Monday, May 6, 2024

The World Sees Atmospheric Pressure at Work

This week is the 30th anniversary of the opening of the EuroTunnel (Chunnel) between England and France. The BBC commemorated the event with a story about the first underground meeting of the tunnels being dug from both sides that took place on Dec 1, 1990, four years before the actual opening of tunnel to traffic in 1994. They met roughly mid channel, with TV cameras at hand.

The fellow on the British side with orange t-shirt is Graham Fagg who in 2010 gave a description of the event, which can be heard on the BBC Witness program. In that recording from (3:59) to (4:28) we learn that when the hole was opened up big enough to walk through there came a sudden wind from the British side to the French side that was strong enough to blow his helmet off.  That wind is the subject at hand.

This wind is quite literally what we call in marine weather a channeled wind! It means the pressure on the UK side was higher than that on the French side and the area between the two sides was confined by a narrow channel. We just have a case here of a very narrow channel, not just steep hills on two sides.

Our goal is to estimate what that wind speed was, which is an exercise in resources—meaning, can we find the actual pressures at both ends at that time, and then can we make some semi-reasonable estimates of the wind speed.

Below shows the Chunnel viewed on Meltemus charts of UK in qtVlm, with overlaid ECMWF reanalyzed surface analysis for the approximated break-though time (11 to 12 UTC, Dec 1, 1990) when the wind was noted. (The New York Times had a good article about the event, but gave the wrong time of day due to a time zone error! — no link here as they no longer let non subscribers read their articles.)

The red line is the route of the Chunnel. The isobars are shown at 0.1mb spacing.  The inserts are meteogram plots of how the pressure varied throughout the day at both ends. The pressure gradient across the channel did not change from 11z to 12z, at (1036.0 - 1035.5)/26.9 = 0.5mb/26.9 nmi.

The ambient surface wind at this time was about 10 kts across the channel, but we must use wild approximations to estimate the wind in the tunnel.

We can for example just use the basic formula for wind responding to isobars that leads to the wind we see on the surface. We derive a simple formula for that in Table 2.4-1 of Modern Marine Weather:

 U = 40 kts/ [D x sin(Lat)]

Where D is the pressure gradient expressed in a special way. Namely it is the distance between 4-mb isobars expressed in degrees of Lat. On a map, we put dividers across adjacent isobars, then move that to the Lat scale. If the distance between the two isobars on either side of the point we care about is 180 nmi, then D = 3.0. 

So we have to convert our tunnel gradient to that format starting with: 0.5 mb = 26.9 nmi. 

0.5 mb x (4/0.5) = 4 mb = 26.9 nmi x (4/0.5) = 215.2 nmi = 3.58 Lat degrees (at 60 nmi per degree).

U = 40 kts / [3.58 x sin (51)] = 14.4 kts

Then for surface winds we have a surface friction reduction of 0.8 or so that leaves us with 11.5 kts, which essentially agrees with the observed surface winds—which should not be a surprise as that is the basic procedure used by the models, with a few subtle corrections.

The above is based on the physics of wind flow, but still a large stretch to project that thinking into the tunnel. It is at least a plausibility argument for the rough magnitude of  the wind.

In our textbook in Sec 6.2 on Wind Crossing Isobars (page 146) we give another way to approximate wind flow in channels that is purely empirical, meaning not computed, just observed. It is a rule we compiled based on how the local NWS forecasted wind speed (in the old days) in the Strait of Juan de Fuca and in the Puget Sound based on the pressure differences at each end of these channels. Our composite guideline is this:

Channel wind (kts) = 800 x Pressure gradient (mb/nmi),

which we can easily apply to what we know:

Channel wind = 800 x (0.5/26.9) = 14.9 kts.

So again, we see the order of magnitude of the wind speed we might expect in the tunnel.  And again, we cannot consider this rigorous science; wind flow in restrictions is very complex. We have just confirmed that indeed the wind was going the direction observed, and also about the right speed. We use this same approach to forecast or anticipate wind changes in our own waters based on pressure changes. It is part of our Local Weather web page.

There is also a physiological element of confirmation. The force of the wind is proportional to the wind speed squared. The force of 14 kts of wind is twice that of 10 kts of wind. At 17 kts it is three times stronger than 10 kts. In other words, there is a dramatic difference in what we experience in 10 kts vs even just 12 kts.

We know from our own experience that we could be in a wind of 10 or 11 kts that could blow our hat off if it hit at the right angle. And it would be noted, but not a focus point for any newscaster's story. But if this wind were much more, we know that it would be a focus of the conversation, which it wasn't. Note too that the wind came not at the moment when the flags were exchanged, but later when they had the hole opened up enough to walk through.

In other words, without any math or science considerations, we might guess the wind was about 8 to 10 kts, because less than that would not blow his helmet off, and much more than that would have clothes rippling in the wind and newscasters talking about it, which they did not.

Such visual effects of the wind is not unlike our view of whitecaps. At 10 kts there are some, if we look carefully; at 15 kts they are easier to see; but at 20 kts they are the dominant factor noted when looking at the water. 


Pressure remains a concern in all such tunnel travel due to the piston effect that can create high pressures in front of the train stressing gear and making travelers uncomfortable. The Chunnel has build in pressure escape valves all along the tunnel to prevent this.

Chunnel prices seem to be like Amtrak, which depends on availably, and season. 

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