Turbulent flow over a boundary is a complex phenomenon for which
there is no complete theory. Nevertheless, much experimental data
has been collected on flows over solid surfaces, both in the laboratory
and in nature, so that from an engineering perspective, the situation
is well understood. The force exerted on a surface varies with the
roughness of that surface and approximately with the square of the
wind speed at a fixed height above it. A wind of 10 meters per second
(about 20 knots, or 22 miles per hour) measured at a height of 10
meters will produce a force of some 30 tons per square kilometer
on a field of mown grass, or of about 70 tons per square kilometer
on a ripe wheat field. On a really smooth surface, such as glass,
the force is only about 10 tons per square kilometer.
When wind blows over water, it is more complicated. The roughness
of the water is not a given characteristic of the surface but depends
on the wind itself. Not only that, the elements that constitute
the roughness, the waves, themselves are mostly in the direction
of the wind. Recent evidence indicates that a large portion of the
momentum transferred from the air into the water goes into waves
rather than directly into making water currents; only as the waves
break or otherwise lose energy does their momentum become available
to generate currents. Waves carry a substantial amount of both energy
and momentum (about as much as is carried by the wind in a layer
about one wavelength thick), and so the wave-generation process
is far from negligible.
A violently wavy surface belies its appearance by acting, as far
as the wind is concerned, as though it were very smooth. At a wind
of 10 meters per second, the force on a wavy surface is much less
than the force would be over mown grass and scarcely more than over
glass; in light winds (2 or 3 meters per second) the force on a
wavy surface is even less than it would be on glass. The waves’
motion seems to modify the airflow so that air slips over the surface
more freely than if it were smooth. This is not the case at higher
wind speeds (above about 5 meters per second), but the force remains
quite low relative to other surfaces.
Unfortunately, there are no direct observations under conditions
when high winds, greater than about 12 meters per second, have had
time and fetch (the distance over water) enough to raise substantial
waves. A few indirect studies, however, suggest that the water’s
apparent roughness may increase under high wind conditions, so that
the force on the surface increases more rapidly than the square
of the wind speed.
If the force increases at least as the square of the wind speed,
high-wind conditions will produce effects far more important than
their frequency of occurrence would suggest, as five hours of 60-knot
storm winds will put more momentum into the water than a week of
10-knot breezes. If it should be shown that, for high winds, the
force on the surface increases even more than the square of the
wind speed, then the transfer of momentum to the ocean will turn
out to be dominated by the occasional storm rather than by the long-term
average winds.
1. According to the passage, several
hours of storm winds (60 miles per hour) over water would:
(A) be similar to the force exerted by light winds for several
hours over glass
(B) create a surface roughness which reduces the force exerted by
the high wind
(C) be more significant in increasing the momentum of the water
than constant light winds over a period of a few days
(D) create a force not greater than 6 times the force of a 10-mile-per-hour
wind
(E) directly affect water current
2. The main purpose of the passage
is to discuss:
(A) oceanic momentum and current
(B) turbulent flow of wind over water
(C) wind blowing over water as related to causing tidal flow
(D) the significance of high wind conditions on ocean momentum
(E) experiments in wind force
.
3. The author’s suggestion that
the transfer of momentum to the ocean is dominated by the occasional
storm would be most weakened if which of the following were true:
(A) air momentum is converted directly into increased ocean current
(B) high speed winds slip over waves as easily as low speed winds
(C) waves do not move in the direction of wind
(D) the force exerted on a wheat field was the same as on mown grass
(E) the force of wind under normal conditions increased as the square
of wind speed
Answer Explanations:
1. According to the passage, several
hours of storm winds (60 miles per hour) over water would:
(A) be similar to the force exerted by light winds for several
hours over glass
(B) create a surface roughness which reduces the force exerted by
the high wind
(C) be more significant in increasing the momentum of the water
than constant light winds over a period of a few days
(D) create a force not greater than 6 times the force of a 10-mile-per-hour
wind
(E) directly affect water current
Type: Main Idea
(C) In the last paragraph, we are told that "several hours of
60-knot storm winds will put more momentum into the water than a week
of 10-knot breezes." In this question we are asked about
winds of 60 miles per hour. How do these winds compare? If we look
back to the first paragraph, we see that 20 knots is equal to 22 miles
per hour. Therefore, these are roughly equivalent measures of comparison,
and we can relate the information in the last paragraph to our question,
choosing C, that the high winds contribute more momentum to the ocean
than do the lighter winds over a longer period.
Choice A is not correct, since we are told in the fourth paragraph
that at 10 meters per second (equivalent to 22 miles per hour), the
surface force is slightly more that the force over glass. Since this
is a much greater wind, we would expect the force to be even greater,
so choice A is not correct. Choice B suggests that the roughness created
by the waves would actually decrease the force of the wind. According
to paragraph three, this is true, though only at lower wind speeds,
not the high speeds described in this question. Choice D compares
the relative forces of two winds. Though you might guess that a wind
that is six times faster might exert a force six times greater, we
are told in the passage that the force actually appears to increase
proportionally with the square of the wind speed. Thus, the force
is closer to thirty-six times greater for the higher wind.
2. The main purpose of the passage
is to discuss:
(A) oceanic momentum and current
(B) turbulent flow of wind over water
(C) wind blowing over water as related to causing tidal flow
(D) the significance of high wind conditions on ocean momentum
(E) experiments in wind force
Type: Definition of a word of phrase
(B) The main idea of this passage is the turbulent flow of
wind over water. The passage introduces the topic in the first paragraph,
by describing the basic physics of turbulent flow over surfaces. The
next four paragraphs then expand this concept to water, and illustrate
the complications in understanding the force of wind on the water
surface. Choices A and C are not correct, in that these concepts are
only briefly mentioned in passing. High winds, like in choice D, are
mentioned frequently, though not specifically for their effect on
the momentum of the ocean. Indeed, the whole passage is applicable
to water in general, not only the ocean. Choice E is not correct.
Although experiments in wind force are described here, it is only
to bolster the author’s argument, not as the main subject of
the passage.
3. The author’s suggestion that
the transfer of momentum to the ocean is dominated by the occasional
storm would be most weakened if which of the following were true:
(A) air momentum is converted directly into increased ocean current
(B) high speed winds slip over waves as easily as low speed winds
(C) waves do not move in the direction of wind
(D) the force exerted on a wheat field was the same as on mown grass
(E) the force of wind under normal conditions increased as the square
of wind speed
Type: Inference
(B) The suggestion that the occasional storm will make a large contribution
to momentum relies on the main argument that high winds can contribute
more to the momentum of water than light winds (see paragraphs two
and four, specifically). High winds can increase the intensity of
waves, or increase the apparent roughness of the surface, which allows
the exertion of more force. With the increased roughness, the force
increases even more than the square of the wind speed (which is the
usual estimation of the force exerted by wind on a surface). Choices
A and D are not relevant to the statement, and thus would not weaken
it if they were true. Choice C, if true, would affect the transfer
of momentum from both high and low winds to water, so this is not
a good choice. Choice E actually is true, and does not weaken the
argument.
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