Turbulence and Energy Fluxes
2. Turbulence and Energy Fluxes#
Here you will find the
corresponding lecture slides.
Exercises
Exercise 1: Given the the following measurements of specific humidity q [g/kg] and potential temperature θ [K] at two heigths, determine the turbulent heat fluxes for each timestep. (Hint: Aussume neutral stability, and \(K_M = 3~m^2s^{−1}\)). Plot \(Q_H\) and \(Q_E\) versus time. Comment on the diurnal variation of the turbulent heat fluxes. What might be the underlying landcover in this study area?
Time |
\(\theta_1\) (1 m) |
\(\theta_2\) (2 m) |
\(q_1\) (1 m) |
\(q_2\) (2 m) |
|---|---|---|---|---|
00:00 h |
278.58 |
278.54 |
3.113 |
3.068 |
06:00 h |
280.12 |
280.17 |
3.051 |
3.065 |
12:00 h |
284.28 |
284.35 |
2.985 |
2.996 |
18:00 h |
280.02 |
280.01 |
2.675 |
2.628 |
Exercise 2: Assume that the mean vertical eddy moisture flux is \(7.2\cdot10^{−4}\) [kg kg-1 m s-1]. What is the turbulent latent heat flux?
Exercise 3: What vertical temperature difference is necessary across the microlayer (bottom 1 mm of the atmosphere) to conduct 300 \(W m^{−2}\) of heat flux?
Exercise 4: Find the effective surface heat flux over a forest at neutral stability when the wind speed is 5 \(m s^{−1}\) at a height of 10 m, the surface temperature is 25ºC, and the air temperature at 10 m is 20ºC. Use an appropriate method to estimate this flux. Discuss the results.
Exercise 5: Given the following measurements from an instrumented tower, find the sensible and latent heat fluxes. Assume a net radiation of 500 \(W m^{−2}\) and a ground flux of 30 \(W m^{−2}\).
z (m) |
T (ºC) |
r (g/kg) |
|---|---|---|
10 |
15 |
8 |
2 |
18 |
10 |
Exercise 6: If the sensible heat flux is 300 \(W m^{-2}\) and the latent heat flux is 100 \(W m^{-2}\), what is the Bowen-ratio? What is the likely surface type?
Exercise 7: Find the drag coefficient (bulk coefficient) in statically neutral conditions to be used with surface winds of 5 \(m/s\) at 10 \(m\) height over (a) villages, and (b) grassland. Also, find the friction velocity and surface stress. Discuss the results.
Exercise 8: On an overcast day, a wind speed of 6 \(m/s\) is measured with an anemometer located 10 \(m\) over ground within a corn field. What is the wind speed at 25 \(m\) height?
Exercise 9: Wind speed is measured at two different heights. Find the friction velocity using an analytical approach (logarithmic wind law).
z (m) |
u (m/s) |
|---|---|
2 |
2 |
10 |
3.15 |
Exercise 10: Given \(K_H=5~m^2 s^{-1}\) for turbulence within a stable background environment, where the local lapse rate is \(\partial\theta/\partial z=0.01~K/m\). Find the kinetic heat flux \(\overline{w'\theta'}\).