Answers to Questions from the Interface Dynamo Homepage

Answer to Question #1

The water accumulated behind a dam is a reservoir not only of water, but also of gravitational potential energy. This potential energy must be first converted into bulk fluid kinetic energy, in order to propel the turbines that drive the plant's generators. The conversion process is simply free fall in the Earth's gravitational field (g): a rock of mass m held at a heigth h above ground has a potential energy content E=mgh, which upon dropping the rock is converted into a (equal) quantity of kinetic energy E=(1/2)mv2 (neglecting frictional losses due to air drag). If the generator plant were to be located on top of the dam, then there would be little or no kinetic energy available to drive the turbines, as the water is effectively at rest, with a high gravitational potential energy content but little kinetic energy. At equal sizes for a water reservoir size, the higher the dam the better !

Answer to Question #2

Think how the water got into the dam's reservoir in the first place; runoff from mountains, hills and valleys located upstream, chanelled into the reservoir via streams and rivers; that water, in turn, got to those hills and mountains in the form of snowfall and rainfall from clouds, themselves formed primarily by the evaporation from large bodies of water. Evaporation occurs through the action, direct or indirect, of solar heating. So here it is: solar thermal energy is converted to gravitational potential energy my moving water upwards in the Earth's gravitational field. Part of this potential energy is loss upon rainfall/snowfall and downflow, but some remains in the waters accumulating behind the dam. This is converted to bulk kinetic energy upon letting the water flow down pipes to the bottom of the dam, then into mechanical (rotational kinetic) energy by forcing the spinning of turbines. Those turbines are connected to dynamo generators, which finally transform the kinetic energy in the form of electric currents, which make their way into your home. And voila, coffee ready, courtesy of the Sun.

Answer to Question #3

Measuring the time interval between successive maxima and minima in the number of sunspots (tracers of the solar magnetic field) yields time intervals between about 9 and 12 years. Sunspots do not care about the polarity (negative or positive) of the deep toroidal magnetic field from which they originate, although their formation is quite sensitive to the absolute magnitude of that field; they are frequent when the underlying magnetic field is strong, and scarce when the field is weak. The eleven years period of the sunspot cycle is then half of the full magnetic cycle, i.e., the time required to return to a magnetic configuration of identical amplitude and polarity.

Answer to Question #4

The toroidal magnetic field (color coded on the animation) is strongest (red and blue) below the core-envelope interface, which runs horizontally through the middle of the cartesian closeup (on the right in the animations). This turns out to be a very important property of interface dynamos in general. Sunspots are believed to be formed following the rise through the convection zone, and emergence through the solar surface, of intense toroidal magnetic flux ropes. Those flux ropes are most likely formed (and stored) in a thin layer located immediately below the base of the solar convective zone, so that sunspots become tracers of this deep toroidal magnetic field.

Answer to Question #5

The sunspot butterfly diagram. Note how for that mode the toroidal field is concentrated at relatively low heliospheric latitudes on either side of the equator, and how the field migrates towards the equator in the course of a cycle, just as sunspots do.

Answer to Question #6

The phasing of the poloidal field with respect to the toroidal field is markedly different for the three dynamo modes. For the hybrid mode the two fields are out of phase by a quarter of a cycle (or pi/2, meaning that the toroidal field is maximum and positive when the poloidal reverses sign from negative to positive). For the polar interface mode the poloidal fields are out of phase by half a cycle (pi), as both fields reaches maximum at about the same time, but have opposite polarities. In the case of the equatorial interface mode, the poloidal field goes from positive to negative approximately as the toroidal field reaches its maximum (positive) strength. Observationally, the phasing between the Sun's poloidal and toroidal field is not trivial to determine. Sunspots are most likely a good tracer of the Sun's toroidal field, but the poloidal field is much harder to measure because it is much weaker, so that at low latitudes it becomes masked by the magnetic field associated with decaying sunspots and active regions. This does not occur at high latitudes, but there the predominantly radial field only has a very small component along the line of sight, making it extremely difficult or even impossible to measure. One possibility consists in using polar faculae as tracers of the poloidal field. If this approach is adopted then it is found that the poloidal field lags the toroidal field by pi/2. This is similar to the approximate pi/2 phase lag to be inferred from the butterfly diagram for the equatorial interface mode.

Last revised June 28, 1996 - P. Charbonneau