Chapter 7. Convection and Complexity

Chapter 7 Convection and complexity ... if your theory is found to be convection has been taken as the classic exam against the second law of ple of thermal convection, and the hexagonal planform has been considered to be typical of thermodynamics, I can give you no convective patterns at the onset of thermal con hope; there is nothing for it but to vection. Fifty years went by before it was real collapse in deepest humiliation. ized that Benard's patterns were actually driven from above, by surface tension. not from below by Eddington an unstable thermal boundary layer. Experiments Contrary to current textbooks ... the showed the san1.e style of convection when the fluid was heated from above, cooled from below observed world does not proceed or when performed in the absence of gravity. This from lower to higher "degrees of confirmed the top-down surface-driven nature of disorder", since when all the convection which is now called Marangoni or B€mard-Marangoni convection. gravitationally-induced phenomena Although it is not generally recognized as are taken into account the emerging such, mantle convection is a branch of the newly result indicates a net decrease in the renamed science of complexity. Plate tectonics may be a self-drivenfarjrom-equilibrium system that orga "degrees of disorder", a greater nizes itself by dissipation in and between the "degree of structuring" ... classical plates, the mantle being a passive provider of equilibrium thermodynamics ... has energy and material. Far-from-equilibrium sys to be completed by a theory of tems, particularly those in a gravity field, can locally evolve toward a high degree of order. Plate 'creation of gravitationally-induced tectonics was once regarded as passive motion of structures' ... plates on top of mantle convection cells but it now appears that continents and plate tecton Gal-or ics organize the flow in the mantle. But man tle convection and plate tectonics involve more Overview than geometry and space-filling considerations. The mantle is a heat engine, controlled by the In 1900 Henri Benard heated whale oil in a laws of thermodynamics. One can go just so pan and noted a system of hexagonal convec far without physics. Conservation of mass and tion cells. Lord Rayleigh in 1916 analyzed energy are involved, as are balancing of forces. this in terms of the instability of a fluid heated Although the mantle behaves as a fluid, mineral from below. Since that time Rayleigh-Bemard physics principles and classical solid-state physics 74 CONVECTION AND C O MPLE XITY are needed to understand this fluid. The effect mant l e as convenient shorthand for wh at they of pressure suppresses the role of the lower ther consider to be the h omo g e n ou s upper mant l e. mal boundary layer at the core-mantle-boundary The u nderlying assumption is that midocean (CMB) interface. ridge basalts, known for their chemical homo The slow uplift of the surface of the Earth geneity, must come from a well-stirred mantle in response to the removal of an ice cap or reservoir. drainage of a large lake changes the shape of the Earth and the geoid; this is not only proof of the fluid-like behavior of the mantle but also pro Generalities vides the data for estimating its viscosity. In con trast to everyday experience mantle convection SOFFE systems are ext raordinarily sen has some unusual characteristics. The container s i tive to boundary and initial conditions. has spherical geometry. The 'fluid' has stress-, The corollary is that small differences between pressure- and temperature-dependent properties. computer or laboratory simulations, or between It is cooled from above and from within (slabs) th em and the mantle, can completely change and heated from within (radioactivity) and the outcome. The effect of pressure suppresses from below (cooling of the core and crystalliza the role of the lower thermal boundary layer tion of the inner core). The boundary conditions (TBL) at the core-mantle-boundary (CMB) inter and heat sources change with time. Melting and face. The state of stress in the lithosphere defines phase changes contribute to the buoyancy and the plates, plate boundaries and locations of mid provide additional heat sources and sinks. Mantle plate volcanism. Fluctuations in stress, due to convection is driven partly by plate motions and changing boundary conditions, are responsible partly by chemical buoyancy. The boundaries are for global plate reorganizations and evolution deformable rather than rigid. None of these char of volcanic chains. In Rayleigh -BEmard con acteristics are fully treated in numerical calcu vecti on, by contrast, temperature fluctuations lations, and we are therefore woefully ignorant are the important parameters. In plume theory, of the style of convection to be expected in the plates break where heated or uplifted by hot mantle. The cooling plates may well organize and buoyant upwellings. Ironically, the fluid flows in drive mantle convection, as well as