Modeling spatio‐temporal nonlocality in mean‐field dynamos

When scale separation in space or time is poor, the mean‐field α effect and turbulent diffusivity have to be replaced by integral kernels by which the dependence of the mean electromotive force on the mean magnetic field becomes nonlocal. Earlier work in computing these kernels using the test‐field method is now generalized to the case in which both spatial and temporal scale separations are poor. The approximate form of the kernel for isotropic stationary turbulence is such that it can be treated in a straightforward manner by solving a partial differential equation for the mean electromotive force. The resulting mean‐field equations are solved for oscillatory α –shear dynamos as well as α² dynamos with α linearly depending on position, which makes this dynamo oscillatory, too. In both cases, the critical values of the dynamo number is lowered due to spatio‐temporal nonlocality.When scale separation in space or time is poor, the mean‐field α effect and turbulent diffusivity have to be replaced by integral kernels by which the dependence of the mean electromotive force on the mean magnetic field becomes nonlocal. Earlier work in computing these kernels using the test‐field method is now generalized to the case in which both spatial and temporal scale separations are poor. The approximate form of the kernel for isotropic stationary turbulence is such that it can be treated in a straightforward manner by solving a partial differential equation for the mean electromotive force. The resulting mean‐field equations are solved for oscillatory α –shear dynamos as well as α² dynamos     

Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo

Mean-field theory describes magnetohydrodynamic processes leading to large-scale magnetic fields in various cosmic objects. In this study magnetoconvection and dynamo processes in a rotating spherical shell are considered. Mean fields are defined by azimuthal averaging. In the framework of mean-field theory, the coefficients which determine the traditional representation of the mean electromotive force, including derivatives of the mean magnetic field up to the first order, are crucial for analyzing and simulating dynamo action. Two methods are developed to extract mean-field coefficients from direct numerical simulations of the mentioned processes. While the first method does not use intrinsic approximations, the second one is based on the second-order correlation approximation. There is satisfying agreement of the results of both methods for sufficiently slow fluid motions. Both methods are applied to simulations of rotating magnetoconvection and a quasi-stationary geodynamo. The mean-field induction effects described by these coefficients, e.g., the α-effect, are highly anisotropic in both examples. An α²-mechanism is suggested along with a strong γ-effect operating outside the inner core tangent cylinder. The turbulent diffusivity exceeds the molecular one by at least one order of magnitude in the geodynamo example. With the aim to compare mean-field simulations with corresponding direct numerical simulations, a two-dimensional mean-field model involving all previously determined mean-field coefficients was constructed. Various tests with different sets of mean-field coefficients reveal their action and significance. In the magnetoconvection and geodynamo examples considered here, the match between direct numerical simulations and mean-field simulations is only satisfying if a large number of mean-field coefficients are involved. In the magnetoconvection example, the azimuthally averaged magnetic field resulting from the numerical simulation is in good agreement with its counterpart in the mean-field model. However, this match is not completely satisfactory in the geodynamo case anymore. Here the traditional representation of the mean electromotive force ignoring higher than first-order spatial derivatives of the mean magnetic field is no longer a good approximation.     

Carbon storage of headwater riparian zones in an agricultural landscape

Background

In agricultural regions, streamside forests have been reduced in age and extent, or removed entirely to maximize arable cropland. Restoring and reforesting such riparian zones to mature forest, particularly along headwater streams (which constitute 90% of stream network length) would both increase carbon storage and improve water quality. Age and management-related cover/condition classes of headwater stream networks can be used to rapidly inventory carbon storage and sequestration potential if carbon storage capacity of conditions classes and their relative distribution on the landscape are known.

Results

Based on the distribution of riparian zone cover/condition classes in sampled headwater reaches, current and potential carbon storage was extrapolated to the remainder of the North Carolina Coastal Plain stream network. Carbon stored in headwater riparian reaches is only about 40% of its potential capacity, based on 242 MgC/ha stored in sampled mature riparian forest (forest > 50 y old). The carbon deficit along 57,700 km headwater Coastal Plain streams is equivalent to about 25TgC in 30-m-wide riparian buffer zones and 50 TgC in 60-m-wide buffer zones.

Conclusions

Estimating carbon storage in recognizable age-and cover-related condition classes provides a rapid way to better inventory current carbon storage, estimate storage capacity, and calculate the potential for additional storage. In light of the particular importance of buffer zones in headwater reaches in agricultural landscapes in ameliorating nutrient and sediment input to streams, encouraging the restoration of riparian zones to mature forest along headwater reaches worldwide has the potential to not only improve water quality, but also simultaneously reduce atmospheric CO₂.     

The Karlsruhe Dynamo Experiment. A Mean Field Approach

At the Forschungszentrum Karlsruhe an experiment is in preparation which it is hoped, in view of the geodynamo and other cosmic dynamos, that a homogeneous dynamo will be demonstrated and investigated. This experiment is discussed within the framework of mean-field dynamo theory. Results are presented concerning kinematic cylindrical mean-field dynamo models reflecting some features of the experimental device, as well as results of detailed calculations of the -effect that apply to arbitrarily high magnetic Reynolds numbers. On this basis estimates of the excitation conditions of the dynamo are given and predictions concerning the geometrical structure of the generated magnetic fields are made.