Q. 83: Is not the theory of rising convection currents in the earth’s mantle fraught with problems?

CPT Q. #83 – 101 Q&A on Catastrophic Plate Tectonics

Question: 83. Can you comment on the widely accepted idea that the mantle is convecting? Is not the theory of rising convection currents in the earth’s mantle fraught with problems that are not being addressed by the secular geologists?

Response: The basic question is, if the mantle is essentially all solid crystalline rock, can it convect like soup boiling in a pan on the stove? The simple answer is, yes. However, some insight concerning how solid mantle rock deforms and flows is helpful in understanding the answer. Experimentally it can be shown that silicate minerals and rocks undergo permanent, or plastic, deformation, especially at higher temperatures, as stress is applied. This permanent deformation occurs as the result of migrations of defects within crystals and motions at mineral grain boundaries. The process is often referred to as solid-state creep. Therefore, when subjected to stresses such as those arising from gravity acting on density variations, mantle rock, though solid, nevertheless deforms in a plastic manner. Although the deformations are extremely slow, the mantle, even though solid, can be treated and understood as an extremely viscous fluid. Here, the more general term fluid (as opposed to liquid) is used because crystalline solids (as well as liquids) do deform and flow.

In regard to convection, the simple case known as Rayleigh-Bénard convection occurs when a thin fluid layer in a gravity field is heated from below and cooled from above. This case was first studied experimentally by Henri Bénard, a French physicist, in 1900. In this type of system, gravity acts to pull the cooler denser fluid from the top of the layer toward the bottom and to draw the warmer less dense fluid at the bottom of the layer toward the top. This gravitational force is opposed by the viscous force involved in deforming the fluid. The balance between these two forces is expressed by a non-dimensional parameter called the Rayleigh number which is defined as Ra = g\,\alpha\,\rho\,\Delta T\,d^3/(\nu\kappa), where g is the gravitational acceleration, α is the volume coefficient of thermal expansion, ΔT is the temperature difference between the top and bottom of the layer, d is layer thickness, ν is the kinematic viscosity, and κ is the thermal diffusivity.

Convective motion can occur in this type of system when what is called the Rayleigh number exceeds a critical value known as the critical Rayleigh number. In 1916 Lord Rayleigh was successful in deriving this value analytically for the case of a plane layer with free-slip boundaries. The value he obtained was 27\pi^4/4 = 657.5. The critical Rayleigh number can also be determined for the case of a spherical shell. For a shell geometry corresponding to that of the earth’s mantle, assuming constant properties throughout the volume and heating from below, the critical Rayleigh number is about 700.

We can use estimates for the average physical properties of the earth’s mantle to estimate its actual Rayleigh number. Using 10 m/s2 for gravitational acceleration, 3 x10-5/°C for the volume coefficient of thermal expansion, 2000°C for the adiabatic temperature difference across the mantle, 3000 km as the mantle thickness, 2 x 1018 m2/s for the kinematic viscosity, and 10-6 m2/s for the thermal diffusivity, we get Ra = 8 x106, a value more than 10,000 times the critical value! This implies that the earth’s mantle is well within the convective regime, and, as far as convective systems are concerned, is convecting vigorously. This value for mantle viscosity is based on present-day GPS observations of the rate at which deformations of the mantle are occurring, a value about 25 orders of magnitude greater than that of water. In spite of this gigantic value for its viscosity, it is the huge thickness d of the mantle that allows the Rayleigh number to be so large and for convection within the mantle to be so vigorous.

To recap, very simple physical considerations show that the earth’s solid mantle must be within the regime of convective flow. Its huge Rayleigh number, which depends on the mantle depth to the third power, requires it. On the other hand, because mantle viscosity is so high, the rates of mantle deformation, or flow, are close to being undetectable to a human observer. They are on the order of a millimeter per week in a few locations on the earth’s surface such as across the San Andreas Fault midway between Los Angeles and San Francisco. On the other hand, GPS techniques are now sufficiently sensitive to measure the surface expressions of these motions to a high degree of precision. So flow in the mantle, though slow, is close to indisputable. However, in the framework of Biblical history, the observed rates of convective flow are so tiny that they are insignificant on time scales of only a few thousand years, apart from the earthquakes and tsunamis which these motions produce.

A final comment relating to question 82 is that because the earth’s mantle is solid practically everywhere, the so-called ‘crossover depth’, applicable only to molten liquid rock, is not relevant to the question of whether solid-state convection, which involves plastic deformation of the solid rock, is taking place.