Wind Velocity And Absolute Temperature

One of the simplest things that I noticed, and wrote about here, is "The Wind Pressure Formula", on the meteorology and biology blog, www.markmeeklife.blogspot.com .

I knew that there were charts of how much force is exerted by winds of various speeds, but I had never seen a simple formula to match wind speed with the force exerted. I was going over a nearby bridge on a windy day, and noticed that there were whitecaps on the waves in the river below. I remembered that whitecaps form on waves when the wind reaches a speed of 22 kph (13.67 mph). I also knew that the atmosphere exerts a downward pressure of 14.7 pounds per square inch (1.03 kg per square cm).

I realized that this could only mean one thing. A wind of 22 kph (13.67 mph) exerted a force that was equal to atmospheric pressure. When this threshold was exceeded, the wind was able to force air into the waves on the water to form whitecaps.

It is necessary to remember to square the proportion of the wind speed threshold. If the wind speed is twice the threshold of 22 kph (13.67 mph) then two must be squared to give a pressure of four times atmospheric pressure. If the wind speed is only half of the threshold, then one half must be squared to give a pressure of one quarter of atmospheric pressure. I did a Google search for wind pressure formula, but did not see anything as simple and as easy to memorize as this.

Today, I would like to provide a simple explanation of a scientific mystery involving wind.

First of all, why is the wind speed what it is? Suppose that there is a gentle breeze of a few kph. Why is it at this speed, and not some other speed? I cannot really find an answer to this anywhere. There is an article on Wikipedia titled "Wind Speed", which provides background information, but does not really explain why the actual speed is what it is.

Second, is a real mystery that concerns the wind speeds on other planets. We know that wind is generated by adjacent differences in heat, as planetary surfaces heat unevenly when exposed to sunlight. So, if wind is generated by heat, then why do the coldest planets have the fastest winds?

Here is an article about this mystery if you wish to read more about it: http://www.csmonitor.com/Science/2013/0517/Why-do-planets-farthest-from-sun-have-highest-winds-Team-closes-in-on-answer

By far the greatest winds in the Solar System are on distant and frigid Neptune. Depending on one's definition of a planet, Neptune is either the most distant planet from the sun, or at least the most distant with a significant atmosphere. One report described typical winds on the planet as like shock waves from a nuclear bomb. Jupiter is far larger than Neptune, it is warmer and rotates much faster than Neptune. We know that heat and rotation are primary factors in wind formation. Yet, Neptune has far greater winds than Jupiter.

My answer to this mystery lies in the temperature scales that we use. We typically use either the Celsius or Fahrenheit scales. But both of these are arbitrary in nature. The Celsius scale defines the freezing point of water as zero degrees and the boiling point as a hundred degrees. A German scientist by the name of Fahrenheit simply picked a very cold day, and designated the temperature as zero degrees since it very rarely gets colder than that in most of northern Europe.

While these scales are fine for everyday use, they do not exactly tell us how much heat there is. That is because, in our everyday lives, this is rarely something that we have to deal with.

Heat, as we know, is actually the kinetic energy of molecular and atomic motion. But if the temperature gets colder and colder, there comes a point where this motion ceases altogether and the temperature cannot get any lower. This lowest possible temperature is known as absolute zero, it is equivalent to -459 degrees Fahrenheit or -273.15 degrees Celsius.

There is an absolute temperature scale, known as the Kelvin Scale. The degrees of this scale are equivalent to Celsius degrees, but the scale begins at absolute zero so that water freezes at 273.15 K and water boils at 373.15 K.

This gives us a quite different view of temperature. Considering how much absolute heat there is, a sweltering summer day has only about 15% more heat than a frigid winter day. The reason that we are so sensitive to a certain range of temperature lies in the nature of water.

I have noticed that, if we consider the amount of heat as absolute temperature, all of the mystery about the wind falls right into place. This includes both why the speed of the wind is what it is and why these speeds are greater on the coldest planets.

The basic reason for wind is that the surface of a planet heats unevenly because dark areas of the surface absorb more solar energy than lighter areas. The earth itself does not conduct heat well so temperature differences due to uneven heating result in wind to even out the differences by convection. As air rises over warm areas, and sinks over adjacent colder areas, a convection cell is set up.

