Vortices: Turn, Turn, Turn
||12 / 1998
||T.R. (Joe) Sundaram
T.R. (Joe) Sundaram owns and operates an engineering research
firm in Columbia, Maryland. He has published widely in both
scientific journals and popular magazines.
Ubiquitous in natural and man-made environments, vortices are
circular motions of gases and liquids that affect our everyday
life in a variety of constructive and destructive ways.
Hurricans and typhoons are huge tropical vortices originating
over open seas that are warm enough from the equator to produce
large scale converging winds set aswirl by the earth's
rotation.Photo by courtesy of NASA-GSFC.
Even those of us who have no firsthand experience with the awesome power of tornadoes and hurricanes recognize them as the most violently destructive of all atmospheric storms. It is not so well known, however, that the swirling, circular winds of tornadoes and hurricanes are but one example of ubiquitous vortex motions in nature as well as in man-made devices and environments. A vortex in a fluid (either a liquid or a gas) is a rotation of the fluid around a common center, often with a slow radial inflow or outflow superposed on the circular flow.
Apart from tornadoes and hurricanes, other types of vortex motions, such as waterspouts, whirlwinds, and dust devils, occur routinely in the atmosphere, often in the presence of wind shear (that is, sliding motion between adjacent layers). Whirlwinds can also be produced by intense fires, such as forest fires. In water bodies, vortex motions are commonly called gyres and whirlpools.
Vortex motions undergird the effective operation of a surprising diversity of technologies, including airplane flight, ship propulsion, the slice or hook of a golf ball, the "singing" of high-tension electrical wires, and many other common events. In nature, vortices occur in a variety of shapes and sizes and can have lifetimes ranging from seconds to several days.
Let us now consider the characteristics of common types of vortex motions, as well as their impact on our everyday lives.
What, when, where, why, and how?
Vortices are whirling masses of liquid or gaseous material. In real flows, the rotation may arise from a variety of sources, although the rotations of tornadoes, hurricanes, and most similar natural phenomena derive ultimately from the earth's spinning motion. The earth's spin is converted to fluid rotation when air or water converges toward a common center. This convergence can be induced by several different mechanisms. As it converges, the fluid, which is usually rotating only slowly when it is far away from the center, begins to rotate faster and faster. The process is surprisingly similar to an ice-skater's spin that accelerates as the skater's outstretched arms are drawn closer to the body.
In other natural flows, rotation may be produced by such factors as shear or buoyancy forces. For example, whirlpools are generally produced by the shearing interaction between tidal currents, while firestorms are driven by the buoyancy of air heated by intense fires.
Tornadoes, waterspouts, and whirlwinds
The swirling winds of the most powerful tornadoes may reach speeds greater than 300 MPH and inflict devastating destruction.
Recent studies indicate that tornadoes are usually spawned in violent storms, dubbed supercells, which contain large-scale rotating systems, or mesocyclones, that may be bigger. The concentration, by a series of meteorological phenomena, of this rotation into a column whose diameter is typically about 100 feet or so is what appears to lead to a tornado.
Vortex motions in an invisible fluid medium like air are in themselves invisible; nevertheless, parts of a tornado funnel become visible due to moisture condensation in the core and dirt and debris caught up in the swirling winds. In general, the radial extent of a tornado is larger than the visible funnel.
Although tornadoes occur in widely dispersed parts of the world, the most violent ones occur in the Great Plains of the United States and the Ganges Delta of Bangladesh. In the United States, about 600 tornadoes occur each year, usually leading to 40--50 deaths and hundreds of millions of dollars in property damage. Tornadic paths of destruction are seldom wider than a few hundred yards or longer than a few tens of miles, and their lifetimes seldom exceed an hour.
Waterspouts are similar to tornadoes but occur over water. Although waterspouts may pose a danger to small fishing vessels, there are few reports of their affecting larger ships.
