J. Marvin Herndon's Physical Impossibility of Earth-Core Convection
The process called convection is easily observed in ordinary experience, but has been greatly misunderstood in the geosciences for decades, being widely assumed to take place in the Earth's fluid core. But convection in the Earth's core, as discovered by J. Marvin Herndon, pictured at left, is physically impossible.
Heat a pot of water on the stovetop. Before it starts to boil, the water begins to circulate from bottom to top and from top to bottom. This is called convection and it can be better observed by adding a few tea leaves, coffee grounds, celery seeds, or the like, which are carried along by the circulation of water. Convection occurs because heat at the bottom causes the water to expand a bit, becoming lighter, less dense, than the cooler water at the top. The warmer, less dense, water rises to the top as the cooler, denser, water descends. This all seems so simple that it is no wonder that the convection process has been widely (but falsely) assumed to occur deep within the Earth’s core.
About 95% of the mass of the Earth consists of just two parts; the fluid, iron-alloy core and the solid, silicate-rock mantle, as illustrated at right. In 1939, Walter Elsasser postulated Earth-core convection to make tenable his idea that the Earth’s magnetic field is generated by convection-driven dynamo action within the Earth’s fluid core . At the time, and until recently, there was no reason to suppose that any fluid, electrically conducting region, except the main core, exists within the Earth [2, 3]. Note that Earth-core convection was not independently observed, but rather, was assumed to exist so as to satisfy the underlying conditions for a different theory.
Subrahmanyan Chandrasekhar , pictured at left, described convection in the following way: “The simplest example of thermally induced convection arises when a horizontal layer of fluid is heated from below and an adverse temperature gradient [i.e., the top is cooler than the bottom] is maintained. The adjective ‘adverse’ is used to qualify the prevailing temperature gradient, since, on account of thermal expansion, the fluid at the bottom becomes lighter than the fluid at the top; and this is a top-heavy arrangement which is potentially unstable. Under these circumstances the fluid will try to redistribute itself to redress this weakness in its arrangement. This is how thermal convection originates: It represents the efforts of the fluid to restore to itself some degree of stability.”
In 1900, Bénard observed the formation of a pattern of cells [convection cells] developing in a thin layer of water heated from beneath . In 1916, Lord Rayleigh  derived a dimensionless number – now called the Rayleigh Number – to quantify the onset of instability, which would lead to convection in a thin, horizontal layer of fluid heated from beneath. For decades, calculation of a high Rayleigh Number has been taken to justify the existence of Earth-core convection. The advice for students, generally speaking, as stated in Herndon's book, Maverick’s Earth and Universe  is to “Look deeper and look questioningly.” And, certainly, that is the case here.
What seems to have been overlooked is that the Rayleigh Number was derived from assumptions that are inconsistent with the physical parameters of the Earth’s core. Rayleigh assumed an “incompressible” fluid, i.e., a fluid of “constant” density throughout, except as modified by thermal expansion at the base, and pressure being “unimportant” (quotes from Lord Rayleigh ). The Earth’s core is not “incompressible”, but consists of a compressible fluid which is, in fact, compressed by the weight of the mantle and crust above and by its own weight. The Earth’s core is not of “constant” density; its base is about 23% more dense than its top due to the pressure of the weight above , illustrated in the figure at right. Thus, the dimensionless Rayleigh Number is an inappropriate indicator of convection in the Earth’s core.
It is instructive to consider and to discuss some of the reasons why convection, as commonly observed on the stovetop and as described above by Nobel Laureate Chandrasekhar, is impossible within the Earth’s core. On the stovetop, convection occurs because heat at the bottom causes the water to expand a bit [much less than 1%], becoming lighter, less dense, than the cooler water at the top. This is a potentially unstable, top-heavy arrangement which the fluid attempts to redress by convection. So, in what ways is that different from the Earth’s core and how do those differences impact the convection process?
The Earth’s core differs from the stovetop example in two important ways. First, as shown in the figure at right, because of the over-burden weight, the Earth’s core is about 23% more dense at the bottom than at the top , as illustrated at right. The tiny, tiny amount of thermal expansion at the bottom cannot make the Earth’s core top-heavy and cannot cause a thermally-expanded “parcel” from the bottom to float to the top of the core as required for convection. Thus, the Earth’s core cannot engage in convection. Second, because the Earth’s core is wrapped in a thermally insulating blanket, the silicate-rock mantle, heat cannot be efficiently removed from the top of the core. So, maintaining an “adverse temperature gradient” [i.e., the top of the core being cooler than the bottom] for extended periods of time, a condition necessary for convection, is impossible .
What is the main implication of no Earth-core convection? From the standpoint of geomagnetic field generation, the implication is quite clear: Either the geomagnetic field is generated by a process other than the convection-driven dynamo-mechanism, or there exists another fluid region within the deep-interior of Earth which can sustain convection for extended periods of time. Herndon has provided the reasonable basis to expect long-term, stable convection in the georeactor sub-shell, and have proposed that the geomagnetic field is generated therein by the convection-driven dynamo mechanism [3, 9-11]. The figure at left is a schematic representation of the interior of the Earth showing Herndon’s georeactor. Heat produced by the georeactor nuclear sub-core is expected to cause convection in the georeactor sub-shell. Heat brought to the top of the sub-shell is expected to be transported away by the thermally-conducting inner core heat sink which is surrounded by an even more massive thermally-conducting fluid core heat sink.
YouTube Demonstration: Origin of Earth's Magnetic Field (click here)
Elsasser, W.M., On the origin of the Earth's magnetic field. Physical Review, 1939. 55, 489-498.
|2.||Herndon, J. M., Sub-structure of the inner core of the Earth. Proceedings of the National Academy of Sciences USA, 1996, 93, 646-648. (click here for pdf)|
|3.||Herndon, J. M., Nuclear georeactor generation of the Earth's geomagnetic field. Current Science, 2007, 93, 1485-1487. (click here for pdf)|
|4.||Chandrasekhar, S., Thermal Convection. Proceedings of the American Academy of Arts and Science, 1957. 86(4), 323-339.|
|5.||Bénard, H., Les Tourbillions cellulaires dans une nappe liquide. Renue generale des Sciences pures et appliquees, 1900, 11, 1261-1271 and 1309-1328.|
|6.||Lord_Rayleigh, On convection currents in a horizontal layer of fluid where the higher temperature is on the under side. Philosophical Magazine, 1916. 32, 529-546.|
Herndon, J. M., Maverick's Earth and Universe. 2008, Vancouver: Trafford Publishing. ISBN 978-1-4251-4132-5.
|8.||Dziewonski, A.M. and Anderson, D. A., Preliminary reference Earth model. Physics of the Earth and Planetary Interiors, 1981. 25, 297-356.|
|9.||Herndon, J. M., Nature of planetary matter and magnetic field generation in the Solar System. Current Science, 2009, 96, 1033-1039. (click here for pdf)|
|10.||Herndon, J. M., Uniqueness of Herndon's georeactor: Energy source and production mechanism for Earth's magnetic field. 2009, arXiv:0901.4509 (click here for pdf)|
|11.||Herndon, J. M., Geodynamic basis of heat transport in the Earth. Current Science, 2011, 101, 1440-1450. (click here for pdf)|