I started thinking about this problem recently when paddleboarding and running with a tidal current through a channel, then paddling against the wind in a canal.
Wind is strongest and builds the most velocity and momentum (and makes the biggest waves) when blowing with the longest fetch, ie, with the longest length of open ocean or low-friction surface for unobstructed flow. The same is true for water currents: when flowing in deeper water with less friction from underwater terrain water currents will be faster and stronger.
Nevertheless, it seems like obstructing and channeling the flow, like with the skyscrapers on the shore of Lake Michigan, will accelerate air movement. Rowing with an incoming tide, you notice that the velocity of water flow seems fastest when it is channeled through the smallest opening.
Assuming that there is equal pressure differential and wind movement (say north to south) over a large area, would I find it easier to row north against the wind on the open ocean or in a canal flanked by two solid walls? The thickness of the walls obviously matters, since thickness at lower limit of 0 parallel to the wind vector would be indistinguishable from no obstacle at all. If the walls were infinitely thick, then all of the air movement would have to be channeled through the opening, leading to the fastest, strongest wind in the canal.
Is there a thickness to the channeling blockade at which the effect of channeling the wind and accelerating it is cancelled out by the effect of friction?
Are there equations for describing these phenomena? Is there a better/easier way to try to think about this?
It should be the same, assuming equal pressure differential and wind movement, but I can’t really tell if you are talking about the effects of the wind, the water, or both.
The change in velocity of flow in a pipe (edit: as the cross section changes) is a function of the principle of conservation of mass. I think the same holds for open channels.
It depends on whether the terrain you’re looking at is in series or in parallel. If the spots are in series, like two points on the same river (without branches or tributaries in between), then the water must flow faster in the more restricted areas, because it’s still pushing the same number of gallons per second through there as at any other point on the river. If, however, the terrain is in parallel (like a river that branches into two channels before reaching the ocean), then the one that’s less obstructed will have the faster-flowing water, since it’s easier for the water to flow that way.
I think you need to be careful about the terms “flow” versus “speed.” A vast river moving at 1KPH has far more flow than a tiny brook moving at 5KPH. For example, if your garden hose is dribbling, and you grab it and pinch it almost closed, you create a high-speed jet of water. By pinching the hose you’ve decreased the flow, and an unobstructed hose will fill a bucket much faster than that narrow high-speed jet. Yet the speed of the tiny jet of water may be vastly higher than the speed of water coming from the unobstructed hose.
Thanks for the replies. (Half of what I was hoping for was help in articulating my question more clearly.)
Maybe a couple more thought experiments will get at what is puzzling me:
Imagine a person (A) standing on a flat featureless shore facing into direct onshore wind.
Now imagine the same scenario except that there is an immense city-block-wide skyscraper with flat concrete walls as the only feature of the shore. Somewhere next to the buiding (in “parallel”) there should be a zone of increased wind velocity. If a person (B) stands to the right or left of the structure but pressed up against the wall, won’t the effect of friction of the building and its walls on the air movement leave them in a zone of lower speed and lower flow? If they are far (say, a mile) to the side of the structure, the altered flow/speed effect on them should be negligible. So, it seems like there should be a point at a certain distance from the wall where the speed of the wind is maximally increased relative to that experienced by (A).
Imagine a similar scenario except this time the walls of the skyscraper are extremely textured, tortuous with deep indentations and random protrusions. Now there should be a wider zone of turbulent, friction-affected air with less consistent directional force on each side of the building. Will there still be a point to the side of the building where there is increased wind velocity? If you continue to make the walls more textured, will the effects of friction on the wind eventually prevent a point of increased velocity relative to the (A) scenario?
To make the scenario more realistic, would a person standing on a flat featureless Lake Michigan shoreline experience faster wind than a person standing between skyscrapers 100 meters apart? What if they were 10 meters apart? 1 meter apart?
I think you are confusing two different cases, first, that of flow inside of a pipe; and second, the flow around an object in an open channel. I think you are assuming a condition that arises from the first case applies in the second case. I don’t think that it does.
Yes, you are correct. Here, for example, is a computational study showing the airflow around a pair of buildings. Velocity contours are mapped in the links under results; as an example, this image shows increased velocity on each side of the two buildings.
Former hang glider pilot here. I currently fly sailplanes. Hang Glider and Paraglider pilots know a lot more about this than pilots of heavier and faster aircraft. As an example, there is a turbulent area at Sandia Crest, NM which the sailplane pilots know to be a bit bumpy. The Hang Glider pilots refer to that same area as “The Cauldron of Hell”.
Wind speed will most defiantly increase through a gap in a mountain range, or at the low spot in a long ridge. If you have a single round hill sticking up in the middle of a plain, then the wind speed will be lowest low on the hill where the hill faces the wind, and will be higher at the top and above the hill and as it goes around the sides…the air kind of gets “jammed up” where it hits the hill, and “squirts” around the jam. The scare quotes are because there is a lot more to it than those words suggest, but they work for a basic understanding of what is going on.
This book is a pretty good practical treatment of weather from global to very small scales. ( if it is, as I suspect, the latest edition of the earlier Dennis Pagen book I have with a different title)
Thanks for the replies! The linked image is exactly what I was looking for - you can see how there is reduced wind speed right next to the wall of the house, but increased wind speed further into the gap, which hits a maximum and then decreases as you get to the midpoint between the houses.
Do you think the same velocity contours would happen if there were two **rows **of houses parallel to the wind direction?
If someone is running against the wind between the rows of houses, would they be best served by running as close to the houses as possible or by running straight down the middle?