Whirlwinds are usually much smaller and far less violent than tornadoes. Unlike tornadoes, which develop downward from a cloud base, whirlwinds form from the ground up. The several types of whirlwinds are distinguished mainly by the entrained material that makes them visible. Thus we have sand devils, dust devils, and snow whirls. Whirlwinds occur mainly over desert areas, in the southwestern United States, the Middle East, Africa, India, China, and Australia. Small animals and insects may be carried aloft by strong whirlwinds.
As already noted, whirlwinds may be produced by intense fires. One well-known example is the powerful firestorm raised by the massive Allied bombing of Hamburg, Germany, on July 27--28, 1943. The resulting whirlwind is reported to have been more than two miles in diameter and three miles in height. Its circular wind speeds exceeded 100 MPH.
Hurricanes and typhoons
Hurricanes and typhoons are particularly intense forms of the weather pattern known as a tropical cyclone. In these large systems, the air spirals inward toward a low-pressure center, with rotation arising from earth's rotation and accelerating toward the center. Cyclones rotate counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.
Although cyclonic winds occur in many parts of the world, intense hurricanes and typhoons originate mainly in the warm waters of the Caribbean, Pacific, Australian, and Southeast Asian regions and are relatively uncommon. Typically, only about 60 hurricanes and typhoons are produced per year throughout the world, with about 10 occurring in the Caribbean and northwest Atlantic region. Nevertheless, hurricanes are extremely important because their high winds, heavy rain, and induced high tides can cause extensive damage and destruction.
From the perspective of our human time frame and commitment to fixed, permanent residences, hurricanes are a spasmodic and destructive phenomenon. Within the coupled ocean-atmosphere system, however, they are important agents for redistributing air, moisture, and heat, vertically mixing the air, and scrubbing the air of accumulated pollutants.
Whirlpools and kolks
Whirlpools occur in the oceans and other large bodies of water. They are strong rotary motions, often with a slowly spiraling inward flow toward a center. Whirlpools are usually caused by the interactions between rising and falling tides, especially in deep, narrow passages that are found in many parts of the world. They are likely the earliest of environmental vortices observed and recorded by man, since they occur at fixed locations.
The poet Homer, for example, wrote about them, and in legends whirlpools were personified as female monsters, such as the famed Charybdis, off the Calabrian coast of Italy. Other well-known whirlpools are the Maelstrom (Dutch for "whirling stream"), off the coast of Norway, and the one in the Naruto Straits, near Japan. Whirlpools often have a pronounced downward current near their centers, so that any unfortunate individuals, or even small ships, caught in them can be drawn inexorably underwater.
When a whirling motion in water is associated with a central upwelling, as sometimes happens, it is called a kolk, or boil. Kolks often occur near sharp bends in deep rivers. They play an important part in the natural deepening of rivers and the distribution of nutrients in vertical columns.
Lines, sheets, spheres, and rings
Vortices can occur in a variety of shapes and configurations, usually characterized according to the curvature of the axis of rotation. For example, tornadoes, whirlpools, and the like are line vortices, since the fluid rotation occurs around a line that is either straight or nearly so.
When a series of elemental line vortices, all with the same sense of rotation, occur adjacent to one another, a vortex sheet is produced. Such vortex sheets occur when two streams flowing in the same direction but with different velocities meet, as happens along the trailing edge of an aircraft wing. Such vortex sheets are extremely important for purposes of analysis, even though in real life they are often unstable and may "roll up" into one or more discrete vortices. The familiar mushroom cloud produced by a nuclear explosion is an example of a particularly complicated type of vortex motion, the spherical vortex.
"Smoke rings" blown by smokers are an example of a ring vortex, in which the axis of rotation forms a ring. Some volcanoes blow such smoke rings, and the smokestacks of old-fashioned steam locomotives did so as well. Ring vortices are often produced, for study, in the laboratory by forcing fluid through a sharp-edged circular nozzle into an initially quiescent fluid.
Flying wings and spinning balls
In addition to the gross effects of large-scale vortices such as hurricanes and tornadoes, smaller vortices, occurring with many times greater frequency than the large-scale vortices, exert profound influence on our human world.
Often, these influences arise through the combination of rotary motion with another motion, such as linear. Such dynamics affect the flight of airplanes, baseballs, tennis balls, and golf balls.
