Problem of the Tornado: Mechanical Quandries

The mechanical mystery of the tornado involves two questions:

• What is the source of rotation of a tornado?
• How does this rotation become so concentrated?

It's often stated (even by scientists) that the rotation of the earth, through the coriolis acceleration, is what gives a tornado its spin. However, if this were true, then there should never be a tornado in the northern hemisphere that turns in an anticyclonic sense. Yet such tornadoes do occur and they are not rare. For instance, in 1980 seven tornadoes struck Grand Island, Nebraska in a single day. Three of these turned in an anticyclonic sense.

Before pursuing these two mechanical questions, let's do two other things. First, define a bunch of mechanical terms to help the novice reader of this material.

Glossary

• Boundary ConditionsThe conditions that a boundary, such as the ground surface, imposes upon a flow of air. For example, because air cannot flow into the ground surface, the surface imposes a condition of zero flow perpedicular to it.
• Boundary LayerThe layer of air near the surface or near some other type of boundary in which friction plays a substantial role. Generally air outside the boundary layer behaves according to a simplified set of equations of motion.
• CirculationThe importance of circulation lies in it remaining a constant for fluid motion in the absense of forces such as buoyancy and friction. This means to flow around a closed path in space. Mathematically it is the product of the area of a surface bounded by a closed path, and the average value of vorticity perpendicular to that surface. (i.e. a surface integral) If there is no net vorticity on a surface, then there is no circulation around the perimeter of that surface.
• Centrifugal ForceAn apparent force that arises from forcing any mass to flow along a curved path. The direction of this force is directed away from the center of curvature of the path.
• ConvergenceAn air flow that tends toward a common center. Air cannot vanish, of course, so a convergence takes place only in two dimensions. Air must turn and flow in the remaining (third) dimension in order to maintain the convergence.
• Coriolis ForceAn "apparent" force that arises in response to motions on a rotating reference frame such as the earth.
• CyclostrophicA system of winds that flow in response to the balance of pressure gradient, Coriolis Force, and Centrifugal Force. It applies mainly to winds that rotate in paths of relatively large curvature because the centrifugal force becomes important only on highly curved paths. Hurricanes and tornados are definitely cyclostrophic winds.
• DivergenceAn air flow that tends away from a common center. Air cannot appear from nowhere, of course, so a divergence takes place only in two dimensions. Air must flow out of the remaining (third) dimension in order to maintain the divergence.
• DissipationThe gradual destruction of a circulation by interaction with the ground surface or other fluid through viscosity. Loss of energy.
• GeostrophicA system of winds that flow in response to the balance of pressure gradient, Coriolis Force, and Centrifugal Force. It applies mainly to very large-scale flow systems such as synoptic cyclones.
• InstabilityGenerally we mean by instability that the layering of air is buoyant. That it has reached a state in which air near the ground would prefer to rise, and air above it would prefer to sink to the surface (i.e. the air would prefer to overturn). However, we may also refer to a flow of air as being unstable if it changes its flow character drastically when disturbed. An example is the tendency of a truly vigourous tornado to form into a family of vortexes that revolve around a common center.
• Pressure GradientThe direction in which pressure increases most rapidly, and which acts as a force to accelerate the air. The change in pressure divided by the distance over which it takes place is the numerical value of the pressure gradient.
• RotationThis is an ambiguous term that means, more or less, that a large mass of fluid has vorticity or that it circulates around some central point.
• ViscosityA measure of the "thickness" of a fluid. Thin fluids have low viscosity. In the context of this web page viscosity mainly refers to the ability of a fluid to transmit motion (momentum actually) from one place to another through internal friction. When eddies transfer momentum within a fluid we generally refer to an "eddy viscosity" that is often much more effective than the ordinary molecular viscosity.
• VorticityRotation of a fluid at a point. Mathematically, in terms of vector calculus, vorticity is half the curl of the wind field. However, it is more useful to think of testing for vorticity by placing a small paddlewheel into the fluid. If the paddlewheel turns, then there is vorticity. There is vorticity in a fluid in many instances where we don't observe rotation per se. For example, there is always vorticity in connection with shear flow near a boundary. The connection between circulation and vorticity assures us that there is no circulation along a path that does not enclose fluid possessing vorticity.

Second, let me examine one further mechanical quandry regarding the tornado on the next web page.

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