Non-local memory effects of the electromotive force by fluid motion with helicity and two-dimensional periodicity

In mean-field dynamo theory, the electromotive force term 〈u′ × B′〉 due to small-scale fields connects the small-scale magnetic field with the large-scale field. This term is usually approximated as the α-effect, assumed to be instantaneous in time and local in space. However, the approximation is valid only when the magnetic Reynolds number Rm is much less than unity, and is inappropriate when Rm ? 1, which is the condition satisfied in the Earth's core or solar convection zone. We introduce a function φ _qr as a non-local and non-instantaneous generalization of the usual α-effect and examine its behaviour as a function of Rm in the range 1/64 ≤ Rm ≤ 10 for a kinematic dynamo model. We use the flow of G.O. Roberts 1972 Roberts, GO. 1972. Dynamo action of fluid motions with two-dimensional periodicity. Phil. Trans. Roy. Soc. London Ser. A, 271: 411–454. [Crossref], [Web of Science ®] , [Google Scholar] (Phil, Trans. Roy. Soc. London Ser. A, 1972, 271, 411–454), which is steady and has non-zero helicities and two-dimensional periodicity. As a result, we identify three regions in Rm space according to the behaviour of the function φ _qr : (i) Rm ? 1/4, where the function φ _qr is local and instantaneous and can be approximated by the traditional α and β effects, (ii) 1/4 ? Rm ? 4, where the deviation from the traditional α and β effects increases and non-localness and non-instantaneousness increase, and (iii) Rm ? 4, where boundary layers develop fully and non-localness and non-instantaneousness are prominent. We show that the non-local memory effect for Rm ? 4 strongly affects the dynamo action and explains an observed augmentation of the growth rate in the dispersion relation. The results imply that the non-local memory effect of the electromotive force should be important in the geodynamo or the solar dynamo.     

Effect of the duration and direction of storm movement on infiltrating planar flow with full areal coverage

Using kinematic wave equations, analytical solutions are derived for flow due to a storm moving up or down an infiltrating plane and covering it completely. The storm duration is assumed in two ways. First, the plane is covered everywhere for the same duration by the storm. Second, the plane is covered in a linearly decreasing manner from the beginning of its coverage of the plane to the other end of the plane. By comparing the flow due to this storm with that due to a stationary storm of the same duration, the influence of storm duration, direction and velocity on flow hydrograph is investigated. It is found that storm movement has a pronounced effect on runoff hydrograph. Copyright © 2002 John Wiley & Sons, Ltd.     

Effects of storm direction and duration on infiltrating planar flow with partial coverage

Using kinematic wave equations analytical solutions are derived for flow resulting from a storm moving either up or down an infiltrating plane but not fully covering it. By comparing the flow resulting from this storm with that from a stationary storm of the same duration the influence of storm duration, direction and velocity is investigated. It is found that the direction of storm movement, duration and velocity of storms, as well as basin infiltration, have a pronounced effect on the discharge hydrograph. Copyright © 2004 John Wiley & Sons, Ltd.     

Effect of the duration and direction of storm movement on planar flow with full and partial areal coverage

Using kinematic wave equations, analytical solutions are derived for flow resulting from storms moving either up or down the plane and covering it fully or partially. By comparing the flow resulting from a moving storm with that from a stationary storm of the same duration and areal coverage, the influence of storm duration, direction and areal coverage is investigated. It is found that the direction, duration and areal coverage of storm movement have a pronounced effect on the discharge hydrograph. The runoff hydrographs resulting from storms moving downstream are quite different from those from storms moving upstream. Likewise, the areal coverage of the storm has a pronounced effect on the runoff hydrograph. Copyright © 2002 John Wiley & Sons, Ltd.