Wednesday, February 5, 2014

No, the Universe Doesn't Hate Us (a little Snow Physics)

My wife called it, rather pointedly, heart attack snow.  It would be heavy and wet and accumulate all day.  Better to shovel several times--not letting it get too deep--than try to clear the driveway all at once at the end. 

So I reminded my wife that the issue is power, not energy.  It takes a certain amount of energy to clear the driveway, and the total amount of energy won't vary too much whether the driveway is cleared in stages, or all at the end.*  (I suppose most of that energy goes into lifting the snow against gravity, though some part goes into throwing it varying distances.)   The demand shoveling snow puts on your cardiovascular system is a matter of power.  Power is energy per unit time.  Any number of units could be used; I like Joules/second, which is the fundamental metric unit, but if you're interested in your use of food energy, or losing weight, you might use, say, Calories/minute. 

Let's imagine that clearing the entire driveway of six inches of  heavy, wet snow requires expending 500 Calories.  You could take it easy, take small bites with your shovel, do it over the course of two hours (don't forget to take breaks!) and exert an average power of 500 Calories/2 hours = 250 Cal/h.  Or you could do a rush job, finishing in one hour, and exert 500 Cal/h -- twice the power does the same job in half the time.  The oxygen to burn those calories (and the carbon dioxide that results) is delivered by your hard-working lungs, heart and blood vessels.  If you don't get much aerobic exercise between snowfalls, I'd recommend option A!  (Or take my wife's advice; or get a snow thrower.) 

You see the distinction between energy and power all the time once you become familiar with it.  It is the reason that my little Hyundai and a Porsche can both drive the speed limit on the highway--but the Porsche can get to that speed from the on-ramp a LOT quicker than I can!  It is also the reason my old dad can still climb the stairs in his house with his failing heart, but he has to take them more slowly than I do.

Now to the main question.  If you live in a snowier clime, you will have noticed that more snow falls where you have just shoveled than in the surrounding areas.  The effect is most noticeable at the edges.  In other words, when it comes to show shoveling the universe seems to punish virtue!  But I'm pretty sure the universe (Splendid though it is) doesn't care about us much one way or the other, and certain it doesn't care that--much less how--we shovel.  What's going on, then?

As I reached the bottom of the driveway on Tuesday morning, a clue appeared in the snow that had accumulated between the cars.

Only five inches between the cars, but eight by
my little Hyundai and a foot by the minivan.

Here's the secret.  Moving fluid carries more and bigger particles the faster it is moving.  That's it.  The rule is usually applied to rivers, but it applies equally to snow-laden air.  Snow falls slowly, so that even a slight breeze will keep some of it suspended until the air slows down.  This is why snow forms drifts: the air slows when it meets an obstacle, and more snow is deposited. (The cars in the driveway are Big obstacles.)  It explains why the snow is deeper at the edges of the driveway (close to the high curb) than it is in the middle of the driveway.  It explains why I will shovel more snow if I shovel more times--each time I shovel, I am making a new "wind shadow" that will slow the air, depositing some of its white load.

This also one reason it is so difficult to measure snowfall: small variations in the landscape--as well as obvious barriers--can lead to different amounts of accumulation.

Another application of the principle explains a lot about rivers.  As the speed of moving water increases, it picks up more and bigger particles of sediment, as it slows it deposits them, beginning with the largest and heaviest.  The lower reaches of the Mississippi River, flowing over nearly level land, meanders because it does: any slight random bend in the river causes the water to slow a bit on the inside of the bend, and speed up on the outside.  Sediments are eroded by the faster moving water on the outside, forming a cut bank, while they are deposited on the inside, forming a point bar.  This makes the river bend greater and greater, as the river digs farther and farther into its outside edge.  In other words, a river meanders because it does! 

By the same token, it explains why the highest land in New Orleans is (against all "common sense") on the banks of the Mississippi River itself.  The land all around the river was created by the river overflowing its banks in periodic floods.  As the sediment-laden water leaves the fast-flowing channel it immediately slows, dropping most of its load.  The water that floods farther into the countryside has less sediment and gains less new land.  The historic French Quarter is right on the bank, while lower areas farther from the river weren't settled until this marshy land could be efficiently drained.  (It's a little jarring to realize that the surface of the river may actually be above your head as you stand only a short distance away.)  By the same token, the flooding of New Orleans after hurricane Katrina left the French Quarter nearly untouched, while it did the most damage to the poorest neighborhoods in these less-desirable lowlands. 

Only the green areas  are actually above sea level; the white are at, the yellow are below, sea level.  Note that the RIVER did not flood after Katrina; the water came from Lake Ponchartrain via the canals.

Since the river is now confined behind high levees where it cannot escape to spread its sediments, the situation of New Orleans must become fundamentally worse with time, as sediment-built land sinks and sea levels rise.

*Actually, it will, but in a way that favors doing it all at once.  And soon you will know why.

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