Add the dashboard page

docs/_toc.yml

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 format: jb-book
 root: index 
 chapters:
+- file: dashboard
 - file: wesc2023_demo
 - file: torque2024_1turbine
 - file: torque2024_4turbine

docs/dashboard.md

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+---
+jupytext:
+  formats: md:myst
+  text_representation:
+    extension: .md
+    format_name: myst
+kernelspec:
+  display_name: Python 3
+  language: python
+  name: python
+---
+
+```{code-cell}
+---
+tags: [hide-input]
+---
+
+# stdlib
+from pathlib import Path
+import matplotlib.pyplot as plt
+import numpy as np
+
+# wcomp
+from wcomp import WCompFloris, WCompPyWake, WCompFoxes
+from wcomp.plotting import plot_plane
+
+# plot settings
+PROFILE_LINEWIDTH = 1.0
+ERROR_LINEWIDTH = 1.5
+
+SMALL_SIZE = 10
+MEDIUM_SIZE = 12
+BIGGER_SIZE = 14
+# plt.rc('font', size=SMALL_SIZE)          # controls default text sizes
+plt.rc('xtick', labelsize=SMALL_SIZE)    # fontsize of the tick labels
+plt.rc('ytick', labelsize=SMALL_SIZE)    # fontsize of the tick labels
+plt.rc('axes', labelsize=MEDIUM_SIZE)
+plt.rc('axes', titlesize=BIGGER_SIZE)
+plt.rc('legend', fontsize=MEDIUM_SIZE)
+plt.rc('figure', titlesize=BIGGER_SIZE)
+
+# Constants for all cases. Copy to a particular code block to change, as needed.
+CASE_DIR = Path('cases_torque2024/one_turbine')
+this_case = CASE_DIR / Path('jensen/wind_energy_system.yaml')
+floris_case = WCompFloris(this_case)
+ROTOR_D = floris_case.rotor_diameter
+XMIN = -1 * ROTOR_D
+XMAX = 20 * ROTOR_D
+YMIN = -2 * ROTOR_D
+YMAX =  2 * ROTOR_D
+```
+
+# Dashboard
+
+This page contains a series of cases that compare various aspects of the integrated
+wake modeling software including the mathematical wake models and other software-specific
+design decisions.
+
+## Wake model implementations
+The mathematical models included in each software are generally grouped into models
+describing the velocity of the wind in a wind turbine wake (velocity model) and
+models describing the magnitude of deflection of the wake (deflection model).
+The models available in each software are shown in the tables below.
+
+:::{table} Velocity models
+:align: center
+:width: 75%
+
+| Wake Model                        | FLORIS | FOXES | PyWake |
+| --------------------------------- | ------ | ----- | ------ |
+| **Jensen 1983**                   | •      | •     | •      |
+| Larsen 2009                       |        |       | •      |
+| **Bastankhah / Porte Agel 2014**  |        | •     | •      |
+| **Bastankhah / Porte Agel 2016**  | •      | •     |        |
+| Niayifar / Porté-Agel 2016        |        |       | •      |
+| IEA Task 37 Bastankhah 2018       |        |       | •      |
+| Carbajo Fuertes / Markfort / Porté-Agel 2018  |        |       | •      |
+| Blondel / Cathelain 2020          |        |       | •      |
+| Zong / Porté-Agel 2020            |        |       | •      |
+| Cumulative Curl 2022              | •      |       |        |
+| **TurbOPark (Nygaard 2022)**      | •      | •     | •      |
+| Empirical Gauss 2023              | •      |       |        |
+:::
+
+:::{table} Deflection models
+:align: center
+:width: 75%
+
+| Wake Model                        | FLORIS | FOXES | PyWake |
+| --------------------------------- | ------ | ----- | ------ |
+| **Jimenez 2010**                  | •      |       | •      |
+| **Bastankhah / Porte Agel 2016**  | •      | •     |        |
+| Larsen et al 2020                 |        |       | •      |
+| Empirical Gauss 2023              | •      |       |        |
+:::
+
+
+### 1-dimension wake profiles
+
+```{code-cell}
+---
+tags: [hide-input]
+---
+
+x_turbine = np.array([0.0, 0.0])
+y_turbine = np.array([-ROTOR_D/2, ROTOR_D/2])
+x_streamwise = np.array([XMIN, XMAX])
+y_streamwise = np.array([0.0, 0.0])
+x_1d = np.array([1 * ROTOR_D, 1 * ROTOR_D])
+x_5d = np.array([5 * ROTOR_D, 5 * ROTOR_D])
+x_10d = np.array([10 * ROTOR_D, 10 * ROTOR_D])
+y_crosswise = np.array([YMIN, YMAX])
+
+fig, ax = plt.subplots(figsize=(6, 3))
+ax.plot(x_turbine, y_turbine, '-', color='black', linewidth=3, label="Turbine")
+ax.plot(x_streamwise, y_streamwise, '-.', color='black', linewidth=2, label="Streamwise")
+ax.plot(x_1d, y_crosswise, linestyle=(0, (2, 3)), color='black', linewidth=2)
+ax.plot(x_5d, y_crosswise, linestyle=(0, (2, 3)), color='black', linewidth=2)
