How was the Earth-Moon system formed? New insights from the geodynamo.

The most widely accepted scenario for the formation of the Earth-Moon system involves a dramatic impact between the proto-Earth and some other cosmic body. Many features of the present-day Earth-Moon system provide constraints on the nature of this impact. Any model of the history of the Earth must account for the physical, geochemical, petrological, and dynamical evidence. These constraints notwithstanding, there are several radically different impact models that could in principle account for all the evidence. Thus, in the absence of further constraints, we may never know for sure how the Earth-Moon system was formed. Here, we put forward the idea that additional constraints are indeed provided by the fact that the Earth is strongly magnetized. It is universally accepted that the Earth's magnetic field is maintained by a dynamo operating in the outer liquid core. However, because of the rapid rotation of the Earth, this dynamo has the peculiar property that it can maintain a strong field but cannot amplify a weak one. Therefore, the Earth must have been magnetized at a very early epoch, either preimpact or as a result of the impact itself. Either way, any realistic model of the formation of the Earth-Moon system must include magnetic field evolution. This requirement may ultimately constrain the models sufficiently to discriminate between the various candidates.

Strong-field dynamo action in rapidly rotating convection with no inertia.

The earth's magnetic field is generated by dynamo action driven by convection in the outer core. For numerical reasons, inertial and viscous forces play an important role in geodynamo models; however, the primary dynamical balance in the earth's core is believed to be between buoyancy, Coriolis, and magnetic forces. The hope has been that by setting the Ekman number to be as small as computationally feasible, an asymptotic regime would be reached in which the correct force balance is achieved. However, recent analyses of geodynamo models suggest that the desired balance has still not yet been attained. Here we adopt a complementary approach consisting of a model of rapidly rotating convection in which inertial forces are neglected from the outset. Within this framework we are able to construct a branch of solutions in which the dynamo generates a strong magnetic field that satisfies the expected force balance. The resulting strongly magnetized convection is dramatically different from the corresponding solutions in which the field is weak.

Limited role of spectra in dynamo theory: coherent versus random dynamos.

We discuss the importance of phase information and coherence times in determining the dynamo properties of turbulent flows. We compare the kinematic dynamo properties of three flows with the same energy spectrum. The first flow is dominated by coherent structures with nontrivial phase information and long eddy coherence times, the second has random phases and long-coherence time, the third has nontrivial phase information, but short coherence time. We demonstrate that the first flow is the most efficient kinematic dynamo, owing to the presence of sustained stretching and constructive folding. We argue that these results place limitations on the possible inferences of the dynamo properties of flows from the use of spectra alone, and that the role of coherent structures must always be accounted for.

Numerical measurements of the spectrum in magnetohydrodynamic turbulence.

We report the results of an extensive set of direct numerical simulations of forced, incompressible, magnetohydrodynamic (MHD) turbulence with a strong guide field. The aim is to resolve the controversy regarding the power-law exponent (alpha, say) of the field-perpendicular energy spectrum E(k) proportional variant k(alpha). The two main theoretical predictions alpha=-3/2 and alpha=-5/3 have both received some support from differently designed numerical simulations. Our calculations have a resolution of 512(3) mesh points, a strong guide field, and an anisotropic simulation domain and implement a broad range of large-scale forcing routines, including those previously reported in the literature. Our findings indicate that the spectrum of well-developed, strong incompressible MHD turbulence with a strong guide field is E(k) proportional variant k(-3/2).

Dynamic alignment in driven magnetohydrodynamic turbulence.

Motivated by recent analytic predictions, we report numerical evidence showing that in driven incompressible magnetohydrodynamic turbulence the magnetic- and velocity-field fluctuations locally tend to align the directions of their polarizations. This dynamic alignment is stronger at smaller scales with the angular mismatch between the polarizations decreasing with the scale lambda approximately as theta(lambda) is proportional to lambda(1/4). This can naturally lead to a weakening of the nonlinear interactions and provide an explanation for the energy spectrum E(k) is proportional to k(-3/2) that is observed in numerical experiments of strongly magnetized turbulence.

Magnetic-field generation in helical turbulence.

We investigate analytically the amplification of a weak magnetic field in a homogeneous and isotropic turbulent flow lacking reflectional symmetry (helical turbulence). We propose that the spectral distributions of magnetic energy and magnetic helicity can be found as eigenmodes of a self-adjoint, Schrödinger-type system of evolution equations. We argue that large-scale and small-scale magnetic fluctuations cannot be effectively separated, and that the conventional model alpha is, in general, not an adequate description of the large-scale dynamo mechanism. As a consequence, the correct numerical modeling of such processes should resolve magnetic fluctuations down to the very small, resistive scales.

Magnetic-field generation in Kolmogorov turbulence.

We analyze the initial, kinematic stage of magnetic field evolution in an isotropic and homogeneous turbulent conducting fluid with a rough velocity field, v(l) approximately l(alpha), alpha<1. This regime is relevant to the problem of magnetic field generation in fluids with small magnetic Prandtl number, i.e., with Ohmic resistivity much larger than viscosity. We propose that the smaller the roughness exponent alpha, the larger the magnetic Reynolds number that is needed to excite magnetic fluctuations. This implies that numerical or experimental investigations of magnetohydrodynamic turbulence with small Prandtl numbers need to achieve extremely high resolution in order to describe magnetic phenomena adequately.