Regional wind systems
3. Regional wind systems#
Here you will find the
corresponding lecture slides.
Exercises
Exercise 1: Given a mean wind speed of \(M_0= 5 m~s^{-1}\) and \(\alpha=2\), find the probability that the wind speed will be between 5.5 and 6.5 \(m~sˆ{-1}\)?
Exercise 2: Find the steady-state updraft speed in the middle of (a) a thermal in a boundary layer that is 1 km thick; and (b) a thunderstorm in a 11 km thick troposphere. The virtual temperature excess is 2ºC for the thermal and 5ºC for the thunderstorm, and \(|g|/ \overline{T_v} = 0.0333~m \cdot s^{-2} \cdot K^{-1}\).
Exercise 3: Find the equilibrium updraft speed (\(m~s^{-1}\)) of a thermal in a 2 km boundary layer with environmental temperature 15ºC and a thermal temperture of 19.5 ºC.
Exercise 4: Winds of 10 \(m~s^{-1}\) are flowing in a valley of 10 km width. Further downstream, the valley narrows to the width of 2.5 km. Find the wind speed in the constriction, assuming constant flow depth.
Exercise 5: Assume \(g/T_v=0.0333~m \cdot s^{-2} \cdot K^{-1}\). For a two-layer atmospheric system flowing through a short gap, find the maximum expected gap wind speed. Flow depth is 300 m, and the virtual potential temperature difference is 5.5 K.
Exercise 6: Anabatic flow is 5ºC warmer than the ambient environment of 15ºC. Find the horizontal and along-slope pressure-gradient forces/mass, for a 30º slope. Furthermore, suppose a steady-state is reached where the two forces are buoyance and drag. Find the anabatic wind speed, assuming an anabatic flow depth of 50 m and a drag coefficient of 0.05.
Exercise 7: Air adjacent to a 10º slope averages 10ºC cooler over its 20 m depth than the surrounding air of virtual temperature 10ºC. Find and plot the wind speed vs. downslope distance, and the equilibrium speed. \(C_D=0.005\). Comment on the differences between the equilibirum speed and the speed derived from the downslope distance.
Exercise 8: Marine-air of thickness 500 m and virtual temperature 16ºC is advancing over land. The displaced continental-air virtual temperature is 20ºC. Find the sea-breeze front speed, and the sea-breeze wind speed.
Exercise 9: Assuming calm synoptic conditions (i.e, no large-scale winds that oppose or enhance the sea-breeze), what maximum distance inland would a sea-breeze propagate? Use data from the previous exercise, for a latitude of 45ºN. What happens if we are near 30º?
Exercise 10: Cold winter air of virtual potential temperature -5ºC and depth 200 m flows through an irregular mountain pass. The air above has virtual potential temperature 10ºC. Find the maximum likely wind speed through the short gap.
Exercise 11: Find and plot the path of air over a mountain, given: \(z_1=500~m\), \(M=30~m~s^{-1}\), \(b=3\), \(\Delta T/\Delta z=-0.005~K~m^{-1}\), \(T=10ºC\), and \(T_d=8ºC\) [Hint: you need to calculate the wavelenght first]. Indicate which waves have lenticular clouds [Hint: the liquid condensation level can be approcimated with \(z_{LCL}=a \cdot (T-T_d)=(125~m~ºC^{-1})\cdot (T-T_d)\)].
Exercise 12: For a mountain of width 25 km, find the Froude number. Assume \(g/T_v=0.0333~m \cdot s^{-2} \cdot K^{-1}\), \(M=2~m \cdot s^{-1}\), and \(\Delta T/\Delta z=5~ºC \cdot km^{-1}\). Draw a sketch of the type of mountain waves that are likely for this Froude number.
Exercise 13: List and explain commonalities among the equations that describe the various thermally-driven local flows.
Exercise 14: What factors might affect rise rateof the thermals, in addition to the ones already mentioned?
Exercise 15: What factors control the shape of the katabatic wind profile?
Exercise 16: What happens to a natural wavelength of air for statically unstable conditions?
Exercise 17: Comment on the differences and similarities of the two mechanisms for createing Foehn winds.
Exercise 18: If air goes over a mountain but there is no precipitation, would there be a Foehn wind?
Exercise 19: Suppose that katabatic winds flow into a bowl-shaped depression instead of a valley. Descrivbe how the airflow would evolve during the night.
Exercise 20: If warm air was not less dense that cold, could sea-breezes form? Explain.