A simple and familiar example of this are land and sea breezes along shorelines. Land absorbs heat faster than water, but also loses heat faster after the sun sets. During the day, air rises over the warmer land but sinks over the cooler water, so that the breeze is over the land from the sea and is known as a sea breeze. At night, the process reverses. The breeze flows out to sea from the land, and is known as a land breeze.

Heat alone does not generate winds, it must be a difference in heat. The analogy is similar to that of tides. It is not gravity that causes tides, but a difference in gravity of the moon and sun between the top and bottom of the ocean. Rotation of the planet would generate only east-west winds as the momentum of the rotation is imparted to the air.

It has got to be the proportional difference in heat between the two adjacent areas, in terms of absolute temperature multiplied by the planet's rotational speed, that determines wind speed. This only applies, of course, to surface non-circular winds that do not include hurricanes or tornadoes. Remember, like we saw in "The Wind Pressure Formula", wind is not complicated. We are dealing with only a few factors, and so the solution must be fairly simple.

Let's consider proportion. The difference between fifty and sixty is ten. The difference between eighty and ninety is also ten. But the proportional difference between fifty and sixty is greater than that between eighty and ninety.

It is proportion which determines the force exerted when two unequal pressures are equalized. There will be a greater equalizing force between pressures of fifty and sixty than between eighty and ninety because the proportional difference is greater. The wind on earth is then the average rotational velocity multiplied by the proportional temperature difference, using the absolute temperature scale, between two adjacent locations which is equalized by wind.

I use the term average rotational velocity because the earth rotates, as does any rotating sphere, at different rates at different latitudes. The circumference at the equator is about 25,000 miles (40,225 km), so that rotational velocity at the equator over 24 hours is 1042 mph (1676 kph). This decreases, due to the nature of a sphere, with latitude until we reach a rotational velocity of zero at the poles. The rotational velocity at any given latitude is the cosine of that latitude multiplied by the velocity at the equator.

The earth's atmosphere is an inter-connected whole, meaning that wind velocities imparted by the rotation will tend to even out in a north-south direction. There cannot be super-fast winds at the equator while there is extremely slow winds at high latitudes due to the slow rotation there. The rotation promotes east-west air movement, as the momentum of rotation is transferred to the air in the atmosphere, but there is likely to be greater temperature differences in north-south directions and this promotes perpendicular movement. The two combine as a vector to give us the resulting wind that we have.

Suppose that there is a temperature difference in two adjacent areas of five degrees Celsius, the two temperatures being 19 and 23 (66.2 and 73.4 degrees Fahrenheit). This makes a proportional difference, in absolute scale of temperature, of 296.15 / 292.15 = 1.01369 - 1 = .01369.

What is the average latitude? That is a somewhat difficult question involving the nature of a sphere. It means that there is just as much surface area in the hemisphere below that latitude as above it. I calculate the average latitude as 26.37 degrees.

The cosine of 26.37 degrees is .896. This means that the average rotational velocity of the average point on the earth's surface is .896 x 1042 mph or 1676 kph = 1162.9 mph or 1501.7 kph. (I realize that there is the possibility of mathematical debate as to whether this is indeed the average rotational velocity on earth. I think that my answer is correct. Even if you do not agree, it is close enough for our purposes here).

To find the wind that would likely result in our example here, multiply the .01369 x 1162.9 mph or 1501.7 kph. We get an answer of 15.92 mph or 20.56 kph. Sure enough, that is about the highest that everyday winds usually get to for such an adjacent temperature difference. Mild breezes originate from less of a temperature difference that ours here. Winds faster than this at the surface do occur, but are very much the exception rather than the rule, and very fast winds are almost always the remnants of a circular storm to which these rules do not apply.

This also gives us our explanation as to why the winds are so much faster on the colder planets in the Solar System, particularly Neptune. It is simply that the colder the planet, the further it is from the sun, the greater the difference in absolute temperature of adjacent areas with a given temperature difference. Remember that the difference between fifty and sixty is ten, and the difference between eighty and ninety is also ten, but the proportional difference between fifty and sixty is greater than the proportional difference between eighty and ninety. That is why the strongest winds in the Solar System is on the planet with a significant atmosphere that is furthest from the sun, and that is Neptune.