Revisiting Mountain Ranges and Conserving Spin

 

#2608 "Red Cedar Snow Load" 16x20 inches
This snow came from a storm that originated in a lee
trough on the eastern flanks of the Canadian Rockies

In "Mountains and Balancing Spin", I tried very hard to explain what happens to air flowing over a mountain barrier. Certainly last week’s description of the dynamical processes that occur when the jet stream crosses a mountain was a bit challenging.

As a Special March Break Version of Science Tuesday, let’s revisit that material in another way before we describe how the mountain ridge of high pressure and the downstream lee trough fundamentally influence our weather. Everyone learns differently but when the concepts get into the grey matter, you will enjoy them for life. 

Conservation of angular momentum is always important and forever working in the background whether you are a figure skater or air moving on the globe. Changes in the skater’s rate of spin seems like magic when the rapid twirl of an "upright spin" slows to the leisurely rotation of the "camel or Campbell". The slow spin does not look anything like the desert dromedary! Apparently the name arose because it sounded similar to an Australian skater  with the Campbell surname who was famous for performing the "camel"  spin - both names sound very much the same. 

The change in rotational speeds arises because angular momentum must be always conserved if there is no friction. A small girth cylinder will spin much quicker than when the cylinder is squashed and that mass spread further from the axis of rotation. As mentioned, the same experiment can be completed using exercise weights and an swivel chair but figure skaters are more entertaining. The physics is the same.

The total spin of an air parcel must also be conserved as it crosses a mountain. That total spin is comprised of the spin in the air and the location of that parcel on the spinning Earth - we can call that "planetary spin".

Crossing the mountain results in the cylinder being squashed on the upwind slope. The resulting slower "camel spin" is offset by a deflection of the air toward the pole and a higher planetary spin. The total spin is unchanged.

After crossing the summit, the air flowing down the lee slope converts the camel into the upright spin. The quicker spin is offset this time by a deflection toward the equator where there is lower planetary spin. Once again the total spin remains the same. 

Looking Down on a North-South Mountain Range in the Northern Hemisphere
and the path of the air as described in words above

The total spin of the air crossing the mountain means that the air is deflected toward the pole on the upwind slopes and toward the equator to the lee of the mountain. The path of the air is simply the wind. 

From "The Answer Really IS Blowing in the Wind", we know that the wind follows the pressure height contours. As a result, the height contours also follow the path of the air - the wind. And thus we have a ridge of high pressure over and upstream from the mountain and a trough of low pressure in the lee.

700 mb Pressure Contour Map 
Essentially the Height Above Sea Level 
where the pressure is 700 mb
Averaging around 10 thousand feet above sea level

Ridge over the Rockies and Lee Trough
of Lower Pressure

Following the pressure height contours on a weather map is like cattle paths tracing height contours on a topographical map. In the free atmosphere without friction, the winds generally follow the height contours. If your left hand points toward low heights and your right hand to higher heights, you must be looking in the direction of the gradient wind. 

That ridge of high pressure over the mountains of western North America and the trough of low pressure in the lee of the Rockies, means a lot for our weather. The Rockies don't move much so the forecast problem reduces to predicting when strong winds will blow roughly perpendicular to the mountain range. The lee troughs have favourite formation locations - western Wyoming and Colorado is one, southern Alberta is another!

Weather is not magic. It can be understood just like appreciating when angular momentum is conserved and figure skaters produce marvellous displays while conserving spin. Skating and the weather can be amazing but they are not magic.

The forces acting on air moving over the mountain reach a physical solution that creates a ridge of high pressure over and upstream and a trough in the lee of that barrier. Air impacting perpendicular to a mountain on a spinning Earth has to move according to the laws of physics and conserve angular momentum… spin. Any confusion that results from this explanation is purely my responsibility. 

Now what does that mean for the weather? Lots! But let's save that for next week. 

Warmest regards and keep your paddle in the water,

Phil the Forecaster Chadwick