It is strongly recommended that you complete the assignment in Python or R, although you can complete it in excel/numbers if necessary. They will download the data for you and get you started with a few blocks of code to make plots and tables. If you are electing to complete the lab in excel, you can find all the relevant data files here here. Note these data are in .csv format. If you plan to work in excel, you should save a copy of the data in a suitable excel format (e.g., .xlsx) before making any charts or doing any calculations.
Please upload your answers including all calculations, discussions, tables, and graphs in a single document (PDF or HTML file). Note that you can download your .ipynb file under ‘File \(\gg\) Download as \(\gg\) HTLM or PDF via Latex’ and submit this as your report. Label the report document with your name and your student number. Upload your answers to Canvas. Do not attach a spreadsheet.
Make Sure your student number is include on each plot you produce, and that each plot is using the correct units.
In this exercise you will use a 30-min data-set measured above an extensively flat cotton field near Kettleman City, CA, US. The actual day / time is selected based on your student number, the timestamp you are responsible for can be found in (Table 1). You will be provided with two tables:
Table1: lists horizontal wind speeds \(\overline{u}\) measured with cup-anemometers installed at six heights on a profile tower averaged over 30 minutes. Air temperature and pressure are also provided in the table header.
Table2: contains longitudinal wind \(u\), lateral wind \(v\) and vertical wind \(w\) measured every second over the same 30 minutes by a fast-response anemometer located at 6.4 m height.
For all questions assume neutral conditions, \(z_d=0\), and \(P_a\) = 100 kPa.
Table 1: The Timestamp you are responsible for analyzing in YYYY (Year) mm (month) dd (day) HH (hour) MM (minute) format. The filename for your date will follow this format: YYYYmmddHHMM.txt. e.g., wind202402141330.txt and turbulence202402141330.txt would be the files for February 14th, 2023 13:30. If you are completing the assignment using Python or R, just edit the filename timestamp in the corresponding template. If you are completing the assignment by hand or in excel, you can find the data files here.
Last digit of student number
date (YYYmmddHHMM)
0
200008021530
1
200008031000
2
200008031030
3
200008031200
4
200008041030
5
200008041100
6
200008041130
7
200008041530
8
200008101230
9
200008101530
Table 1 Metadata:
# EBEX 2000, Kettleman City, CA, USA
# Wind profile measured by cup anemometers
# Start: 2000/08/19 16:30 PST
# Average values over 30 min
# Air temperature: 33.4 deg C
# Air pressure: 101.444 kPa
Table 1 Data:
Height (m) Wind Speed (m/s)
0 0.95 1.77
1 1.55 2.18
2 2.35 2.47
3 3.72 2.85
4 6.15 3.37
5 9.05 3.67
Table 2 Metadata:
# EBEX 2000, Kettleman City, CA, USA
# Turbulence data measured at 1 Hz by fast-anemometer at 6.4 m
# Start: 2000/08/19 16:30 PST
# u (m/s) : longitudinal wind vector component
# v (m/s) : lateral wind vector component
# w (m/s) : vertical wind vector component
Table 2 Data preview:
u (m/s)
v (m/s)
w (m/s)
TIMESTAMP
2000-08-19 16:30:00
3.0774
0.0560
-0.1993
2000-08-19 16:30:01
2.9384
-0.0827
0.0345
2000-08-19 16:30:02
2.9198
-0.1783
-0.1177
2000-08-19 16:30:03
3.0079
0.0066
0.2113
2000-08-19 16:30:04
3.1117
0.0649
0.0785
Question 1
Estimate \(z_0\) from the measured values vertical wind profile provided. Indicate your estimate of \(z_0\) in m and produce a log wind profile plot. You can either use a spreadsheet/software or by hand using semi-logarithmic graph paper. Note: If you solve this question using a semi-logarithmic paper, use a ruler and your graphical judgement (subjective) to create the best fit through the points.
Question 2
Based on the slope of the curve in Question 1, calculate the friction velocity \(u_{\ast}\).
Question 3
Estimate the surface shear stress \(\tau_0\) from the result in Question 2 and with help of the ideal gas law:
\[
PV=nRT
\tag{1}\]
here,\(R\) is the ideal gas constant (\(8.31446261815324 Pa\ m^3\ mol^{-1} K ^{-1}\)), \(T\) is temperature (in Kelvin!), \(P\) is air pressure, \(V\) is volume, \(n\) is the amount of the gas in mols; with \(n=m/M\), where \(m\) is mass and \(M\) is the molar mass. The molar mass of air is \(\approx .028964 kg mol^{-1}\)
Question 4
Estimate the eddy diffusivities for momentum \(K_M\) using the wind gradients \(\Delta \overline{u}\) in Table 1 between (a) \(z=0.95\) and \(1.55\) m, (b) \(z=1.55\) and \(2.35\) m, (c) \(z=2.35\) and \(3.72\) m, (d) \(z=3.72\) and \(6.15\) m, and (e) \(z=6.15\) and \(9.05\) m. How does \(K_M\) change with height? Explain why.
Question 5
From the values in Table 1, calculate the aerodynamic resistance of the momentum flux \(r_{a_M}\) for the layer from the surface to 9.05 m.
Question 6
From the turbulence data provided in Table 2, calculate \(\overline{u}\), \(\overline{v}\), and \(\overline{w}\). How does the magnitude of \(\overline{u}\) compare to \(\overline{v}\), and \(\overline{w}\)?
Question 7
From the data in Table 2 calculate \(\overline{u^{\prime 2}}\), \(\overline{v^{\prime 2}}\), and \(\overline{w^{\prime 2}}\). Name those parameters.
Question 8
From the data in Table 2 calculate the turbulence intensities \(I_u\), \(I_v\), and \(I_w\).
Question 9
From the data in Table 2 calculate the mean turbulent kinetic energy per unit mass \(\overline{e}\). What is the ratio of \(\overline{e}\) to the mean kinetic energy per unit mass?
Question 10
Which of the three wind components, \(u\), \(v\) or \(w\), contains most turbulent kinetic energy per unit mass. Speculate about the shape of the eddies.
Question 11
From the data in Table 2 calculate (a) \(\overline{u^{\prime}v^{\prime}}\) and (b) \(\overline{u^{\prime}w^{\prime}}\)
Question 12
Calculate \(r_{uv}\) and \(r_{uw}\). Discuss your results.
Question 13
Plot a scatter graph of \(u^{\prime}\) (\(x\)-axis) vs. \(w^{\prime}\) (\(y\)-axis). Comment your graph and discuss if it looks like you expected.
Question 14
Using your result in question 11 (b), calculate the friction velocity \(u_{\ast}\) based on the high-frequency data and compare it to your answer in question 2.