+ax.plot(x_10d, y_crosswise, linestyle=(0, (2, 3)), color='black', linewidth=2, label="1D, 5D, 10D cross sections")
+ax.set_title("One-turbine velocity profiles")
+ax.set_xlabel("X (m)")
+ax.set_ylabel("Y (m)")
+ax.set_ylim([-1000, 1000])
+ax.axis('equal')
+ax.grid()
+ax.legend()
+```
+
+
+#### Jensen
+```{code-cell}
+---
+tags: [hide-input]
+---
+
+this_case = CASE_DIR / Path('jensen/wind_energy_system.yaml')
+floris_case = WCompFloris(this_case)
+foxes_case = WCompFoxes(this_case)
+pywake_case = WCompPyWake(this_case)
+
+fig, ax = plt.subplots(figsize=(6,4))
+floris_case.streamwise_profile_plot(wind_direction=270, y_coordinate=0.0, xmin=XMIN, xmax=XMAX)
+foxes_case.streamwise_profile_plot(wind_direction=270, y_coordinate=0.0, xmin=XMIN, xmax=XMAX)
+pywake_case.streamwise_profile_plot(wind_direction=270, y_coordinate=0.0, xmin=XMIN, xmax=XMAX)
+ax.plot([1*ROTOR_D, 1*ROTOR_D], [0, 10], color="black", linestyle='--', linewidth=PROFILE_LINEWIDTH)
+ax.plot([5*ROTOR_D, 5*ROTOR_D], [0, 10], color="black", linestyle='--', linewidth=PROFILE_LINEWIDTH)
+ax.plot([10*ROTOR_D, 10*ROTOR_D], [0, 10], color="black", linestyle='--', linewidth=PROFILE_LINEWIDTH, label="Cross-stream profile locations")
+lines = ax.lines
+x1, y1 = lines[0].get_data()
+x2, y2 = lines[1].get_data()
+x3, y3 = lines[2].get_data()
+e1 = np.abs(y1 - y2)
+e2 = np.abs(y2 - y3)
+ax.plot(x1, e1, color="black", linestyle='-.', linewidth=ERROR_LINEWIDTH, label="|FLORIS - FOXES|")
+ax.plot(x1, e2, color="black", linestyle=':', linewidth=ERROR_LINEWIDTH, label="|FOXES - PyWake|")
+ax.set_title("One-turbine streamwise velocity profile")
+ax.set_xlabel("X (m)")
+ax.set_ylabel('U (m/s)')
+ax.set_ybound(lower=0.0)
+ax.legend()
+ax.grid()
+
+fig, ax = plt.subplots(3, 1, figsize=(6,4))
+fig.suptitle("One-turbine cross section velocity profile")
+X_D = [1, 5, 10]
+for i, D_X in enumerate(X_D):
+    plt.axes(ax[i])
+    floris_case.xsection_profile_plot(wind_direction=270, x_coordinate=D_X * ROTOR_D, ymin=YMIN, ymax=YMAX)
+    foxes_case.xsection_profile_plot(wind_direction=270, x_coordinate=D_X * ROTOR_D, ymin=YMIN, ymax=YMAX)
+    pywake_case.xsection_profile_plot(wind_direction=270, x_coordinate=D_X * ROTOR_D, ymin=YMIN, ymax=YMAX)
+    ax[i].set_title(f"{D_X} D")
+    ax[i].set_ylabel("U (m/s)")
+    ax[i].set_ybound(lower=0.0, upper=12.0)
+    ax[i].grid()
+    if i < len(X_D) - 1:
+        ax[i].xaxis.set_ticklabels([])
+    else:
+        ax[i].set_xlabel("Y (m)")
+        ax[i].legend()
+fig.tight_layout()
+```
+
+
+:::{dropdown} Grid points
+Dropdown content
+:::
+
+:::{dropdown} Rotor velocity average
+Dropdown content
+:::
+
+:::{dropdown} Partial wake
+Dropdown content
+:::
+
+## Spatial discretization and rotor average velocity
+Since the focus is specifically on analytical wake models, this class of software does not
+require a specific type of grid to model the wake.
+In practice, each software can choose a grid that meets its design and use objectives.
+However, the grid type has an impact on the results of the model through the computation
+of the thrust coefficient from a rotor-averaged velocity.
+The grid-types and methods for rotor averaging are compared here.
+
+### Point placement
+
+Show the locations in space and note that the points are used in combination with a velocity average method.
+
+
+### Rotor velocity average
+
+Develop a test case that demonstrates how the rotor-averaged velocity method performs.
+Ideally, this would be case that compares the methods outside the context of a wake model simulation,
+so something like average a function that analytically averages to 1.
+
+### Partial wake treatment
+
+Describe how the rotor average velocity is computed for a turbine where part of the
+rotor is waked.
+
+### Grid dependency
+
+plot of some quantity that's a function of the incoming wind (power, rotor average velocity...)
+as a function of grid resolution
+
+
+## Overlapping wakes
+The mathematical models included in each software are generally grouped into models
+describing the velocity of the wind in a wind turbine wake (velocity model) and
+models describing the magnitude of deflection of the wake (deflection model).
+The models available in each software are shown in the tables below.
+
+## Wind shear and veer
+
+Compare how the software model wind shear and wind veer