themselves. A the experi men ts by Benard, which motivated mantle with continents on top will convect dif the Rayleigh theory of t h ermal convec ferently from one with no continents. tion, were driven by surface tension, i.e. stresses The theory of convection in the mantle can at the surface. not be decoupled from the theories of solids Computer simulations of mantle convection and petrology. The non-Newtonian rheology, the have not yet included a self-consistent thermo pressure and temperature sensitivity of viscosity, dynamic treatment of the effect of temperature, thermal expansion, and thermal conductivity, pressure, melting and volume on the physical and the effects of phase changes and compress and thermal properties; understanding of the ibility make it dangerous to rely too much on 'exterior' problem (the surface boundary con the intuition provided by oversimplified fluid dition) is in its infancy. Plate tectonics itself dynamic calculations or labora tory experiments. is implicated in the surface boundary condi There are, however, some general characteris tion. Sphericity, pressure and the distribution of tics of convection that transcend these details. radioactivity break the symmetry of the prob Technical details of normal or classical thermal lem and the top and bottom boundary condi convection can be found in textb ooks on man tions play quite different roles than in the simple t l e convection. Plate tectonics and mantle calculations and cartoons of mantle dynam motions, however, are far from normal thermal ics and geochemical reservoirs. Conventional convection. (Rayleigh- Benard) convection theory may have lit Geochemists consider convection and stir tle to do with plate tectonics. The research oppor ring to be equivalent. They use convecting tunities are enormous. GENERALITIES 75 The history of ideas Aegean plate is an example of a ' rigid' plate col Convection can be driven by bottom heating, lapsing, or falling apart, because of changes in top or side cooling, and by motions of the stress conditions. boundaries. Although the role of the surface The mantle is generally considered to convect boundary layer and slab-pull are now well under as a single layer (whole mantle convection), or at stood and the latter is generally accepted as most two. However, the mantle is more likely to the prime mover in plate tectonics, there is a convect in multiple layers as a result of gravita widespread perception that active hot upwellings tional sorting during accretion, and the density from deep in the interior of the planet, inde difference between the mantle products of differ pendent of plate tectonics, are responsible for entiation. 'extraordinary' events such as plate reorganiza tion, continental break-up, extensive magmatism. Instabilities and events far away from current plate bound Rayleigh-Taylor (RT) instabilities form when a aries. Active upwellings from deep in the mantle dense, heavy fluid occurs above a low-density are viewed as controlling some aspects of surface fluid, such as a layer of dense oil placed, care tectonics and volcanism, including reorganiza fully, on top of a layer of water. Two plane tion, implying that the mantle is not passive. This parallel layers of immiscible fluid are stable, is called the plume mode of mantle convec but the slightest perturbation leads to release of tion. This has been modeled by the injection of potential energy, as the heavier material moves hot fluids into the base of a tank of motionless down under the (effective) gravitational field, and fluid. the lighter material is displaced upwards. As Numerical experiments show that mantle the instability develops, downward-moving dim convection is controlled from the top by con ples are quickly magnified into sets of inter tinents, cooling lithosphere, slabs and plate penetrating RT fingers or plumes. This process motions and that plates not only drive and is evident not only in many examples, from boil break themselves but can control and reverse ing water to weather inversions. In mantle geo convection in the mantle. Studies of the physics, plumes are often modeled by inserting a time dependence in 3D spherical mantle light fluid into a tank of a static higher density convection with continental drift show fluid. This is meant to mimic the instability of a the extreme sensitivity to changes of conditions hot basal layer. In the later situation, the insta and give results quite different from simpler sim bility develops naturally and the density con ulations. Supercontinents and other large plates trast is limited. In the injection experiment, the generate spatial and temporal temperature vari density contrast is imposed by the experimenter, ations. The migration of continents, ridges and as is the scale of the upwelling. There is a dif trenches cause a constantly changing surface ference between upwellings of intrinsically hot boundary condition, and the underlying man basal layers and intrinsically light chemical lay tle responds passively.

Load more