2 V_{ref}/\mathrm{ETMc}+3)(u_{hub}/\mathrm{ETMc}-4)+10)\]

    • For IECwindtype == ‘xEWM1’ | ‘xEWM50’, the same value of Vref apply and

      \[\sigma = 0.11 V_{ref}\]
Lambda(zhub)[source]

Compute the value of Lambda for height zhub.

See also

pyts.misc.Lambda()

pyts.specModels.kelley_coefs module

pyts.specModels.kelley_coefs.calc_nwtcup_coefs(zL)[source]

pyts.specModels.nwtc module

This module contains the nwtc spectral models.

class pyts.specModels.nwtc.NWTC_stable(Ustar, zL, coef=None)[source]

Bases: pyts.specModels.nwtc.genNWTC

The NWTC ‘stable’ spectral model.

Parameters:

Ustar : float

friction velocity [m/s].

zL : float

The z/L stability parameter [non-dimensional]

coef : array_like((3,2),dtype=float)

spectral coefficients for this model.

See also

s_coef
These are the hard-wired \(\mathrm{scoef}\) coefficients.

Notes

The specific form of this model is,

\[S_k(f) = \frac{U_{*}^2 A_k \hat{f}^{-1}\gamma}{1+B_k(f/\hat{f})^{5/3}} \qquad k=0,1,2\ (u,v,w)\]

Where,

\(\gamma=(\phi_E/\phi_M)^{2/3}\)

\(\hat{f}=\frac{\bar{u}\phi_M}{z}\)

\(\phi_E=(1+2.5 (z/L)^{0.6})^{1.5}\)

\(\phi_M=1+4.7*z/L\)

\(\bar{u}\), is the mean velocity at each grid-point, (taken from the profile model)

\(A_k=\mathrm{scoef}[k,0] \mathrm{coef}[k,0]\)

\(B_k=\mathrm{scoef}[k,1] \mathrm{coef}[k,1]^{5/3}\)

model(z, u, comp)[source]

Calculate the spectral model for height z, velocity u, and velocity component comp.

s_coef = array([[ 79. , 263. ], [ 13. , 32. ], [ 3.5, 8.6]])
class pyts.specModels.nwtc.NWTC_unstable(Ustar, zL, ZI, p_coefs=None, f_coefs=None)[source]

Bases: pyts.specModels.nwtc.genNWTC

The NWTC ‘unstable’ spectral model.

\[S_k(f) = U_\mathrm{star}^2 G_k(f,\bar{u},z,ZI) \qquad k = u, v, w\]

Where \(G_k\) is a function that depends on the frequency, \(f\), the mean velocity \(\bar{u}\), the height \(z\), and the mixing layer depth \(ZI\). The exact form of \(G_k\) can be found in this class’s ‘model’ method.

Parameters:

Ustar : float

The friction velocity (at the bottom boundary).

zL : float

The ratio of the HubHt to the Monin-Obhukov length.

ZI : float

The friction boundary layer height.

p_coefs : array_like(3,2), optional

Fit coefficients for this model.

f_coefs : array_like(3,2), optional

Fit coefficients for this model.
L
model(z, u, comp)[source]

Computes the spectrum for this ‘unstable’ spectral model.

Parameters:

z : array_like (nz)

Height above the surface [m].

u : array_like (nz,ny)

Mean velocity [m/s].

comp : int {0,1,2}

Index (u,v,w) of the spectrum to compute.
Returns:

spec : specObj

The spectral object which contains the ‘array’ (property) of spectra at each point in the grid.

Notes

The form of the u-compenent spectrum is:

\[S_u(f) = U_\mathrm{star}^2 \left( p_{u,1}\frac{\alpha}{1+( F_{u,1} \hat{f})^{5/3}} + p_{u,2}\frac{\beta}{( \delta_u + F_{u,2} f' )^{5/3} } \right )\]

The form of the v-compenent spectrum is

\[S_v(f) = U_\mathrm{star}^2 \left( p_{v,1}\frac{\alpha}{(1 + F_{v,1} \hat{f})^{5/3}} + p_{v,2}\frac{\beta}{( \delta_v + F_{v,2} f' )^{5/3} } \right )\]

The form of the w-compenent spectrum is:

\[S_w(f) = U_\mathrm{star}^2 \left( p_{w,1}\frac{\alpha}{(1 + F_{w,1} \hat{f})^{5/3}} \gamma + p_{w,2}\frac{\beta}{ 1 + F_{w,2} {f'} ^{5/3} } \right )\]

Where,

\(\hat{f} = f ZI/\bar{u}\)

\(f' = f z/ \bar{u}\)

\(\alpha = ZI^{5/3}/(-\bar{u}L^{2/3})\)

\(\beta = z(1-z/ZI)^2/\bar{u}\)

\(\delta_u = 1+15 z/ZI\)

\(\delta_v = 1+2.8 z/ZI\)

\(\gamma = \frac{f'^2+0.09(z/ZI)^2}{f'^2+0.0225}\)

class pyts.specModels.nwtc.genNWTC[source]

Bases: pyts.specModels.base.specModelBase

An abstract base class for NWTC spectral models.

__call__(tsrun)[source]

Create and calculate the spectral object for a tsrun instance.

Parameters:

tsrun : tsrun

A TurbSim run object.
Returns:

out : specObj

An NWTC spectral object for the grid in tsrun.
pyts.specModels.nwtc.nwtcup(Ustar, Ri, ZI=None)[source]

Compute the ‘nwtcup’ spectral model.

Parameters:

Ustar : float

The bottom-boundary friction velocity [m/s].

Ri : float

The Richardson number stability parameter.

ZI : float, optional

mixing layer depth [m]. Only needed for Ri<0.
Returns:

specModel : NWTC_stable (Ri>0), or NWTC_unstable (Ri<0)
pyts.specModels.nwtc.smooth(Ustar, Ri, ZI=None)[source]

Compute the ‘smooth’ spectral model.

Parameters:

Ustar : float

The bottom-boundary friction velocity [m/s].

Ri : float

The Richardson number stability parameter.

ZI : float, optional

mixing layer depth [m]. Only needed for Ri<0.
Returns:

specModel : NWTC_stable (Ri>0), or NWTC_unstable (Ri<0)

Module contents

This is the PyTurbSim ‘spectral models’ package. This package contains pre-defined spectral models that can be implemented in a PyTurbSim run.

The wind spectral models are more fully described in the Original-TurbSim user manual.

For more information and to use this module import the api package, e.g.

>>> import pyts.specModels.api as sm