# 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 \(\overline{w'\theta'}\).