The effects are usually explained in relation to a long, rotating cylinder placed in and perpendicular to a uniform fluid flow. As the fluid divides to flow past the rotating cylinder, one side of the stream meets a cylinder wall moving in the opposite direction to the flow, while the other side meets a cylinder wall moving in the same direction as the flow.
On the side where the two movements are opposing, pressure is increased, while on the side where the two movements are additive, pressure is decreased. In this phenomenon, called the Magnus effect, the resulting differences in pressure lead to a sideward force on the cylinder.
The lift on an airplane wing is considered to be a Magnus effect, since a wing generates lift by the circulation it induces around itself due to its specially chosen shape. Similarly, the Magnus effect is present when a rotating sphere is moving through a fluid such as air. Thus the Magnus effect is responsible for the hooks and slices of golf balls, the lobs and slices used by better tennis players, and the curve and breaking balls thrown by baseball pitchers.
Singing wires and galloping bridges
In contrast to the steady forces of the Magnus effect, oscillatory forces can be produced if a nonrotating cylinder is placed in a stream flowing perpendicular to the cylinder's axis. Under these conditions and within a certain velocity range, vortices are shed periodically and alternately from the two sides of the cylinder, producing sideward forces of alternating directions on the cylinder. This characteristic vortex pattern is known as the Karman vortex street, after the great Hungarian-born American aerodynamicist, Theodor von Karman. It is important to note that the unsteady sideward forces are produced even when the oncoming stream is perfectly steady, since the forces are caused by the basic instabilities in boundary layer separation from the walls of the cylinder.
Dramatic examples of the Karman vortex street can be seen in rivers downstream of the cylindrical columns supporting bridges. Vortex streets are also produced by airflow past such diverse objects as tall smokestacks; power plant cooling towers; missiles launched vertically into a steady, horizontal wind; high-tension electrical transmission lines; and aboveground gas and oil pipelines. The "singing," or eolian tones, of power lines is indeed due to the plucking effect of the oscillatory sideward forces generated by the vortex shedding.
The frequency of vortex shedding will depend on the velocity of the oncoming flow, the diameter of the cylinder, and the viscosity of the fluid.
Although the shedding vortices may not seem too significant, they can be profoundly destructive if the oscillatory frequency of vortex shedding coincides with the natural vibrational frequency of a cylindrical structure. In such cases, resonant buildup of the oscillatory forces can occur, eventually leading to structural failure.
Perhaps the most notable example of the destructive power of resonant vortex shedding was provided by the Tacoma Narrows Bridge, the first suspension bridge across Puget Sound. It collapsed spectacularly because design engineers failed to take resonant vortex shedding into account. On the morning of November 7, 1940, four months after its opening, the main span of the bridge went into uncontrollable torsional oscillations in a steady wind of about 42 MPH and then completely broke up. Since the bridge had already been closed to traffic, there were no fatalities.
Several early tall smokestacks and cooling towers suffered similar failures due to oscillatory loads produced by vortex shedding. The effect can be overcome by proper aerodynamic design and by separating the shedding frequency and the natural vibrational frequency as much as possible, so as to avoid resonant conditions.
Vortex shedding is still an area of active research, and several techniques for its suppression, as well as for enhancement (for constructive use) are being developed.
One, two, three ...
Scientists have discovered that vortices can occur not only singly but in pairs and groups of even larger numbers. Such groups are quite important, since they can have the unexpected property of self-convection (that is, because of their interaction, they move). The phenomenon is most easily understood by considering first a pair of entrained vortices. Interacting through the fluid medium even when separated at distances many times as great as the combined diameters of the two vortices, each vortex induces a linear movement in the other that is perpendicular to the line joining them. If the two are rotating in opposite directions, the induced velocities are in the same direction and the pair can move as a unit with a constant separation distance. During its forward motion, the pair will "capture" a surrounding volume and transport this volume with it, giving rise to a moving, closed cell of fluid. Such vortex pairs and their "captured volumes" can be quite long lived.
