The Froude Number and Stable Flow: Mountain Blocking


A powerful low amplitude shortwave ejected into Montana this morning in association with a 160 kt Pacific Jet.

The 0Z NAM from yesterday clearly depicts this feature:

Large scale and mesoscale ascent developed rapidly as the jet core amplifed over the region.  Note the large increase of high level moisture associated with a region of strong vertical ascent:

0545Z:

Three hours later at 0845Z:

Low amplitude intense shortwaves such as these have a tendency to develop significant upward vertical velocity/downward vertical velocity couplets which support rapid cyclogenesis and regions of strong pressure gradients over small areas (i.e. rapid intensification, or the second partial of p with respect to x, gradient of the gradient).

Note the rapid pressure rises, on the order of 8+ mb’s / 3 hours over northern MT as extreme cold air advection set in behind the front.

The surface analysis depicts the strong surface ridging associated with the extreme subsidence mainly owing to strong cold air advection behind the cold front.  Also note how surface ridging amplifies as the high pressure region interacts with the Rockies.  The Rockies “block” the subsident air from progressing westward, therefore air builds at a faster rate east of the Continental Divide resulting in stronger surface ridges:

The Great Falls sounding at 0Z shows the flow was mainly out of the N in the low levels and NW in the mid levels.

Great Falls is around 3700 feet, so in this sounding, stable N flow extended to nearly 10,000 feet, or over 6000 feet AGL.

The Belt Range south of Great Falls extends to around 6000-8000 feet and reaching top elevations greater than 9000 feet.  Also note they form a “bowl” type shape around the region.  This makes it very difficult for air to flow around the mountains.

The Froude number,

relates the inertial forces to the gravitational force.  Think of it as a relation of kinetic energy to potential energy where V is velocity, N is the brunt vaisala frequency, and L is the height of the mountain.  Therefore, think of it as relating KE= 1/2mv^2 to PE = mgh.  The brunt vaisala frequency is: 

Note the gravity term (remember mgh) and the static stability d-theta/d-z (the more stable the air mass is, the greater the kinetic energy will need to be for air to ascend the range).

A series of radar images shows how stable N-NW flow “bunches up” into the valley as stable flow is blocked by the mountains south of the valley.  Low level stable air builds into the valley and it acts to “uplift” air above it, much like Cold Air Damming:

Note in the surface obs the heaviest snow develops coincident with rapidly rising pressure as stable air builds into the valley while V simultaneously weakens (weak V, which means lower kinetic energy, therefore the flow can not ascend the mountain).  Note also that downslope flow into the valley was not able to kill of the qpf.  Also note the powerful cold front (green) with G into the 60s.

High res models were trying to show a large weather hole over Great Falls associated with downsloping into the valley.  A good example showing high res models can struggle mightily in compex terrain:

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About jason ahsenmacher

I am a meteorologist, and I like baroclinic instability. View all posts by jason ahsenmacher

One response to “The Froude Number and Stable Flow: Mountain Blocking

  • Dale

    I saw your blog link in your signature at americanwx.com. I enjoy your posts and thought you blog might be interesting. I guess it isn’t being updated. I would be interested in reading it if you started posting again.

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