# Dynamic wakes¶

For spatially uniform timeseries input data, `foxes` can compute dynamic wake propagation. This in principle works by following a flow trace backwards in time for each point of interest, and identifying it with a wake trajectory if it hits a rotor.

Since all `foxes` computations are based on chunks of input states, this concept only works if

• either all states fall into a single chunk,

• or the `Iterative` algorithm is used for the calculation.

The later is necessary in case the wake originates from a state previous to the chunk of evaluation, since the default `Downwind` algorithm does not allow cross-chunk communication during the calculation.

These are the inlcudes for this example:

``````In [1]:
``````
``````%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
plt.rcParams["animation.html"] = "jshtml"

import foxes
import foxes.variables as FV
import foxes.constants as FC
``````

We create a case with a regular 3 x 3 wind farm layout:

``````In [2]:
``````
``````mbook = foxes.models.ModelBook()

states = foxes.input.states.Timeseries(
data_source="timeseries_100.csv.gz",
output_vars=[FV.WS, FV.WD, FV.TI, FV.RHO],
var2col={FV.WS: "ws", FV.WD: "wd", FV.TI: "ti"},
fixed_vars={FV.RHO: 1.225, FV.TI: 0.07},
)

farm = foxes.WindFarm()
farm,
xy_base=np.array([0.0, 0.0]),
step_vectors=np.array([[1000.0, 0], [0, 800.0]]),
steps=(3, 3),
turbine_models=["DTU10MW"],
verbosity=0
)

algo = foxes.algorithms.Iterative(
mbook,
farm,
states=states,
rotor_model="centre",
wake_models=["Bastankhah_linear_k004"],
wake_frame="timelines",
partial_wakes_model="auto",
chunks={FC.STATE: 500, FC.POINT: 5000},
verbosity=1
)
``````

Notice the wake frame choice `timelines`, which is a pre-defined instance of the class `Timelines` from the model book.

Let’s run the wind farm calculation:

``````In [3]:
``````
``````with foxes.utils.runners.DaskRunner() as runner:
farm_results = runner.run(algo.calc_farm)
``````
```
Algorithm Iterative: Iteration 0

[########################################] | 100% Completed | 101.61 ms
[########################################] | 100% Completed | 202.14 ms

Algorithm Iterative: Iteration 1

[########################################] | 100% Completed | 101.05 ms
[########################################] | 100% Completed | 202.47 ms

DefaultConv: Convergence check
REWS: delta = 1.324e-01, lim = 1.000e-05  --  FAILED
TI  : delta = 0.000e+00, lim = 1.000e-06  --  OK

Algorithm Iterative: Iteration 2

[########################################] | 100% Completed | 101.11 ms
[########################################] | 100% Completed | 203.57 ms

DefaultConv: Convergence check
REWS: delta = 0.000e+00, lim = 1.000e-05  --  OK
TI  : delta = 0.000e+00, lim = 1.000e-06  --  OK

Algorithm Iterative: Convergence reached.

```

Notice the iterations and the convergence behaviour. Now the farm results are ready:

``````In [4]:
``````
``````farm_df = farm_results.to_dataframe()
print("\nFarm results data:\n")
print(farm_df[[FV.AMB_REWS, FV.REWS, FV.P]])
``````
```
Farm results data:

AMB_REWS      REWS            P
state               turbine
2023-07-07 12:00:00 0             6.0  6.000000  1532.700000
1             6.0  6.000000  1532.700000
2             6.0  6.000000  1532.700000
3             6.0  5.063574   845.738040
4             6.0  5.063574   845.738040
...                               ...       ...          ...
2023-07-07 13:39:00 4             6.0  5.063574   845.738040
5             6.0  5.063574   845.738040
6             6.0  4.693421   640.016335
7             6.0  4.693421   640.016335
8             6.0  4.693421   640.016335

[900 rows x 3 columns]
```

This timeseries has a time step of 1 minute. Let’s visualize the wake dynamics in am animation:

``````In [5]:
``````
``````with foxes.utils.runners.DaskRunner() as runner:

fig, axs = plt.subplots(2, 1, figsize=(5.2,7),
gridspec_kw={'height_ratios': [3, 1]})

anim = foxes.output.Animator(fig)

# this adds the flow anomation to the upper panel:
of = foxes.output.FlowPlots2D(algo, farm_results, runner=runner)
of.gen_states_fig_xy(
FV.WS,
resolution=30,
quiver_pars=dict(angles="xy", scale_units="xy", scale=0.013),
quiver_n=35,
xmax=5000,
ymax=5000,
fig=fig,
ax=axs[0],
ret_im=True,
title=None,
animated=True,
)
)

# This adds the REWS signal animation to the lower panel:
o = foxes.output.FarmResultsEval(farm_results)
o.gen_stdata(
turbines=[4, 7],
variable=FV.REWS,
fig=fig,
ax=axs[1],
ret_im=True,
legloc="upper left",
animated=True,
)
)

ani = anim.animate()
plt.close()
print("done.")

print("Creating animation")
ani
``````
```Creating animation data
[########################################] | 100% Completed | 101.49 ms
[########################################] | 100% Completed | 101.33 ms
[########################################] | 100% Completed | 21.57 s
done.
Creating animation
```
``````Out[5]:
``````