Vortex pairs are produced behind any lifting surface, such as a bird's wings or an airplane wing, and have great practical importance in aviation. When jumbo jets were introduced, smaller aircraft that attempted to land behind them frequently experienced uncontrollable overturning forces, often severe enough to cause them to crash. It was subsequently determined that the overturning forces were caused by the vortex pair from the wings of the jumbo jets, which tends to persist on the runway, even several minutes after the jet has landed and departed for the gate. In response, authorities have imposed stringent regulations on the minimum elapsed time between the landing of large aircraft and the landing of smaller aircraft behind them.
The "contrails" (short for condensation trails) of high-flying jet aircraft, which are so readily visible on a clear day, are also direct manifestations of vortex pairs behind the aircraft. These vortex pairs become visible because they trap the hot exhaust gases of the jet engines, confining the gases as the moisture in them condenses in the cold ambient environment, making the pair visible. It has recently been found that because the exhaust gases contain sulfur and other contaminants that can act as nucleation sites, contrails tend to grow with time. Several can eventually coalesce, thus contributing to increases in cloud cover.
`These alternate-side vortices known as Karman vortex street
are highlighted here by smoke released into the flow of a gas
past a cylindrical object. Photo by courtesy of P.Bradshaw and
P.W Bearman\Imperial college London.
Eddies of varying sizes and time scales are always present in any turbulent flow. In general, in natural flows the eddies are produced by some mechanism at a large scale, and then their kinetic energy cascades down into smaller and smaller scales, as the large eddies break up into smaller and smaller ones.
Vortex, vortex, everywhere
While natural visible vortices such as tornadoes have received the most public attention, most natural vortices are invisible and thus are not appreciated. Nevertheless, the overall impact of the myriad of invisible vortices can be more far-reaching than that of the visible ones. As noted, vortices are present in all natural fluid flows, including those in the atmosphere and the oceans. While many of the naturally occurring vortices are short-lived, more long-lived and structured vortices also occur in numerous situations.
For example, when air flows past a rectangular building, the flow tends to separate ahead of the structure, a closed region containing a stationary eddy forms there, and the air will simply continue to recirculate within this region. Such regions can have a significant effect on the environment around a building, as they can entrap atmospheric pollutants, leading to localized high concentrations.
Designers of transportation vehicles ranging from automobiles to airplanes and ships take vortices into account when they streamline a vehicle to minimize drag, which results from the inevitable formation of vortices as the vehicle moves through a fluid.
The fact that very low pressures can be created at the center of vortices leads to a variety of effects. Many of these are related to gas cavities that form as the low pressures at the center release gases dissolved in the liquid. If the interaction of liquid flows and a solid surface produces line vortices near and roughly perpendicular to the surface, the gas cavities may collapse near the surface, giving rise to pitting erosion known as cavitation. Under certain conditions, severe cavitation erosion can occur in and around rotating machinery, such as a ship's propeller or a centrifugal pump.
On the positive side, vortices and vortex phenomena have many beneficial effects and applications. For example, the fact that low pressures are created at the center of a vortex is used in constructive ways in equipment that separates fine solids suspended in liquids or gases. Air scrubbers, for example, separate dust particles from air by applying this principle. Vortices have been investigated for and are being used in novel applications ranging from magnetohydrodynamic power generation to fluidic control devices.
It is also probable that vortices occur throughout the universe. Visible even to a small telescope, for example, is Jupiter's giant red spot, which is thought to be a long-lived vortex in Jupiter's atmosphere.
Vortex motions are ubiquitous in fluid flows. Some, such as hurricanes and tornadoes, are readily visible to us, whereas vortex pairs produced by wings are usually invisible. Recognizing the importance of vortices and that there is surely a lot we still don't understand about how to harness them for good or minimize their damage, some institutions have set up vortex technology centers. For example, the Vortex Technology Center at the University of Houston works to understand the details of vortex motions and to build and test prototypes of novel devices that use vortex dynamics for their operation. With such attention now being paid to vortices, we can fully expect that they will exert an even greater impact on society in the coming decades.